ABSTRACT. AYGÜN, SEYMEN MURAT. Processing Science of Barium Titanate. (Under the direction of Jon-Paul Maria.)

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1 ABSTRACT AYGÜN, SEYMEN MURAT. Processing Science of Barium Titanate. (Under the direction of Jon-Paul Maria.) Barium titanate and barium strontium titanate thin films were deposited on base metal foils via chemical solution deposition and radio frequency magnetron sputtering. The films were processed at elevated temperatures for densification and crystallization. Two unifying research goals underpin all experiments: 1) To improve our fundamental understanding of complex oxide processing science, and 2) to translate those improvements into materials with superior structural and electrical properties. The relationships linking dielectric response, grain size, and thermal budget for sputtered barium strontium titanate were illustrated. (Ba 0.6 Sr 0.4 )TiO 3 films were sputtered on nickel foils at temperatures ranging between C. After the top electrode deposition, the films were co-fired at 900 C for densification and crystallization. The dielectric properties were observed to improve with increasing sputter temperature reaching a permittivity of 1800, a tunability of 10:1, and a loss tangent of less than for the sample sputtered at 400 C. The data can be understood using a brick wall model incorporating a high permittivity grain interior with low permittivity grain boundary. However, this high permittivity value was achieved at a grain size of 80 nm, which is typically associated with strong suppression of the dielectric response. These results clearly show that conventional models that parameterize permittivity with crystal diameter or film thickness alone are insufficiently sophisticated. Better models are needed that incorporate the influence of microstructure and crystal structure.

2 This thesis next explores the ability to tune microstructure and properties of chemically solution deposited BaTiO 3 thin films by modulation of heat treatment thermal profiles and firing atmosphere composition. Barium titanate films were deposited on copper foils using hybrid-chelate chemistries. An in-situ gas analysis process was developed to probe the organic removal and the barium titanate phase formation. The exhaust gases emitted during the firing of barium titanate films were monitored using a residual gas analyzer (RGA) to investigate the effects of ramp rate and oxygen partial pressure. The dielectric properties including capacitor yield were correlated to the RGA data and microstructure. This information was used to tailor a thermal profile to obtain the optimum dielectric response. A ramp rate of 20 C/min and a po 2 of atm resulted in a permittivity of 1500, a loss tangent of and a 90 % capacitor yield in 0.5 mm dot capacitors. Yield values above 90% represent a significant advantage over preexisting reports and can be attributed to an improved ability to control final porosity. Finally, the dramatic enhancement in film density was demonstrated by understanding the processing science relationships between organic removal, crystallization, and densification in chemical solution deposition. The in situ gas analysis was used to develop an each-layer-fired approach that provides for effective organic removal, thus pore elimination, larger grain sizes, and superior densification. The combination of large grain size and high density enabled reproducing bulk-like dielectric properties in a thin film. A room temperature permittivity of 3000, a 5 μf/cm 2 capacitance density, and a dielectric tunability of 15:1 were achieved. By combining the data sets generated in this thesis with those of comparable literature reports, we were able to broadly rationalize scaling effects in polycrystalline thin films. We

3 show that the same models successfully applied to bulk ceramic systems are appropriate for thin films, and that models involving parasitic interfacial layers are not needed. Developing better models for scaling effects were made possible solely by advancing our ability to synthesize materials thus eliminating artifacts and extrinsic effects.

4 Processing Science of Barium Titanate by Seymen Murat Aygun A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Materials Science and Engineering Raleigh, North Carolina 2009 APPROVED BY: Jon-Paul Maria Associate Professor Materials Science and Engineering Committee Chair Zlatko Sitar Professor Materials Science and Engineering Gregory Parsons Professor Chemical Engineering Yuntian Zhu Associate Professor Materials Science and Engineering

5 DEDICATION To my family ii

6 BIOGRAPHY Seymen Aygün was born on August 11, 1980 to parents Baykut and Sezer Aygün in Ankara, Turkey. He graduated from METU (Middle East Technical University) High School and enrolled at the Metallurgical and Materials Science Department of METU. He received his B.S. in After that, he decided to continue his journey in the US and he worked with Dr. David Cann at Iowa State University of Science and Technology where he received his master s degree in After spending a year and a half as a postmaster researcher under supervision of Dr. Jon-Paul Maria at North Carolina State University, he decided to pursue Ph.D. and received his degree in iii

7 ACKNOWLEDGEMENTS First I would like to thank my mentor and friend Professor Jon-Paul Maria for the opportunities, guidance, and convincing me to pursue Ph.D. I am grateful for the four years I have spent at NCSU. I would also like to thank my friends at MSE; Jon Ihlefeld, Brian Laughlin, Mark Losego, Dipankar Ghosh, Spalding Craft, Patrick Daniels, Peter Gaifun Lam, Jimster, Erin Gross, Michelle Casper, Elizabeth Paisley, Jesse Jur, James Steel, and Tony Rice. I would like to acknowledge the help of Dr. Bill Borland with my research. I would like to thank Dick Parham and Edna Deas for their help and patience with my administrative problems. Also to my friends Metin, Eren, Erdem, Berna, and Arun. To Utkan for her love and support. Finally, and most importantly, I would like to express my gratitude to my family. Thank you for your constant love, support and patience. I could not have accomplished this without you. iv

8 TABLE OF CONTENTS LIST OF FIGURES... viii LIST OF TABLES... xiii CHAPTER 1. INTRODUCTION...1 CHAPTER 2. LITERATURE REVIEW Dielectrics Classification in Terms of Crystal Symmetry Ferroelectricity Theory of Ferroelectricity Dielectric Properties of Ferroelectrics Perovskite Structure and The Archetypical Ferroelectric BaTiO Crystal Structure and Phase Transitions Dielectric Properties Compositional Modification with SrTiO Stress-Strain Effects Scaling Effects in BaTiO Scaling Effects in Bulk BaTiO Scaling Effects in Thin Film BaTiO Processing of BaTiO 3 (Ba,Sr)TiO 3 Thin Films Magnetron Sputtering Chemical Solution Deposition...63 v

9 2.6.3 Firing of Thin Films on Base Metal Substrates...81 References...85 CHAPTER 3. EXPERIMENTAL PROCEDURES Barium Strontium Titanate Sputtering on Base Metal Foils Chemical Solution Deposition of Barium Titanate Low po 2 Processing of Thin Films Firing of Sputtered BST Thin Films Firing and Probing the Phase Evolution of CSD Barium Titanate Thin Films Reoxidation Anneals Physical Characterization of the Thin Films Electrical Characterization of The Thin Films References CHAPTER 4. HOT SPUTTERING OF BARIUM STRONTIUM TITANATE ON BASE METAL FOILS Hot Sputtering of Barium Strontium Titanate on Nickel Foils Introduction Experimental Procedure Results and Discussion Summary Hot Sputtering of Barium Strontium Titanate on Copper Foils References vi

10 CHAPTER 5. PROCESS-PROPERTY RELATIONSHIPS IN CHEMICAL SOLUTION DEPOSITED BARIUM TITANATE THIN FILMS Abstract Introduction Experimental Procedure Results and Discussion Summary References CHAPTER 6. HIGH DENSITY CHEMICAL SOLUTION DEPOSITED BARIUM TITANATE THIN FILMS Experimental References CHAPTER 7. CONCLUSIONS AND FUTURE WORK Conclusions Future Work References vii

11 LIST OF FIGURES Figure 2.1 Schematic representation of dielectric polarization....4 Figure 2.2 Schematic representation of the frequency dependence of complex permittivity in the presence of various polarization mechanisms...9 Figure 2.3 Schematic representation of the spontaneous polarization as a function of temperature for a first order (a) and a second order (b) phase transition...16 Figure 2.4 Schematic representation of the polarization with a finite wavelength and infinite wavelength...19 Figure 2.5 Schematic representation of (a) 180 and (b) 90 domain walls...20 Figure 2.6 Polarization vs. electric field curves for a single crystal ferroelectric, a polycrystalline ferroelectric, and a ferroelectric in the paraelectric state Figure 2.7 Relative permittivity vs. electric field curves for a ferroelectric and a paraelectric material...25 Figure 2.8 Schematic representation of frequency dependencies of (1) three-quantum, (2) four quantum, and (3) quasi-debye mechanisms. o and o are the softmode frequency and damping...30 Figure 2.9 Perovskite unit cell shown with the BO 6 octahedron Figure 2.10 Cubic and tetragonal unit cells of BaTiO Figure 2.11 Schematic potential wells...35 Figure 2.12 Dielectric constants K a and K c for single crystal BaTiO Figure 2.13 Relaxation of ferroelectric BaTiO viii

12 Figure 2.14 Curie temperature dependence of Ba x Sr 1-x TiO 3 on Ba concentration Figure 2.15 Dielectric constant of BaTiO 3 as a function of grain size...46 Figure 2.16 Temperature dependence of permittivity of BaTiO 3 with changing thickness Figure 2.17 Temperature dependence of permittivity of BST films with changing thickness Figure 2.18 Schematic depiction of magnetron sputtering...59 Figure 2.19 Schematic plot of an amorphous CSD film, the supercooled liquid, and the crystalline perovskite phase...73 Figure 2.20 TTT and sintering curves for an amorphous material Figure 2.21 Nucleation (I v ) and growth (u) rate data for anorthite...77 Figure 2.22 po 2 versus temperature diagram for the oxidation of metals...83 Figure 3.1 Atomic force microscopy images of Cu and Ni foils Figure 3.2 (a) Schematic illustration of the sputtering system and (b) nickel and copper samples on a quartz plate Figure 3.3 Process flow for barium titanate chemical solution deposition Figure 3.4 Illustration of the system used for low po2 firing Figure 3.5 Physical and chemical processes that occur during firing of a chemical solution deposited thin film Figure 3.6 Schematic illustration of the system used for in-situ experiments Figure 3.7 Defect concentrations in undoped-batio3 as a function of po ix

13 Figure 4.1 po2 vs. temperature diagram showing the processing window in which the oxides of Ba, Sr, and Ti are stable with metallic Ni Figure 4.2 X-Ray diffraction patterns of the samples for (a) as-deposited and (b) fired at 900 C Figure 4.3 Capacitance and loss tangent vs. field curves for the as-deposited samples sputtered at 100 C and 400 C Figure 4.4 (a) Capacitance and loss tangent vs. field curves for the samples sputtered in the range C (b) Tunability vs. sputtering temperature plot Figure 4.5 SEM surface image of the sample, which was sputtered at 400 C (de-wetted light colored areas are Pt) Figure 4.6 Field dependency of (a) Dielectric constant and (b) Leakage current density of the sample sputtered at 400 C Figure 4.7 Atomic force microscopy images of the samples sputtered at (a) 100 C, (b) 200 C, (c) 300 C, and (d) 400 C Figure 4.8 Temperature dependency of dielectric constant and loss tangent for the samples sputtered at C Figure 4.9 Comparison of dielectric constant values as a function of crystal dimension taken from several reports Figure 4.10 XRD patterns of the (a) as-deposited samples and (b) those fired at 900 C Figure 4.11 Optical microscope image of a 0.5 mm diameter Pt electrode x

14 Figure 4.12 Permittivity and loss tangent vs. field curves for the samples sputtered in the range of C Figure 5.1 Changes in the partial pressure of carbon dioxide as a function of time and temperature for different flow rates Figure 5.2 (a) X-Ray diffraction patterns and (b) Raman spectra of the barium titanate thin films Figure 5.3 Changes in the carbon dioxide partial pressure as a function of time and temperature for the ramp rates of (a) 3 C/min and (b) 1 C/min Figure 5.4 Plane view images of the samples fired with (a) 20 C/min, (b) 1 C/min, and (c) rapid ramp rates Figure 5.5 Cross-sectional images of the samples fired with (a) 20 C/min, (b) 1 C/min, and (c) rapid ramp rates Figure 5.6 Permittivity versus applied bias curves for the samples fired with a ramp rate of (a) rapid, (b) 20 C/min, (c) 3 C/min, and (d) 1 C/min Figure 5.7 Changes in the carbon dioxide partial pressure as a function of time and temperature for the oxygen partial pressures of (a) atm and (b) atm above 700 C Figure 5.8 Plane view images of the samples fired at a po2 of (a) atm and (b) atm above 700 C Figure 5.9 Cross-sectional images of the samples fired at a po2 of (a) atm and (b) atm above 700 C Figure 5.10 Permittivity versus applied bias of the samples fired at a po 2 of (a) xi

15 atm and (b) atm above 700 C Figure 6.1 Plane view images of (a) one-step, (b) two-step, and (c) each-layer-fired samples Figure 6.2 Cross-sectional images of (a) one-step, (b) two-step, and (c) each-layer-fired samples Figure 6.3 Fracture images of (a) one-step, (b) two-step, and (c) each-layer-fired samples Figure 6.4 (a) Permittvity vs. applied bias and (b) temperature dependent permittivity curves for the three firing conditions Figure 6.5 Grain size dependence of permittivity comparison for pertinent data sets in the literature xii

16 LIST OF TABLES Table 4.1 Summary of the atomic force microscopy results Table 5.1 Summary of the SEM and yield studies Table 6.1 Summary of the scanning electron microscopy results xiii

17 CHAPTER 1. INTRODUCTION The ever-increasing advancements in electronic systems require continuous miniaturization of electronic circuits. As the sophistication and functionality of commercial and industrial electronics increase, the number of active circuit components such as integrated circuits (ICs) and passive components (resistors, inductors, and capacitors) must scale similarly and the price for each component must go down. For instance, the number of capacitors in a modern cellular phone has surpassed 500, while the average price has remained constant. This technology trend cannot be sustained using the conventional surface mounting approach. One avenue to shrink the size of these circuits is embedding passive components such as thin film capacitors within the printed wiring board. There are three main advantages of this method. First, surface space can be freed allowing more ICs; second, the inductive losses from metallization are reduced since the passive components can be located directly underneath the ICs, and third; the low cost of planar parallel processing compared to the series pick-and-place assembly. However, the lack of a reliable process for integration, insufficient capacitance density, and the cost issues stemming from expensive electrode materials has slowed down the progression of this approach. This thesis discusses the research efforts to understand the structure-process-property relationships that regulate ferroelectricity in thin layers, and to develop high quality ferroelectric thin films suitable for embedded applications. The research was conducted through collaboration between North Carolina State University and DuPont Microelectronics. Methods for sputtering and chemical solution deposition of BaTiO 3 and (Ba,Sr)TiO 3 (BST) 1

18 thin films directly on base metal foils are discussed in addition to an expanded understanding of scaling effects in ferroelectric thin films. Process-property relationships are investigated by systematic selection and variation of three principle synthesis parameters: (i) thermal budget, (ii) atmosphere control, and (iii) thermal profiles for organic removal. Chapter 4 focuses on the sputtering of BST on copper and nickel foils. The ability to observe large permittivity in fine grain ceramic films is demonstrated and a hypothesis is supported which attributes scaling effects to crystal mosaicity as opposed to crystal dimension. Chapter 5 explores the processing of BaTiO 3 deposited on copper foils via chemical solution deposition and specifically how heat treatment profiles influence the evolution of crystal structure, microstructure, and the dielectric properties. An In-situ experimental capability is developed to enable our study of process-property relationshiops. In Chapter 6, we use the information learned by our in situ experiments and develop an eachlayer-fired approach which optimizes BaTiO 3 properties and produces thin layers with permittivity values of

19 CHAPTER 2. LITERATURE REVIEW 2.1 Dielectrics Dielectrics, also called insulators, are materials with a small number of charge carriers (<10 6 e - /m 3 ) and large band gaps, E g > 2.5 ev [1]. These materials can store energy by neutralizing charges at the dielectric/electrode interface in a capacitor [2]. This phenomenon is known as polarization, which arises from a finite displacement of positive and negative charges, i.e. formation of dipoles, under applied electric field. This is different from conduction, where there is a finite average velocity of charge motion under applied electric field. If a dielectric material is inserted between the plates of a capacitor, it increases the charge storage ability per unit voltage by a factor of r, where r is the relative permittivity (or dielectric constant). Faraday was the first to recognize this increase in capacitance due to the polarization of the dielectric medium between the capacitor plates in the 1830s [3]. This can be pictured as the free ends of dipole chains neutralizing the opposite charges on the terminating metal plates, as shown in Figure 2.1. The dielectric material between the metal plates responds to the applied electric field by forming dipoles. Each dipole, which is a pair of opposite charges +q and q, creates a dipole moment, which is given by v p = q v d Eq. (2.1) 3

20 where q is the charge and v d is the charge separation (vector). Polarizability, which is the ability of an atom or molecule to become polarized, relates the dipole moment to the applied field through v p = E v Eq. (2.2) where is the polarizability. The sum of all the dipole moments gives the polarization, which is defined by v P = N v p Eq. (2.3) where N is the number of dipoles per cubic meter. Ideally, the applied field, polarization, dipole moment, and separation vectors are parallel. v E applied v P dipole - + v p Figure 2.1. Schematic representation of dielectric polarization. 4

21 In dielectrics, the material s ability to polarize is quantified by the dielectric constant (or relative permittivity) or the dielectric susceptibility. The material polarizes by either creating dipoles or modifying existing fixed dipoles in linear dielectrics, or by reorienting reorientable dipoles in non-linear dielectrics. The relationship between polarization and electric field is given by v v P = o E or P v v = ( r 1) o E Eq. (2.4) where is the dielectric susceptibility, o is the permittivity of vacuum, and r is the relative permittivity. It is also important to differentiate between free and bound (polarization) charges [4]. In Figure 2.1, the charges stored on the plates are free, since they are the electrons in the metal. On the other hand, the polarization charges in the dielectric are bound to the parent ion/atom cores. The free charge on the capacitor plates is Q o when there is no dielectric in between them. Under the application of an electric field, we may divide by the electrode area to define the electric flux density (or the dielectric displacement) as v D = Q o A = o v E Eq. (2.5) When a dielectric material is inserted, the free charges on the electrodes increase. This increase is due to the neutralization of the polarization charges, Q P. Therefore, the final free 5

22 charge on the plates is Q= Q o + Q P. The free surface charge density on the plates after the dielectric inserted is given by v D = P v v + o E Eq. (2.6) If the thickness of the dielectric is t, then the net capacitance is C = o r A t Eq. (2.7) At the microscopic level there are 4 main contributions to the polarization. These are (i) electronic polarization, which arises from the deformation of electron cloud surrounding the nucleus, (ii) ionic polarization, which arises from the displacement of lattice ions from their equilibrium positions, (iii) dipolar (orientational) polarization, which arises from the orientation of a permanent dipole, and (iv) space charge (interfacial) polarization, which arises from the migration of charge carriers within a heterogeneous material. The electronic polarization mechanism is present in all materials, since there will always be electron clouds around individual atoms/ions or electrons participating in covalent bonds. Ionic polarization is present in most of the materials except covalent crystals as Si and Ge. In both electronic and ionic polarization there are no dipoles if there is no applied field. Dipolar polarization is observed in molecules with reorientable permanent dipoles such as H 2 O (l), BaTiO 3 and NO 2 (g). Finally, space charge polarization occurs whenever there is a possibility for field-induced charge accumulation at an interface or boundary. For instance, these could be 6

23 dielectric/electrode interfaces or grain boundaries in the material. The dielectric constant of a material is the sum of all polarization mechanisms r = r,el + r,ion + r,dip + r,sc if present Eq. (2.8) In general, covalently bonded materials, which only have electronic polarization, have very low permittivities ( r <10), ionic bonded materials, which have electronic and ionic polarization mechanisms, have permittivities in the range 10-40, while materials with dipolar or space charge contributions can have permittivities exceeding The magnitude of r also depends on the electronic structure, stiffness of the lattice, density, and defects. When there is an alternating field (i.e. a sinusoidal wave, E=E o sin( t)) applied across the capacitor, which is mostly the case in electrical circuits, the polarization of the dielectric leads to an ac permittivity. This complex permittivity is given by * = r i r Eq. (2.9) The real part r corresponds to polarization in response to an electric field and is used as the relative permittivity in calculating the capacitance. The imaginary part r corresponds to the finite energy loss associated with the physical polarization process. It is usually quantified by the term loss tangent, 7

24 tan = r Eq. (2.10) r The phase difference between capacitor charging and discharging under an ac field (or the phase angle between the imaginary and the real components of permittivity) is 90 o for perfect insulators with no loss and 0 o for perfect conductors. Real capacitors have phase angle values in between these end points. Loss tangent is proportional to the heat generated per cycle. Therefore, at high frequencies this can become an issue. As it can be seen from the above equations, both relative permittivity and loss tangent are frequency dependent. The frequency response of permittivity and loss tangent depends on the active polarization mechanism in that frequency range. The frequency dependencies in the presence of space charge, dipolar, ionic, and electronic polarization are shown in Figure

25 Figure 2.2 Schematic representation of the frequency dependence of complex permittivity in the presence of various polarization mechanisms (adapted from Kasap [4]). Electronic and ionic polarization mechanisms can be thought as simple harmonic oscillators in which the driving force is the oscillating electric field and the restoring force is the Coulombic attraction between the species. These two mechanisms are active up to their resonant frequencies ( el and ion ), the point after which the oscillation of the electric field is too fast for them to respond. Electronic polarization is active up to very high frequencies, Hz, since electrons have very low mass. Above the electron resonance frequency the material behaves no different than a vacuum ( r ~1). The ionic polarization is able to keep up with the oscillating field up to ~10 12 Hz, the lattice vibration frequency, above which the restoring force and the mass of ions are too large to support a dipole formation that fast. Dipolar polarization can be generically visualized as charged species jumping between the sites in a lattice. In the absence of an applied field these sites are equivalent, 9

26 however when a bias is applied a preference between the sites is generated. The collective of preferential jumps will then result in net dipole formation [5]. There are mainly two factors opposing the alignment of dipoles with the applied field. The first one is friction due to the dipole s interaction with the neighbors during its rotation in a viscous medium. So, at high enough frequencies, megahertz to gigahertz region, the dipoles cannot follow the field, above this frequency range relaxation occurs. The reciprocal of the frequency ( r ) at which the polarization process can no longer respond is called the relaxation time ( ). This corresponds to the average time spent in each dipole orientation. The complex permittivity equations for dipolar polarization are given by the Debye relationships which include the relaxation time, r = + o r = ( o ) Eq. (2.10) where the real part of the permittivity r is a constant equal to o for frequencies << r and equal to for frequencies above r. The Debye-model assumes one unique relaxation time for the system which is a good approximation for crystals but not for glasses [6]. The second factor is thermal agitation. When the temperature is low an applied electric field can orient the dipoles, however as the temperature increases there is enough thermal energy to randomize dipole orientation despite the presence of an ac field. In this situation, the effective polarizability, thus permittivity decreases. Since the dipole reorientation rate is temperature dependent, the relaxation is also thermally activated thus temperature dependent. It is important to note that this is in contrast to the electronic and 10

27 ionic polarization mechanisms, which are temperature independent. The reason is that dipolar polarization requires microscopic diffusion, in the electronic and ionic mechanisms, the charge displacement distances are so short that diffusion concerns can be effectively ignored. Space charge polarization occurs when the motion of charged defects can create net charge separation. There is no motion with an average velocity, however there is a finite displacement of charges since continuous current is impeded by insulating barrier(s). Often times this is the result of a heterogeneous structure such as combinations of an insulating phase & a conducting phase or insulating grain boundaries & conducting grains. All materials contain defects, impurities, various charge carriers, and heterogeneities, hence space charge is always present to a certain extent. Space charge gives rise to very high dielectric constants on the order of , however it is limited to low frequency applications ( Hz). One common application of space charge polarization is the barrier layer capacitor. These are based on the limited reoxidation of a reduced material to obtain conducting grains and insulating grain boundaries [7]. As in the case of dipolar mechanisms, polarization involves a diffusional process, thus the temperature dependence is pronounced and a relaxation mechanism describes the frequency dependence. 2.2 Classification in Terms of Crystal Symmetry All crystals can be divided into 32 point groups, where a point group is defined as the minimum combination of symmetry elements required to describe the crystal s symmetry. Among these, there are 21 non-centrosymmetric point groups 20 of which are piezoelectric. 11

28 The word piezo is derived from the Greek piezein meaning press or squeeze, hence piezoelectricity is the generation of a charge displacement under applied mechanical stress. This is known as the direct piezoelectric effect. The direction of the polarization (charge displacement) depends on the direction of the applied stress. The direct piezoelectric effect is defined using the tensor notation by, P i = d ijk X jk Eq. (2.11) where P i is the polarization (a first rank tensor), d ijk is the piezoelectric coefficient (a third rank tensor), and X jk is the mechanical stress (a second rank tensor). These crystals also produce mechanical strain when they experience an electric field, which is known as the converse effect. Centrosymmetric crystals cannot be piezoelectric, because even under stress the center of positive and negative charges in a unit cell will still coincide and result in zero net polarization. Classifying further, 10 out of the aforementioned 20 groups have a spontaneous and permanent polarization in the absence of an applied field or a mechanical stress. This polarization also changes with temperature, hence these crystals are called pyroelectric. They are also called polar due to their spontaneous polarization. A subgroup of pyroelectrics is ferroelectrics, in which the spontaneous polarization is strongly nonlinear and can be reoriented by an applied electric field. 12

29 2.3 Ferroelectricity A Brief History The observation of polar materials possibly reaches back to Ancient Greece. More than 23 centuries ago, philosopher Theophrastos noted that lyngourion (possibly the mineral tourmaline) attracts wood particles [8]. The detailed work began with the advent of formalized crystallography in the 18 th century, and pyroelectricity and piezoelectricity was discovered in Rochelle salt (NaKC 4 H 4 O 6 4H 2 O) in the 19 th century [9]. These findings enabled the discovery of ferroelectricity, when in 1921 Valasek reported that the spontaneous dipole moment in Rochelle salt can be reoriented by an external electric field [10]. The term ferroelectricity, which indicates polarization hysteresis with applied electric field, is used in analogy to ferromagnetism, which exhibits magnetization hysteresis with applied magnetic field. In the early 1940s, critical steps were taken in understanding piezoelectricity and ferroelectricity with the work on BaTiO 3, as indicated by Jaffe [11]. These were (1) the discovery of the unusually large dielectric constant, (2) the discovery that this high value was due to ferroelectricity, and (3) the discovery of the reorientation of the dipoles with a process called poling. There were concurrent studies in the United States, USSR, Japan, and England. The publications started to appear after the World War II. In the United States, Thurnauer and Deaderick synthesized ceramics with a dielectric constant of 1100 [12]. The reports of Wainer and Salomon from 1943 show the temperature dependence of permittivity and the effects of compositional modification [13], however these were not published since

30 [14]. The work of Wul and Goldman in the USSR and von Hippel in the US discovered that the origin of the high dielectric constant was ferroelectricity [15, 16]. There were also independent discoveries in Japan by Ogawa in 1944 and in England by Coursey and Brand in 1946 [17, 18]. The third significant step was the discovery of the poling process. Gray showed that a sufficiently high voltage can reverse the dipole moments of a ferroelectric ceramic [19]. These were followed by single crystal and then thin film studies. Today, ferroelectric materials find many application areas including high density capacitor applications, piezoelectric transducers, positive temperature coefficient resistors, and microwave filters with their interesting dielectric, piezoelectric, thermal, and optical properties Theory of Ferroelectricity The two important criteria for ferroelectricity are the presence of spontaneous polarization and the reversibility of this polarization with an applied electric field. This is different in the parent analogue, ferromagnetism, where the presence of spontaneous moments also means that they can be reversed by an external field [20]. Another precondition is that the ferroelectric phase arises from a structural transition from a high symmetry phase to a low symmetry phase. The temperature at which this transition occurs is known as the Curie point and the temperature dependence of the dielectric constant above this temperature is given by the Curie-Weiss law, 14

31 r = o + C T T o Eq. (2.12) where r is the relative permittivity, o is the permittivity of vacuum, C is the Curie constant, and T o is the Curie temperature. Above the transition temperature, the crystal is in the paraelectric state, which is the non-polar state with no net dipole in the unit cell. Below the transition temperature, the material undergoes a phase transition into the ferroelectric state, a polar state with spontaneous polarization. If the transition is due to the displacement of the ions, then this is called a displacive transition. For example in BaTiO 3, which has a cubic perovskite structure in the paraelectric state, the displacement of the Ti 4+ ion from the cell center creates a dipole moment. Ferroelectric transitions are generally classified into first and second order phase transitions. In a first order transition, spontaneous polarization exhibits a discontinuity at the transition temperature (Figure 2.3a), also there is a volume change and a latent heat associated with the transition. In a second order transition, the spontaneous polarization decreases continuously as the temperature decreases and reaches zero at the transition temperature as shown in Figure 2.3b. There is no volume change and no latent heat associated with the transition. 15

32 Figure 2.3 Schematic representation of the spontaneous polarization as a function of temperature for a first order (a) and a second order (b) phase transition. There are two main approaches to explain the microscopic origin of ferroelectricity and the ferroelectric phase transition [21]. The first one is the polarization catastrophe approach. In this model, at a critical temperature the local electric field caused by the dipole moment in the unit cell becomes larger than the restoring force stabilizing the polarization. Polarization is given by, v P = N E v loc Eq. (2.13) where E loc is not the external field, but the microscopic electric field felt by the polarizing atom. This Lorentz local field is given by, v E loc = E v + 1 v P Eq. (2.14) 3 o 16

33 Substituting Equation 2.14 into 2.13 and using Equation 2.4 to eliminate v E and v P, a relationship between r and is obtained, r 1 r + 2 = N 3 o Eq. (2.15) This relationship is called the Clausius-Mossotti equation. Rearranging this gives, 1+ 2N 3 r = o 1 N Eq. (2.16) 3 o This expression shows that when N 3 o, r approaches infinity. So, when the product of number density and polarizability of the dipoles are at a critical level, the material becomes infinitely polarizable. This physically means that the dielectric will polarize even in the absence of an applied electric field. Neglecting electronic and ionic contributions the total polarizability is equal to the dipolar polarizability, dip = v p 2 3kT Eq. (2.17) 17

34 Substituting into Equation 2.16 we get, r C T T o Eq. (2.18) which is the Curie-Weiss law for the dielectric constant. This dipolar model predicts that as the temperature approaches the transition temperature from above, the permittivity becomes infinite, the system becomes unstable and a phase transition occurs. This divergence at T o is called the polarization catastrophe. Even though this dipolar model leads to the Curie-Weiss law for a ferroelectric transition, it has shortcomings when it is applied to polar liquids. For instance, according to this model the water should become ferroelectric at T o = 1100 K [5]. However, water even does not become ferroelectric below its freezing temperature. The other approach to explain ferroelectricity is associated with ionic polarizability. In ionic polarization, the permittivity can be related to the vibration mode frequency using a simplified version of the Lyddane-Sachs-Teller relationship by [22], r 1 2 TO Eq. (2.19) 18

35 This relation suggests that if the lattice vibration frequency which produces polarization goes to zero, the permittivity reaches infinity. A specific transverse optic mode, known as the ferroelectric soft mode, displays a decrease in frequency as temperature decreases, and at the point that it becomes zero the host lattice becomes unstable and the ferroelectric phase transition occurs. When the frequency is non-zero (finite wavelength) the vibration of the ions will result in transient dipoles. However, the net instantaneous polarization will be zero since the oppositely oriented dipoles will cancel each other. The implication of the zero frequency is that when the wavelength becomes infinite, all the ions will be shifted from their equilibrium high temperature positions. The high temperature structure will be distorted into another structure and result in a net instantaneous polarization at any time as shown in Figure 2.4. Figure 2.4 Schematic representation of the polarization with a finite wavelength and infinite wavelength. 19

36 In the ferroelectric phase, the direction of polarization is not necessarily uniform throughout the material. The dipole moments in neighboring unit cells align themselves into regions of uniform polarization which are called ferroelectric domains. In the absence of an applied electric field, each domain will have a net polarization, however the average of all domain orientations will sum to zero. The polarization can be made uniform by the application of an external field in the paraelectric state and cooling with the field applied. This process is called poling, which can potentially reorient domains in the direction of the applied field. When an electric field is applied, the domains reorient so that there is a net polarization parallel to the applied field. Domain walls separate domain states and have a thickness that is dependent on wall orientation and material quality in the absence of extrinsic factors, domain walls are only ~ 2 unit cells thick. The types of domain walls in a ferroelectric crystal depend on the symmetry. For example, while in a tetragonal perovskite 180 and 90 domain walls can occur, in the rhombohedral phase the polarization along the body diagonals result in 180, 71, and 109 domain walls [23]. The walls which separate the oppositely oriented domains are called the 180 o walls (Figure 2.5a) and the ones which Figure 2.5 Schematic representation of (a) 180 and (b) 90 domain walls. 20

37 separate the perpendicularly oriented domains are called the 90 o (Figure 2.5b) domain walls. Key difference between them is the strain associated with the 90 o domain walls. Ferroelectric domains form to minimize the electrostatic energy due to depolarization fields and the elastic energy associated with spontaneous strain. Depolarization fields are required by any change in or gradient in polarity. This could be due to a change polarization near the surface or a gradient across a grain boundary. When the material experiences a phase transition mechanical constraints can increase the elastic energy by confining the spontaneous strain associated with the structural change. The formation of domains reduces the energy associated with both effects, however, 180 domain walls are only ferroelectric, while other domain wall orientations (like 90 walls) have also a ferroelastic component Dielectric Properties of Ferroelectrics Polarization Hysteresis The unique characteristic of a ferroelectric is the polarization switching with an applied electric field. This results in a hysteresis loop when the polarization in the material is measured as a function of the applied electric field. This is a large signal measurement during which a strong ac field with a frequency ~100 Hz is applied to the material. The hysteresis arises from the energy needed to reorient ferroelectric dipoles during each field cycle. In the paraelectric state there are no domains but the material exhibits a non-linear response without hysteresis. Polarization vs. electric field loops for a single crystal ferroelectric, a polycrystalline ferroelectric and a paraelectric are depicted in Figure 2.6. In polycrystalline 21

38 ferroelectrics there is usually a large amount of stress in the material. This stress is relieved by 90 o domain walls which results in lower switchable polarization values. Figure 2.6 Polarization vs. electric field curves for a single crystal ferroelectric, a polycrystalline ferroelectric, and a ferroelectric in the paraelectric state. As the applied electric field is increased the domains start to align with the field and the measured polarization increases until all the domains become parallel to the field. This 22

39 point is called the saturation. When the applied field strength is decreased to zero, some of the domains switch back, however there is still a net polarization, which is called the remanent polarization, P r. As the field is applied in the reverse direction, more domains switch back and zero polarization is reached when the electric field is at E C, coercive field, the amount of field needed to switch the polarization. Nevertheless, this is not an absolute value. If a lower electric field is applied for a sufficient amount of time, the polarization will eventually switch [24]. Spontaneous polarization can be found from the figure by drawing a tangent to the saturation and finding the polarization intercept. Since the P-E relation is hysteretic and the Equation 2.4 does not hold for the non-linear response, a definition in terms of the change in polarization could be written, P = o ( r 1) E Eq. (2.20) Since the derivative P / E gives the permittivity, the slope at any point gives the large signal permittivity. The area of the loop represents the energy dissipated as heat. For this reason, the experiment is usually run at low frequencies (~100 Hz) [11]. The shape and the position of the hysteresis loop give additional information about the material. For instance, an off-centered loop indicates an internal field which could be caused by space charge or aging [23]. The magnitude of the coercive field can be an indication of the grain size (e.g. large coercive field means smaller grain size), while the loop squareness and sharpness are indicative of general material quality and high resistivity [9]. 23

40 Dielectric Permittivity and Tunability The dielectric permittivity of a ferroelectric material can be parameterized by Landau theory which is based on an expansion of the Helmholtz free energy with respect to polarization [25]. The first two terms of this expansion is given by, F = 2 P2 + 4 P4 Eq. (2.21) Using the equation of state, F / P = E, taking the derivative of the above expression, E = P + P 3 Eq. (2.22) Then, the dielectric permittivity can be written as, r = 1 o P E = 1 o P 2 Eq. (2.23) This equation describes the permittivity both in the absence and presence of an applied field. When there is no field, polarization is set to zero and in the presence of a field, the polarization is set to the induced polarization value and permittivity is calculated. It can be observed from the equation that the permittivity is maximum at zero field and decreases as the applied field is increased. This behavior is observed experimentally via capacitance- 24

41 voltage (C-V) measurements. C-V measurements are small signal measurements where a small ac field (e.g V) superimposed with a dc field is applied. The oscillating voltage is used to measure the capacitance and then plotted as a function of the dc field. Generally, permittivity is calculated from capacitance, electric field is calculated using thickness, and the permittivity data are plotted as a function of the applied dc field. Figure 2.7 shows the typical r vs. E curves for a ferroelectric and a paraelectric material. Figure 2.7 Relative permittivity vs. electric field curves for a ferroelectric and a paraelectric material. Measurements for ferroelectric materials are usually made with two sweeps, i.e. one from negative to positive bias and the other from positive to negative to show the hysteresis. The initial rise in the permittivity with applied field is due to the increased domain wall 25

42 movement which is locked-in by defects at zero bias and partial switching of the domains [26]. The maximum permittivity is observed when most of the domains are in the process of switching and the domain wall movement contribution to the polarization is maximum. At higher fields, the permittivity decreases due to two reasons. First, the number of domains and hence the domain walls decrease as they align with the dc field. Second, the oscillation of any residual domain walls is inhibited by the large dc bias. The only contributions to the permittivity at high fields are the intrinsic polarization mechanisms (e.g. ionic and electronic polarization). In the paraelectric state the material does not exhibit any hysteresis, therefore the measurements can be made with a single sweep. A high permittivity is observed (at low fields), even though there are no domains or domain wall contributions. At temperatures not much higher than the transition temperature, the frequency of the lattice vibration mode TO (Eq. 2.19) is very low. At this point the restoring forces opposing the poling of the crystal are still weak, so the transient dipoles can interact with the applied ac field resulting in a high permittivity. The change in permittivity with the applied field makes these materials attractive for high frequency voltage-tunable devices such as resonators, phase-shifters and microwave filters [25, 27-29]. The dependence of permittivity on the applied dc field is called the tunability. The tunability is defined as, n = max min Eq. (2.24) 26

43 where max is the permittivity at zero field and min is the permittivity at saturation fields. Another way of defining tunability is the relative tunability which is given by, n r (%) = max min max 100 Eq. (2.25) In general, the higher the permittivity the higher the tunability [25]. Tunability can be used as a means to compare the extrinsic response to the intrinsic response. For instance, for materials with the same composition, since the intrinsic (lattice) response would be similar, tunability might enable a comparison of extrinsic properties such as phase purity, homogeneity, microstructural properties (e.g. grain size), and crystal quality. This comparison will be used routinely in this thesis to evaluate material quality Dielectric Loss Dielectric loss is a critical parameter in microwave applications since a figure of merit is defined based on dielectric loss and tunability for these devices, whereas in high capacitance density applications permittivity is of high importance [25, 29-31]. The dielectric losses in ferroelectric materials can be categorized as extrinsic and intrinsic contributions. The main extrinsic contribution to the ferroelectric loss is the domain wall movement [23, 32]. Domain wall motion includes interactions with the surroundings, which cause 27

44 internal friction. Real materials contain charged defects, local polar regions, impurities and the interaction of these with the ac field also contributes to dielectric losses. Presence of defects can increase the conductivity of the material resulting in dielectric losses. Additionally, domain wall movement can also be clamped or pinned by these defects. These defects include oxygen vacancies and electrons trapped in the domain wall area, making the domain switching more difficult and hindering the domain wall motion [33]. In the paraelectric state there are no domains, so the dielectric loss is in principle much lower. For that reason, the non-polar paraelectric phase is used for high frequency applications where low loss tangent is crucial. The other extrinsic mechanisms play a similar role in the paraelectric state. The second group of phenomena that contribute to the dielectric loss is the intrinsic mechanisms. The following is a very brief summary of the models that were derived to explain their origins [25, 34, 35]. For the intrinsic loss, typically the higher the permittivity and the measurement frequency, the higher the loss [25]. The origin of the intrinsic loss is the interaction between the applied ac field and the lattice vibrations in the material. The loss is due to the absorption of energy quantum of the electromagnetic field by the thermal phonons during collisions. Phonons have much higher energies and this results in three possible schemes of collisions; three-quantum, four-quantum, and quasi-debye mechanisms [25]. The three-quantum process involves an energy quantum and two phonons. This interaction can only occur if the frequency (or energy) difference between the phonons is small, i.e. on the order of the ac field frequency. This is possible between two degenerate vibrational modes. Since degeneracy arises from the symmetry of the crystal, the temperature and the frequency 28

45 dependence of the three quantum mechanism are sensitive to the crystal symmetry. In the four-quantum mechanism where three phonons are involved, the energy restrictions are not that strict. In the two-phonon process, the momentum conservation allows only vertical transitions, whereas three-phonon processes can occur in a greater variety without violating the momentum conservation [36]. For that reason, phonons with different energies can take place in this process. Therefore, the temperature and the frequency dependence of the four quantum mechanism are insensitive to the crystal symmetry. The quasi-debye mechanism is only active in non-centrosymmetric crystals and in the local polar regions of the centrosymmetric crystals. In this mechanism, the interaction between the electromagnetic field and the phonon changes the phonon frequency which results in dielectric relaxation with a corresponding loss. The contribution of the quasi-debye mechanism is higher than the three-quantum and four-quantum mechanisms in the frequency range of interest ( << TO ). Figure 2.8 shows the comparison of the loss tangents for the above mechanisms as a function of frequency. 29

46 Figure 2.8 Schematic representation of frequency dependencies of (1) three-quantum, (2) four quantum, and (3) quasi-debye mechanisms. o and o are the soft-mode frequency and damping (average frequency of inter-phonon collisions), respectively (taken from Tagantsev et al. [25]) Dielectric Properties of Ferroelectric Thin Films The dielectric properties of ferroelectric thin films are usually different than that of their bulk counterparts. Typically, thin films exhibit lower dielectric permittivity and higher loss tangent than the bulk ceramics with the same composition. The origins of these differences in the properties can be categorized under three main groups: (i) difference in processing conditions (e.g. processing temperature), (ii) presence of stress (or strain) in thin films due to substrate constraints, and (iii) scaling effects. Actually, when parameterizing the dielectric properties usually it is observed that all these factors have a cause-and-effect 30

47 relationship. For instance, typically, the processing window available to thin films are dependent on the thermal expansion mismatch, chemical reactivities, and difference in other physical properties (e.g. melting point) between the film and the substrate. It affects the dielectric response through properties such as crystallinity, grain size, chemical composition, defect equilibrium, and residual stress. Finally, very thin films can degrade the dielectric properties through low permittivity passive layers with thicknesses comparable to the film. All of these thin film effects will be discussed in detail in the following sections, specifically for barium titanate & barium strontium titanate thin films. 2.4 Perovskite Structure and The Archetypical Ferroelectric BaTiO Crystal Structure and Phase Transitions The perovskite structure, which takes its name from the mineral perovskite (CaTiO 3 ), is a versatile structure with a very wide range of properties and functions [37]. The generic structure has the chemical formula ABO 3 with a simple cubic unit cell. This can be visualized as the A-site cation on the corners, B-site cation in the body center, and oxygens in the centers of the faces. The resulting structure is a BO 6 octahedral network with the smaller cation filling the octahedral holes (6-coordination) and the large cation filling the dodecahedral holes (12-coordination). Figure 2.9 shows the cubic perovskite unit cell with the oxygen octahedron. 31

48 Figure 2.9 Perovskite unit cell shown with the BO 6 octahedron. Goldschmidt studied a large number of perovskites by substituting a variety of cations including BaTiO 3 before the discovery of its high dielectric constant and the structural relationship to ferroelectricity [38]. The geometric relationship that gives the size range of ions that can be substituted in the perovskite structure is given by, t = R A + R O 2(R B + R O ) Eq. (2.26) where t is the Goldschmidt tolerance factor, R A, R B, and R O are the ionic radii of large cation, small cation, and anion respectively. Typically, structures with a t ~ are cubic, those with lower tolerance factor values are slightly distorted (often via octahedral rotations) but not ferroelectric, and those with higher values are ferroelectric [11]. In addition to this structural requirement, the presence of a degree of covalency in the B-O bond (small cation- 32

49 anion) is necessary for the lattice distortion and ferroelectricity [39-41]. Since the ionic forces are central forces and ionic bonding is not directional, the anions in the octahedron would be expected to hold the B-cation in the center, i.e. equidistant from all neighbors. However, for ferroelectricity to occur the cation must be closer to one of the anions which requires bond directionality. Megaw showed that the presence of abnormal volume conditions could result in the off-center position of the B-cation. In BaTiO 3, this condition is accommodated by the large Ba ion, which moves apart the oxygen network, so that the average Ti-O distance is larger than the sum of their ionic radii [39, 40]. Through local density approximations (LDA) Cohen demonstrated that the covalency results in hybridization between the titanium 3d states and the oxygen 2p states, which is essential for ferroelectricity [42]. Barium titanate, the first ceramic in which the ferroelectricity was observed, exhibits the prototypical perovskite cubic structure (m3m, a=4.009 Å) above its Curie temperature. Below T c (~125 o C), the structure slightly distorts due to the displacement of the Ti 4+ (11 pm) and Ba 2+ (6 pm) cations opposite to the oxygen sublattice (3 pm) and becomes tetragonal (4mm, a=3.992 Å, c=4.035 Å) as shown in Figure Since there are six equivalent <100> directions in the unit cell, the polar axis can be parallel to any of these directions. Upon further cooling, two more phase transitions occur. First, the unit cell elongates along a face diagonal and the structure changes from tetragonal to orthorhombic at 0 o C. Second, the unit cell elongates along a body diagonal and an orthorhombic to rhombohedral at transition occurs at 90 o C. 33

50 Figure 2.10 Cubic and tetragonal unit cells of BaTiO 3. The displacement of the Ti 4+ cation along the c-axis can be visualized in terms of potential wells. In the tetragonal phase, the cation occupies one of the two equilibrium positions which are shifted from the center of the unit cell as shown in Figure It can jump from one equilibrium position to the other, if enough energy is provided to overcome the potential barrier. If an electric field (larger than coercive field) is applied opposite to the polarization direction, then Ti 4+ cation can jump to the adjacent site and reverse the polarity in that unit cell. This will reduce the energy barrier for the neighboring ions and the region affected by the electric field will eventually switch polarization [7]. The switching can also occur by 90 o, however there is an associated dimensional change since the lengths of the c and a-axes are different. In addition to an electric field, 90 o switching can also be induced by applying mechanical stress. 34

51 Figure 2.11 Schematic potential wells Dielectric Properties When discussing the dielectric properties of BaTiO 3 it is important to note that there are no absolute values for the permittivity and the loss tangent. Even the slightest chemical or physical change has a dramatic effect on the dielectric properties. The Curie point also shifts with these changes. For that reason, in the following discussion, the general trends will be pointed out and the effects of deviations from ideality on the dielectric properties will be discussed in the extrinsic effects (i.e. stress-strain, scaling effects) section. Above the Curie point, BaTiO 3 is in the paraelectric state and the dielectric constant obeys Curie-Weiss law, = C /T T o, showing a peak at the transition temperature. Below the transition temperature the permittivity decreases with decreasing temperature yet it is still high due to the domain wall contribution. The temperature dependence of the permittivity for 35

52 single crystal BaTiO 3 is shown in Figure 2.12 [43]. Since the single crystal is strongly anisotropic, the permittivites measured along c and a-axes are different. At room temperature, the permittivity along the a-axis is ~4000, and along the c-axis is ~160. The reason for the difference is that the displaced Ti 4+ is tightly bound by the ferroelectric displacement along the polar c-axis, while it can still vibrate freely in the non-polar a-axis giving higher permittivity. A polycrystalline ceramic would have a permittivity value in between those single crystal values due to the random orientation of the grains. Figure 2.12 [43]). Dielectric constants K a and K c for single crystal BaTiO 3 (taken from Merz 36

53 When BaTiO 3 cools through the transition temperature, spontaneous polarization results in surface charges and an accompanying depolarizing field. The crystal responds to this by twinning (domain formation), in which the crystal splits into regions of oppositely signed polarization minimizing the electrostatic energy. The other ways to minimize the electrostatic energy are compensating the surface charge by conduction through the crystal or external conduction by a surrounding material [23]. The effects of mechanical stress during the paraelectric/ferroelectric transition result in the formation of 90 o domains to minimize the strain energy at the expense of domain wall energy so that their sum becomes a minimum [44]. The 90 o domains follow a head-to-tail arrangement to minimize the charge. Figure 2.13 Relaxation of ferroelectric BaTiO 3 (taken from von Hippel [45]). 37

54 In the tetragonal phase, the permittivity of BaTiO 3 shows a frequency dependence with a drop at around 10 GHz, as shown in Figure 2.13 [45]. This frequency corresponds to the piezoelectric resonance which is also accompanied by a high dielectric loss. In the cubic phase, piezoelectric resonance cannot occur, since the structure is centrosymmetric. For that reason, the paraelectric phase is used for high frequency applications with its comparatively low loss tangent values Compositional Modification with SrTiO 3 The dielectric properties of BaTiO 3 can be modified via cation substitutions with high solubility limits. The effects of these substitutions include shifting the Curie point, restricting domain wall motion, introducing compositional gradient, controlling grain size, and controlling the oxygen vacancies [7]. The Curie point of BaTiO 3 is usually shifted due for two application-based reasons. First, if the transition temperature is shifted down, higher permittivities can be achieved at room temperature. Second, if the paraelectric phase is required, for example for high frequency applications, it can be obtained by shifting the Curie point to a temperature below room temperature. Solid solutions of BaTiO 3 -SrTiO 3 (BST) are used for this purpose. SrTiO 3 is an incipient ferroelectric material, which forms a complete solid solution with BaTiO 3 [46, 47]. For the substitution of Sr 2+ for Ba 2+ a linear drop of ~3.5 o C per mol% in transition temperature is observed [11]. The substitution of the small cation for the large one reduces the cell volume and results in a linear decrease in T c similar to the effect of application of 38

55 hydrostatic pressure [48]. Depending on the solid solution composition the material exhibits permittivity maximum in the temperature range 230 o C o C. Temperature dependence of the dielectric constant with changing composition is given in Figure 2.14 [25, 49]. It is interesting to note that BST solid solutions have higher permittivity peak values than that of pure BaTiO 3 and the highest permittivity is observed around the 50/50 composition. Figure 2.14 Curie temperature dependence of Ba x Sr 1-x TiO 3 on Ba concentration (taken from Tagantsev et al. [25], modified version of Smolenskii s data [49]). 39

56 2.4.4 Stress-Strain Effects Application of a mechanical stress has substantial effects on the dielectric properties of barium titanate. The effects of stress on the Curie point and the permittivity of ceramic and single crystal BaTiO 3 have been studied by various authors [48, 50-53]. Merz showed that the Curie point of single crystal BaTiO 3 decreases linearly with increasing hydrostatic pressure [48]. This was also confirmed in polycrystalline ceramic samples by others [50, 53]. The reason for the decrease in the transition temperature is that the hydrostatic compression will favor the smaller volume phase. The cubic paraelectric phase has a smaller volume, so it is stable down to lower temperatures under hydrostatic stress. On the other hand, when a two-dimensional stress is applied the Curie point shifts to higher temperatures [50-52]. This can be explained as the stabilization of polarization in certain direction by the applied biaxial stress. If the stress is compressive, it compels tetragonality normal to the compression by contracting the axes in the direction of the stress and expanding the third, so stabilizing polarization normal to the stress plane. If the stress is tensile, it stabilizes the polarization parallel to the stress plane. Mechanical stress effects on the permittivity of bulk samples have also been studied [50]. However, since in a polycrystalline ceramic sample the stress systems acting on each crystallite are complex, it is more difficult to explain the trends in those systems. Especially, if the material is in the ferroelectric state, the piezoelectric effects, the changes in domain orientations, and domain wall motions complicate the situation. Shirane and Sato studied the effects of hydrostatic and two-dimensional pressure on the permittivity of polycrystalline BST samples [50]. They observed a decrease in the permittivity in the cubic phase with hydrostatic pressure. Since, the material obeys Curie-Weiss law in the 40

57 paraelectric state, a shift in the transition temperature will increase T, hence the permittivity will decrease. Samara made the same observation in single crystal samples, however the permittivity measured along c-axis in single crystal samples showed an increase [53]. This was attributed to the switching of some c-domains into a-domains leading to higher permittivity along c-axis. The two-dimensional stress is especially important for thin films, since the films are biaxially constrained on the substrate. The interaction between the film and the substrate can result in significant mechanical stresses in the film. The origins of the stress in thin films can be classified into intrinsic, extrinsic and thermal stresses [54]. The intrinsic stress is generated by the atoms or ions which are not in their lowest energy state and it depends on the growth parameters such as temperature, pressure, reactant concentration, and impurities. Extrinsic stresses are caused by dimensional changes. For example, densification during structural evolution or crystallization from an amorphous phase can produce tensile stresses in thin films. For epitaxial thin films, the lattice mismatch between the film and the substrate can cause tensile or compressive stresses depending on the relative lattice parameters. The third and generally the most important one is the thermal stress that arises due to the thermal expansion coefficient difference between the film and the substrate. These stresses occur during cooling down from a high temperature deposition or firing and their magnitude is given by, th = E f 1 f ( f s ) T Eq. (2.27) 41

58 where E f is the elastic modulus, f is the Poisson s ratio of the film, T is the temperature change, and f and s are the thermal expansion coefficients of the film and the substrate, respectively. Depending on the sign of the difference ( f s ) the stress can be compressive or tensile. It is believed that this stress in the plane of the film causes a change in the dielectric permittivity through a converse electrostrictive effect, i.e. presence of strain results in a quadratic change in dielectric displacement, which is given by [55], 1 = 1 4Q 12 Eq. (2.28) f u where f is the permittivity of the stressed film, u is the permittivity of the unstressed film, and Q 12 (<0) is the electrostrictive coefficient. It is important to note that this formula is valid when the film is in the paraelectric state. This is again due to the complexity introduced by piezoelectric and domain wall contributions in the ferroelectric state. The effects of biaxial stress on the dielectric properties of thin films have been studied both experimentally [54-58] and theoretically [59-60]. Shaw et al. measured that their BST films on Si had tensile stress ~600 MPa which resulted in a 25% decrease in the permittivity [55]. Taylor et al. sputter deposited BST on five different substrates to observe the effects of a systematic change in thermal strain [57]. They observed that the permittivity of the samples, which had tensile stress, decreased with increasing amount of stress. 42

59 Pertsev et al. made a thermodynamic model of epitaxial mismatch strain suggesting that presence of biaxial stress, compressive or tensile, would shift the Curie point to higher temperatures [59]. Desu et al. reached similar results using a different free energy expression [60]. Experimental work of Choi et al. demonstrated that the transition temperature of epitaxial barium titanate films can be boosted to very high temperatures by biaxial compressive strain. The authors achieved a transition temperature of 680 C with a coherently strained BaTiO 3 on DyScO 3 [61]. These are also in agreement with the observations in bulk ceramics [50-52]. Contrary to these results, Maria et al. and Streiffer et al. observed a decrease in the transition temperature with thermal stress [56, 58]. Both studies attributed this to the presence of a polarization normal to the plane of the film which is unable to switch. In Pertsev s model, polarization can switch freely to minimize its energy. Therefore, in the presence of an in-plane stress, polarization is forced to have an in-plane component to minimize its energy. This in-plane component stabilizes the ferroelectric phase to up to higher temperatures. However, when there is a fixed polarization axis normal to the film, presence of tensile stress counteracts this spontaneous polarization and shifts the transition to lower temperatures. 2.5 Scaling Effects in BaTiO 3 The ever-increasing miniaturization in electronic devices brings in the need for working at smaller scales. A decrease in size generally changes the parameters including grain size, composition, defect concentration and stress altering the properties of the 43

60 ferroelectric material. Therefore, a fundamental understanding of scaling effects on properties is needed to make high quality materials. The scaling effects on the ferroelectric properties of barium titanate have been studied for bulk [62-70], particles [71-73], and thin films [74-77]. Even though, the bulk effects seem to be well understood, the trends in thin film properties are much more difficult to explain due to the complicated electrical (e.g. electrodes and depolarization effects) and the mechanical (stress-strain due to being clamped) boundary conditions Scaling Effects in Bulk BaTiO 3 The grain size effects on the dielectric properties can be divided into three size regions [78]. In the first region the grain size (or particle size) is large (<1 μm) and the structure is in a multi-domain state with 180 and 90 domain walls. As the grain size decreases the density of the 90 domain walls decreases and at a critical size (~0.5 μm) the material becomes single domain. With further decrease in grain size, at around few tens of nanometers, true size effects come into play and surface energy and depolarization energy suppress the ferroelectricity [79]. However, it is important to note here that there is no clear experimental proof of this argument in the literature. Looking at the r -T characteristics, typically, scaling effects result in the following: (1) a shift in the transition to lower temperatures, (2) decrease in the permittivity values in the ferroelectric state, and (3) broadening of the dielectric anomalies. 44

61 Buessem et al. reported that the permittivity of the fine-grained BaTiO 3 (1 μm) is higher than that of the large-grained (10 μm) ceramics [62, 63]. To explain the authors referenced Little s work, who measured the thickness of a 90 domain wall as about 0.4 μm [80]. This means that it is physically impossible to have domain walls in a 1 μm grain. Therefore, it was suggested that the fine-grained samples were single domain, i.e. there were no 90 domain walls to relieve the stress. The high permittivity was attributed to the presence of internal stress which forces the structure back to the cubic state. Their thermodynamic model showed that with a reasonable amount of stress, the transition can be shifted to obtain a permittivity close to Kinoshita et al. measured a series of samples with grain sizes ranging from 1-50 μm observing the same trend, i.e. increase in the permittivity with decreasing grain size in the ferroelectric state [64]. The permittivity of the paraelectric phase did not show a dependence on the grain size. They also attributed the high permittivity to internal stresses. However, none of these studies investigated the lattice and the domain structure until the comprehensive work of Arlt et al. [65]. By preparing a systematic sample set with grain sizes of μm and doing electron microscope investigations, Arlt et al. were able to study both sides of the critical grain size at which the permittivity was maximum. The highest permittivity was again obtained around μm as shown in Figure TEM and SEM studies revealed two important points. Domain width is grain size dependent and 90 domain walls persist to much lower grain sizes than previously expected. 45

62 Figure 2.15 al. [65]). Dielectric constant of BaTiO 3 as a function of grain size (taken from Arlt et It was shown that for decreasing grain size the total 90 domain area increases. The increasing permittivity with decreasing grain size down to 1 μm was explained by this increased domain wall density contributing to the permittivity. Below 0.7 μm, the micrographs revealed a decrease in the number of 90 domains decrease accompanied by a structural change observed in the X-Ray patterns. The room temperature structure changed from tetragonal to a pseudocubic structure with peaks ascribed to the orthorhombic phase. The decrease in tetragonality and the shift of orthorhombic-tetragonal transition to higher temperatures was also observed by other authors [64, 67, 71]. In addition to the global structure study by XRD, local symmetry probed by Raman-scattering displayed peaks that 46

63 are attributable to the orthorhombic phase supporting the idea that grain-size reduction enhances the stability of that phase [67]. Arlt et al. also observed a shift in the Curie point to lower temperatures with decreasing grain size. However, at this point it is important to note that different preparation methods were used for the specific size ranges for this study due to the difficulty in preparing dense nanocrystalline ceramics. Using metalloorganic decomposition Frey et al. was able to make fine-sized powders and then ceramics which were nearly identical in composition and density, so the grain size was the only varying parameter [68]. The sample set had a grain size ranging between μm. The temperature dependence of the permittivity with changing grain size in this study is shown in Figure Figure 2.16 Temperature dependence of permittivity of BaTiO 3 with changing thickness (taken from Frey et al. [18]). 47

64 A number of observations can be made from the plot: (i) the maximum permittivity (at the transition temperature) decreases with grain size, (ii) there is a dielectric anomaly even for the smallest grain size (0.07 μm) material, and (iii) the transition temperature does not shift appreciably even down to a 0.07 μm grain size. The second and third observations are contrary to Uchino et al. s report in which the room temperature crystal structure of BaTiO 3 particles were observed to decrease in tetragonality with decreasing grain size and became cubic and non-ferroelectric below 0.01 μm [71]. However, Uchino s results were on particles which have different boundary conditions than the ceramics. The first observation was explained in terms of a dilution effect on the permittivity from the grain boundaries. It was shown that the data can be modeled for a diphasic structure with high permittivity grains isolated by low permittivity grain boundaries. This brick-wall model in which the grains are connected to the grain boundaries in series explains the decrease in permittivity with a grain boundary thickness of 8 Å and a permittivity of 130. Therefore, even at very fine grain sizes, the grain interiors can undergo a ferroelectric transition in the presence of defective grain boundaries. The brick-wall model had previously been used by Shaikh et al. who applied a combined series and parallel mixing of grains and grain boundaries. However, the parallel and series mixing model resulted in high grain boundary thicknesses in an ultra finegrained material [66]. It was suggested by Frey et al. that in a situation where the permittivity of the grain is much larger than the permittivity of the grain boundary, electric flux moves away from the grain boundaries which are in parallel resulting in a series dielectric mixing [68]. 48

65 McCauley et al. further refined the size effect study by preparing fine-grained BaTiO 3 ceramics (20-80 nm) in a glass matrix [69]. This changed the electrical boundary condition for the grain surfaces which were covered with an insulating (glass) matrix. By this way, the charge compensation at the grain surfaces could be limited which would otherwise compensate for the depolarization fields. The authors observed a shift in the transition temperature with decreasing grain size which was attributed to the presence of depolarization fields. In the absence of surface charge to compensate for the depolarization fields, the material creates a polarization gradient in the regions close to the surfaces. According to the Binder model for scaling effects, these gradients result in a shift and broadening of the phase transition [70] Scaling Effects in Thin Film BaTiO 3 The dielectric properties of thin films are generally inferior to their bulk counterparts due to the limitations in processing conditions and the difference in the applied electrical and mechanical boundary conditions. For instance, due to a substrate constraint the thermal budgets for the material synthesis could be limited resulting in poor crystalline quality and/or small grain size. The thickness of the film is also very important since the electrical boundary conditions could affect the dielectric properties substantially in very thin films. The effects of microstructure and thickness have been studied widely in the literature. The microstructural effects that result in lower permittivities for thin films are mainly due to two reasons, (i) the grain size being much smaller than the 0.7 μm maxima observed 49

66 in the bulk [65, 68] and (ii) the relatively poor crystal quality of the thin films. The low thermal budgets compared to bulk processing is the main reason for these effects, especially for films deposited on silicon substrates with processing temperatures less than 750 C [74, 75, 81-85]. Above this temperature metal electrode hillocking and delamination problems arise because of the metal electrode-substrate thermal expansion mismatch [86, 87]. Low processing temperatures result in small grain sizes and the permittivities of these films are typically less than 800. The grain structure (columnar vs. equiaxed) was also shown to affect the permittivity. Hoffmann et al. demonstrated that by tailoring a columnar solution deposited BaTiO 3 structure on silicon wafers, the room temperature can be increased from 500 to 900 [75]. This is, in fact, expected from the brick-wall model, since the dilution from the grain boundaries connected in series with the grains is minimized by through-thethickness grains. The thermal expansion mismatch problem can be overcome by using metal foils as substrates [76, 88, 89]. Contrary to thick and rigid substrates such as silicon and sapphire, the thin and compliant foils enable temperatures close to the bulk processing of barium titanate. Permittivities higher than 1500 can be achieved by firing the thin film samples at temperatures in excess of 900 C. Typically, due to the refractory nature of the barium titanate system, extensive grain growth cannot be achieved up to temperatures above 1200 C. Recently, Ihlefeld et al. showed that, applying the bulk processing strategies to thin film synthesis it is possible to enhance the grain size, the density, and the crystal quality of the chemical solution deposited thin films [77]. The authors used barium borate glass flux to make use of the liquid phase sintering to enhance densification and grain growth. By 50

67 limiting the amount of this second phase to avoid the detrimental effects of a glass phase on the dielectric properties, they were able obtain permittivities in excess of 3000 at room temperature. In addition to the grain size, the crystal quality of the material is also very important. The crystal perfection of a polycrystalline thin film can be quantified by measuring the coherent scattering size. Coherent scattering regions are tiny blocks in a grain which are slightly disoriented one from another [90]. Because of this mosaic structure, the lattice vibrations in neighboring blocks become incoherent. Since ferroelectricity is due to the longrange interactions of dipoles in neighboring unit cells, an interruption to these interactions affects the dielectric properties [91, 92]. A small coherent size means an effectively high defect concentration within each grain, limiting the coherent scattering size reaching the actual grain dimensions which degrades the dielectric properties. Higher processing temperatures anneal out the defects, enhancing the crystal quality and the permittivity of the thin films [93, 94]. This is important especially for sputtered films where the high energy bombardment of the particles may damage the lattice resulting in high defect concentrations. The crystallinity of sputtered BaTiO 3 thin films was characterized by Surowiak et al. by measuring the crystallite dimension and the lattice strain in the crystallites [95]. The authors found that the films which were sputtered via a high energy bombardment exhibited low permittivity and polarization values. They were able to obtain higher crystallite and lower strain values when the conditions were not as rigorous which resulted in better dielectric properties. 51

68 In a ferroelectric material, the surface requires termination of the spontaneous polarization. However, for phase stability in the ferroelectric the dielectric displacement must be continuous across an interface. The continuity can be maintained by the accumulation of free charge in the presence of an electrode or creating a polarization gradient towards the surface [96, 97]. In a thin film capacitor, a depolarization field forms when the polarization cannot be compensated for by free charges. The depolarization field is strongly film thickness dependent and can have dramatic effects on the phase stability and the dielectric properties [98]. The other phenomenon that is related to thickness dependent scaling effects is the formation of dead layers at the electrode-ferroelectric thin film interfaces. These layers act as parasitic capacitors connected in series with the ferroelectric, decreasing the capacitance especially for very thin films, typically below 100 nm. The most common explanations for these layers are (i) Schottky barrier formation between the electrode and the film [99, 100], (ii) variation of the polarization at the electrode-ferroelectric interface [ ], and (iii) size-related soft-mode hardening [105]. The effect of the dead layer capacitance on the film response is typically modeled by the following equation, A C = t 2t s o b + 2t s o s Eq. (2.29) where A is the capacitor area, C is capacitance, t and t s are the thicknesses of the film and the dead layer, and o, b, and s are the permittivity of vacuum, the film, and the dead layer 52

69 respectively. A plot of inverse capacitance as a function of the film thickness is used to quantify the thickness and the permittivity of the dead layer. The y-intercept of the line gives the dead layer capacitance. When a semiconductor is brought into contact with a metal, due to the difference in the work functions, a Schottky contact might form. The charge carriers near the surface of the semiconductor move into the metal, leaving behind a charge carrier depleted region. This results in the separation of charges which acts similar to a parallel plate capacitor. The capacitance of this layer is much lower than that of the ferroelectric film and can have a dramatic effect on the overall capacitance when the film thickness is very small [99, 100]. The other explanation for the observed thickness dependence of permittivity is the intrinsic dead layer effect. This model considers the effect of a surface termination on the dipole-dipole interactions. According to Zhou and Newns s description, the dipoles located near the surface environment contain fewer neighboring dipoles. The absence of the enforcing field from the surrounding results in the hardening of the surface dipole. This reduces the polarization and the permittivity of the surface region forming a dead layer [101]. Again, when the thickness is small enough, this dead layer with very low capacitance becomes very important. To understand the fundamentals of this intrinsic effect, Sirenko et al. studied the lattice dynamics of strontium titanate thin films via infrared ellipsometry [105]. They measured the soft mode frequency and the permittivity as a function of temperature. The results revealed that the lattice goes under soft-mode hardening as the film thickness is reduced which degrades the permittivity. The authors suggested that the softmode hardening involves the whole lattice not just an interfacial layer and they pointed the 53

70 role of strain and defects in this thickness dependent phenomenon. Other groups also suggested the possibility of a through-film effect [106, 107]. The work of Basceri et al. pointed out that the thickness dependence of the permittivity could be due to a true size effect and the dielectric response, which is a cooperative phenomenon, might be affected by the reduced thickness [106]. Sinnamon et al. fit their thickness series data for their BST films with ( nm) using the series capacitor model (Eq. 2.29) [107]. The authors hypothesized that if there is a dead layer, an anomaly should appear in the data when the dead layer thickness exceeds the thin film thickness. However, they did not observe such an anomaly down to 7.5 nm suggesting that either that number is the upper limit for the dead layer thickness or such a distinct dead layer does not exist an the drop in permittivity is due to a through-the-thickness effect. A later paper by the same group demonstrated that it is possible the model the thickness dependent permittivity of the films using a grain boundary dead layer model [108]. It was shown that low permittivity grain boundary layers perpendicular or parallel to the high permittivity grains can be used to model the thickness dependence with the same effectiveness as the interfacial dead layer model. A comprehensive experimental study investigating the thickness effect on the permittivity, the transition temperature, and the broadness of the transition was conducted by Parker et al. which also questions the validity of the dead layer model [109]. The authors prepared BST films on Pt-coated silicon wafers by liquid-source chemical vapor deposition with thicknesses ranging from nm. The temperature dependence of permittivity with changing film thickness is shown in Figure It is clear from the plot that the permittivity values decrease with decreasing thickness, the temperature at which the permittivity 54

71 Figure 2.17 Temperature dependence of permittivity of BST films with changing thickness (taken from Parker et al. [109]). maximum occurs shifts down to lower temperatures, and the transition broadens with reduced thickness. It was stated that the series model cannot be used to explain this data, since that model assumes that the film and the dead layer permittivities are thickness independent. However, the thickness dependency of T max (the transition temperature) shows that this assumption cannot be made. If they were indeed thickness independent, then the differences in the -T curves would be due to the changes in the relative volume fractions of the film and the dead layer without a change in the transition temperature. Therefore, the data 55

72 can be explained by a model which considers the thickness, transition temperature, and diffuseness. The authors suggested an explanation based on the Binder model [70]. This model accounts for the thickness dependencies of T max, max, and the broadness of the transition by assuming a polarization gradient at each surface through the material. Lookman et al. suggested that Parker s data could be modeled using the series capacitor model with a temperature independent interfacial capacitance [110]. They claimed that instead of using the overall permittivity, by using the film permittivity ( b ) in Eq and making corrected Curie-Weiss plots the transition temperature for the film comes out to be temperature independent. However, this result arises suspicion in that the transition temperature of the film is thickness independent and the interfacial layer is completely temperature independent yet their overall response results in a thickness dependent transition temperature. While the debates on the origin of the thickness dependency were continuing, Saad et al. showed that bulk-like permittivity values and phase transition behavior can be obtained in thin free standing barium titanate single crystals [111]. The thin films were obtained by cutting thin slabs from a single crystal with a thickness range of nm. After evaporating gold electrodes and annealing out the defects caused by the ion-milling process, the authors measured permittivities on the order of 25,000 for the 75 nm films. The same films showed very sharp transition peaks at ~125 C, which is very close to the bulk value, and they noted the absence of any shift in the phase transition temperature or a change in the broadness with a change in thickness. The importance of this work lies in suggesting that the observed scaling effects in thin films are possibly not due to intrinsic effects and they strongly depend on the electrical and mechanical boundary conditions applied on the film. 56

73 Therefore, by minimizing the detrimental extrinsic effects it could be possible to obtain bulklike properties in ferroelectric thin films. It must be noted for the sake of completion that there is some suspicion regarding the thinned single crystal data. There remains a question regarding the electroding geometry of this thinned crystal experiment specifically, the experimental procedure allowed for a finite amount of the thicker crystal to be sampled by the probing field and the extent to which this component contributed to the measured properties remains unclear. 2.6 Processing of BaTiO 3 (Ba,Sr)TiO 3 Thin Films The thin films of BaTiO 3 (Ba,Sr)TiO 3 have been synthesized by various deposition techniques including metalorganic chemical vapor deposition (MOCVD) [106, 109], pulsed laser deposition (PLD) [107, 110, 112], radio frequency (RF) magnetron sputtering [28, 74, 89, ], and chemical solution deposition (CSD) [75, 76, 88, 117, 118]. Each technique has its advantages and drawbacks, therefore each could be the choice of deposition method depending on the selection criteria. For instance, for capacitor applications cost is very important, since these capacitors should be one of the least expensive components in an electronic device. In this case, CSD techniques can be used since they offer a low cost, largescale production with very high compositional uniformity. RF magnetron sputtering can also be used with its relatively low cost, ease of composition control, and repeatability. On the other hand, for high performance applications such as tunable microwave devices MOCVD techniques can be used to obtain very high quality epitaxial thin films [29]. Regardless of the 57

74 deposition method used, the goal is to obtain thin films with controlled stoichiometry, high purity and density, good thickness uniformity, and high crystal quality. By fulfilling these requirements, high permittivity (and tunability) and low dielectric loss values can be achieved. Magnetron sputtering and chemical solution deposition will be discussed in detail, since these two are the deposition methods used in this thesis Magnetron Sputtering Basics of Sputtering Sputtering is a physical vapor deposition (PVD) process, where atoms from a target (Pt, Cu, etc.) are ejected by high energy ion bombardments and deposited onto a substrate (Figure 2.18). After the vacuum chamber is evacuated a sputtering gas, typically argon, is introduced into the chamber. Several kilovolts of dc bias is applied to the negative terminal of the magnetron gun, which accelerates the electrons towards the anode. The electrons follow a cycloidal path on the cathode with the applied magnetic field and collide with argon atoms. An electron with high enough energy can knockout an electron from argon converting it into a positively charged ion (Ar + ). Then, the positive Ar + ions are driven to the cathode where they collide with the target atoms and eject (sputter) them through momentum transfer. The plasma is initiated by the multiplication of these collisions. The chamber pressure is usually kept at between 5-50 millitorrs during sputtering. After a visible plasma is obtained it is observed that a current flows and the target material is deposited onto the surfaces with 58

75 potential higher than that of the cathode (i.e. substrate, chamber walls). This dc discharge is sustained due to the generation of ion-induced secondary electrons at the cathode. Figure 2.18 Schematic depiction of magnetron sputtering. If an insulating material is used as the target material, a practically impossible amount of dc voltage (~10 12 V) is needed to achieve the same current density as in a conducting target [119]. This barrier can be overcome by applying an ac signal at high frequencies. At low frequencies (e.g. 60 Hz) dc sputtering conditions occur and the cathode and the anode alternate at each half of the cycle. The frequency factor becomes effective above ~1 MHz [120]. In this range, the electrons oscillating back and forth by the electric field gain sufficient energy to ionize argon atoms. This is in addition to the acceleration away from the target. Since these field-driven electrons generate ions directly, sustaining the plasma does not rely on the secondary electrons emitted from the target. Even though the process seems symmetric considering the cycles, it is asymmetric due to the system geometry. The target 59

76 area is much smaller than the other electrode (substrate, chamber walls), hence resulting in higher energy bombardment of the target [121]. At radio frequencies, voltage can be coupled through any impedance, therefore the electrode resistivity does not matter. Due to the lower discharges at the target the rf sputtering yields deposition rates a factor of ~2 lower than dc sputtering Sputtered (Ba,Sr)TiO 3 Thin Films The structure and the properties of sputtered BST thin films depend on the deposition parameters including rf power, working pressure, argon to oxygen gas ratio, target to substrate distance, substrate material, substrate temperature as well as the post-anneal conditions. Therefore, these parameters need to be optimized to achieve the best dielectric properties. The effects of these sputtering conditions on the structure and the dielectric properties have been studied by many researchers. Group of York at University of California Santa Barbara studied the effects of Ar/O 2 ratio on the dielectric properties of (Ba 0.5 Sr 0.5 )TiO 3 films sputtered on platinized silicon at 550 C [113]. The authors observed an increase in (100) texturing with decreasing oxygen content. The permittivity also increased with decreasing oxygen. It was suggested that the (100) texturing resulted in the in-plane enhancement of the polar axis (c-axis) making the a- axis normal to the films surface. Since in tetragonal barium titanate the a-axis permittivity is much larger, the increase could be explained this way. In a later paper, the same group showed that the oxygen also has an effect on the Ti nonstoichiometry and A/B site ratio 60

77 [114]. By systematically changing the Ar/O 2 ratio from 90/10 to 60/40 it was observed that the permittivity and the loss tangent could be altered substantially. While low oxygen resulted in high permittivity and tunability films with moderate loss, increased oxygen pressure resulted in low permittivity and very low loss. With increasing oxygen the A/B site ratio ((Ba+Sr)/Ti) was measured to decrease from 1.00 to The authors suggested that this excess Ti segregated at grain boundaries making them more insulating, thus giving a lower loss tangent. The A-to-B site ratio was also shown to depend on the total pressure [115]. It was demonstrated that by increasing the total pressure from 20 to 60 mtorr, the ratio could be changed from 0.73 to Again, the more Ti-excess films gave lower permittivity values with lower loss tangents. Tsai et al. studied the effects of Ar/O 2 ratio on (Ba 0.5 Sr 0.5 )TiO 3 films sputtered on platinized silicon at various temperatures [122]. Contrary to York group, the authors did not observe any change in the A-to-B site ratio in an Ar/O 2 range of 100/0 to 40/60. Furthermore, the dielectric constant increased with increasing oxygen content reaching a maximum at a ratio of 50/50. Crystallinity of the films was also increased with increasing oxygen content. The effects of gas ratio was also studied by Lee et al. and Chen at al. [123, 124]. Both groups observed an increase in the permittivity with increasing oxygen content. All these results suggest that in addition to sputtering conditions, the stoichiometry and the structure of the films depend on many additional parameters such as system geometry, target composition and purity, and gas purity. Baniecki et al. investigated the crystallization and the effects of deposition temperature on the dielectric properties of BST films [81]. The authors sputtered 61

78 (Ba 0.7 Sr 0.3 )TiO 3 thin films on platinized silicon in a deposition temperature range from 100 to 650 C. The X-Ray data showed the onset of crystallization at 250 C. Transmission electron microscopy (TEM) study confirmed this data revealing a mixture of crystalline layer on top and a less crystalline phase on the bottom. It was noted that above 350 C there was no distinct less-crystalline layer. Below 500 C the films were mainly (110) textured and above this temperature the films became (100) textured. The change in texturing was also observed by other authors, above 600 C [74, 123]. The permittivity increased with increasing deposition temperature due to the enhanced crystallinity and grain size reaching a value of 600 with a deposition temperature of 650 C. In addition to silicon, number of other substrates have been used for the sputtering of BST thin film microwave devices, including LaAlO 3, MgO, sapphire, and polycrystalline Al 2 O 3 [116, 125, 126]. Since these devices use interdigitated electrodes instead of the metalinsulator-metal configuration, i.e. do not require bottom electrodes, the hillocking and delamination problems caused by the bottom electrodes are eliminated in these structures. Therefore, depending on the lattice mismatch these can be fired at temperatures higher than 750 C which is silicon s limit. It was also shown that base metal foils could be used to take advantage of high annealing temperatures to obtain high permittivity values with low dielectric loss. Laughlin et al. sputtered (Ba 0.6 Sr 0.4 )TiO 3 films directly on copper foils at 100 C [89]. The authors demonstrated that by doing low po 2 anneals at 900 C it was possible to crystallize the films without oxidizing the copper which was confirmed by XRD and transmission electron microscopy (TEM) results. A permittivity of 600 and a 3.5:1 tunability with a loss tangent of were obtained in these metal-insulator-metal devices. It will be 62

79 shown in this thesis that, this method could be extended to nickel foils to take advantage of even higher processing temperatures to get higher permittivity and tunability values Chemical Solution Deposition Chemical solution deposition (CSD) is a widely used technique to synthesize ferroelectric thin films with its low capital cost and compatibility with other semiconductor fabrication techniques [127]. This method offers many other advantages including high purity, high compositional homogeneity due to the mixing of the species at the molecular level, ability to control structural evolution, fabrication over large areas, and easy variation of stoichiometry. Nevertheless, this easy variation in the composition is also this method s major drawback because it makes repeatability of the process much more difficult. The other disadvantages include poor step coverage and difficulty in depositing epitaxial films. In thin film processing, the term sol-gel is often used interchangeably with chemical solution deposition (even though it is only a CSD approach), since all the CSD routes involve preparation of a solution and then gelation of this solution. A sol is defined as a suspension of nanoscale solid particles in a liquid. This forms a gel through solvent evaporation and polymerization of the molecules or through forming a network via attractive dispersion forces. Therefore, a gel can be defined as a solid network of molecules or particles enclosing a continuous liquid phase [128]. With the application of heat, the gel can be dried into an amorphous phase and then densified and crystallized into a ceramic. Thus, the steps of thin film chemical solution deposition are (i) solution preparation, (ii) solution deposition, and 63

80 (iii) thermal treatments for structural evolution. Structural changes observed during the heat treatments can be divided into three regions [128]. Region I, which is typically between C, involves gelation and the evaporation of water and the solvent. Region II, which is typically between C, involves condensation reactions, removal of organics, and structural relaxation. Finally, region III involves sintering and crystallization of the material. All these steps will be discussed in detail in the following sections Solution Preparation Chemical solution deposition is generally categorized into three groups depending on the solution chemistry and the chemical reactions that occur. These are classical sol-gel processes which use alkoxide precursors and alcohols as solvents, metalorganic decomposition routes which use carboxylate precursors and non-polar solvents, typically xylene, and the hybrid processes which combine the first two utilizing both carboxylate and alkoxide precursors [129, 130]. In sol-gel processing of perovskite thin films, typically metal alkoxide precursors are dissolved in 2-methoxyethanol and they go under hydrolysis and condensation reactions to form metal-oxygen-metal (M-O-M) bonds: M(OR) x + H 2 O M(OR) x 1 (OH) + ROH hydrolysis 2M ( OR) x 1 ( OH ) M 2O( OR) 2x 3 ( OH ) + ROH condensation (alcohol elimination) 2 M ( OR) x 1 ( OH ) M 2O( OR) 2x 2 + H 2O condensation (water elimination) 64

81 Since alkoxide precursors are highly reactive, they easily undergo hydrolysis and condensation. To avoid premature hydrolysis and condensation, there is another key reaction which decreases the sensitivity of the precursor to water. This reaction is the alkoxy exchange in which 2-methoxyethanol forms a methoxyethoxide which is less reactive: M ( OR) + xr OH M ( OR ) xroh alkoxy exchange x x + Condensation reactions of monomers form intermediate size molecules called oligomers. This polymerization can continue to build larger and larger molecules which results in the formation of a solid network in a continuous liquid phase forming a gel. The extent and the rates of these reactions can be controlled by controlling the temperature, ph, refluxing, distillation, and the water content to tailor the solution and the final material properties. However, these procedures require extensive knowledge of chemistry and for a non-chemist they can be quite complex. Furthermore, the solvent 2-methoxyethanol is known to cause birth defects inhibiting the industrial use [130]. Metalorganic decomposition routes use carboxylates and -diketonates (acac-type compounds) which are much less sensitive to water than the alkoxides. The large carboxylate compounds are usually dissolved in xylene and combined to achieve the desired stoichiometry. Since the species are not very reactive, the synthesis is rather simple and the final precursor strongly resembles the starting compounds. However, this simplicity also limits the ability to engineer the solution and hence the material properties. Another disadvantage of this process is that the large organic molecules result in excessive weight loss and shrinkage during heat treatment steps causing cracking of the films [129]. 65

82 The third group is the hybrid processes which are commonly used for the perovskite film synthesis. Generally, the A-site carboxylate precursor (e.g. Ba-acetate) is dissolved in a carboxylic acid (e.g. acetic acid). The more reactive B-site alkoxide precursor (e.g. Tiisopropoxide) is first chelated, i.e. modified to decrease its reactivity against water, and then added to the A-site solution. The chelating reaction is the key in the hybrid route which enables the handling of the alkoxide in ambient air. This route is very attractive for the nonchemist due to the relative simplicity of the solution preparation, even though the chemistry is quite complex due to the number of reactions that occur [130]. A disadvantage of the hybrid-chelate processes is that the solutions remain reactive after the synthesis degrading the solution properties and eventually causing precipitation Solution Deposition Once the solutions are prepared thin film deposition is usually accomplished by using spray coating, dip coating, or spin coating. In spray coating a wet mist or aerosol is delivered onto the substrate by using a nebulizer. An inert carrier gas is usually used and the settling is achieved by the gravitational or electrostatic forces [130]. The advantage of this method over the others is the conformal step-coverage. By using a high frequency nozzle with small droplet size, conformal deposition over the non-planar structures such as steps and trenches are possible [131]. In dip coating the substrate is immersed into the coating solution and then removed during which the deposition occurs. The process could be batch or continuous. The batch 66

83 process involves five steps; immersion, where the substrate is completely dipped into the coating solution, start-up, where pulling the substrate out of the solution begins, deposition, drainage, and solvent evaporation [128]. The thickness of the film is a result of the competition between various forces including gravity, viscous drag forces, and the surface tension in the concavely curved meniscus. In spin coating the substrate is held on a spinner by a vacuum chuck and then is flooded with excess solution. Then it is rotated at a speed of rpm to achieve uniform coverage. The spin coating can be divided into four stages which are deposition, spin-up, spin-down, and evaporation [132]. During the spin-up stage the solution flows radially outward to the perimeter due to the centrifugal forces. During the spin-down stage, the extra fluid flows off the substrate edges. The thickness in these stages is determined by the competition between the centrifugal and viscous drag forces, i.e. spin speed vs. viscosity. As the film gets thinner, the viscosity increases due to the increased concentration of nonvolatile components, and the resistance to flow decreases. After that, evaporation becomes the major mechanism for further thinning. For Newtonian liquids, in which the viscosity is not shear rate dependent, once the liquid film reaches a uniform thickness it stabilizes [128]. Therefore, the thickness can be controlled by solution viscosity, spin speed, and spin time Gelation and Drying In thin films, due to the high surface to volume ratio gelation and drying occur simultaneously. Gelation can be divided into two groups as physical and chemical [130]. 67

84 Physical gels are formed from particulate sols which are held together by van der Waals forces. These can be reverted to their sol state by dissolving in their parent solvent. Physical gels usually become chemical gels in time or with the application of heat. Chemical gelation involves the formation of a metal-oxygen-metal network through hydrolysis and condensation reactions. These reactions result in the formation of clusters, as the clusters grow they collide and form bonds with each other. At the gel point, they produce one giant cluster which extends throughout the liquid. This point is the onset of elasticity, since there is a continuous solid network [128]. In time, other clusters continue to attach to the spanning cluster increasing its stiffness. This further condensation, in fact, is not desired, because it results in a porous structure. Formation of a cross-linked stiff network does not allow structural rearrangements which results in a low density. Generally, it was observed that by using lower reactivity precursors, and volatile solvents films with higher density were obtained [133, 134]. Drying involves evaporation of the solvent and an accompanied shrinkage due to the capillary pressure. The dried gel, which is called a xerogel, can be reduced in volume up to an order of magnitude. When the liquid evaporates, it leaves behind solid-vapor interfaces with higher energy than solid-liquid interfaces. Therefore, to minimize the interfacial energy the liquid tends to cover the exposed solid surfaces. Assuming a cylindrical pore with radius r and length l, the change in the energy can be written as, E = 2 rl( SV SL ) Eq. (2.30) 68

85 where SV and SL are the surface tensions of the solid-vapor and the solid-liquid interfaces, respectively. By rising in the pore the liquid does work against gravity which is equal to P c V, where P c is the capillary pressure and the volume of the liquid moved is V= r 2 l. By equating this to the energy change and using Young s equation for the balance of surface tensions ( = + cos ) the capillary pressure can be written as, SV SL LV P c 2 ( SV SL) 2 LV cos = = Eq. (2.31) r r where is the contact angle. The negative sign means that the liquid is in tension (the sign convention for pressure is opposite to that for stress). This tension is balanced by compression in the solid which results in the shrinkage of the gel [135]. The displacement of the liquid also creates a pressure gradient driving the flow from the interior. At the drying stage, shrinkage mainly depends on the competition between evaporation (drives network contraction) and the condensation reactions (drives network stiffening). While the network is still compliant, capillary pressure can contract the solid network, however once the network gets stiff enough (through condensation reactions) that the capillary forces cannot overcome the modulus of the network, the shrinkage is significantly reduced and further evaporation results in porosity. Thin films are generally much denser than bulk gels, because the rapid evaporation causes films to remain compliant, so that the pores are collapsed by the capillary pressure during drying. 69

86 The pressure gradient caused by the low permeability of the solid network causes a difference in the shrinkage rates between the interior and the exterior regions resulting in a drying stress. The differential shrinkage would result in a tensile stress in the solid reaching up to ~100 MPa. Above a critical thickness these stresses can cause cracking. This thickness dependence is related to the minimization of energy. The presence of stresses increases the elastic energy. The system forms cracks and creates new surfaces to reduce this elastic energy at the expense of increase in the surface energy. At a critical thickness, the reduction in the elastic energy cannot compensate for the increase in the surface energy, and hence the crack cannot propagate. Typically, thin films with thicknesses <0.5 μm do not crack regardless of the drying rate, whereas films thicker than 1 μm almost always crack [128]. The critical thickness can be increased by decreasing the elastic modulus of the solid through precursor chemistry and by controlling the evaporation/condensation rates Structural Evolution during Thermal Treatments After the gel is dried, the obtained xerogel is further heat treated at elevated temperatures to synthesize the ceramic with desired properties. In the xerogel state, the material can be considered as a high surface area ( m 2 ) network of M-O species with adsorbed carboxylate and hydroxyl groups. As the temperature is increased, in the temperature range C, desorption of water and residual solvent occurs with an accompanied weight loss and a small amount of shrinkage due to the capillary pressure. With further increase in temperature, in the C range there are three processes that 70

87 contribute to shrinkage. These are the organic removal reactions, condensation reactions, and structural relaxation [128]. Organic removal involves thermolysis (without oxygen) or pyrolysis (with oxygen) and oxidation reactions. In thermolysis and pyrolysis organic species are removed by breaking M-O-C and M-O-H bonds. In barium titanate systems, oxidation reactions occur that form refractory carbonate (M-O-CO 2 ) phases. Removal of organics results in significant weight loss with a small amount of shrinkage. In thin film deposition, generally, the heat treatments are conducted in two steps. Before the high temperature treatment there is a first step that involves a hot plate dry ( C) after the deposition of each layer to avoid cracking. The condensation and pyrolysis that occur during the heating of a xerogel give off large volumes of gas. This can generate high pressures due to the low permeability of the structure resulting in the crack formation in large thicknesses. By the two-step process the organic constituents can be removed completely before the densification and the crystallization of the film. The second mechanism for shrinkage in the C range is condensation reactions. In these reactions hydroxyl groups are eliminated as water leaving behind M-O-M bonds. These reactions result in both shrinkage and weight loss. Finally, structural relaxation also contributes to shrinkage. In this process, to decrease the free energy, the excess free volume is removed through bond restructuring or rearrangements without any weight loss. The process occurs by diffusive motions of the network [128]. In general, there are no thermodynamic barriers to condensation and structural relaxation. They depend on material transport and so are kinetically limited. 71

88 At elevated temperatures the densification is accomplished by sintering mechanisms. Sintering is the reduction in the area of a consolidated particle mass, driven by gradients in curvature. Material is transported by viscous flow (in amorphous materials) or diffusion (in crystalline materials) to eliminate the porosity and decrease the solid-vapor interfacial area. In bulk materials, the transport of material via viscous flow and diffusion from the grain boundary area to the neck area between two particles results in densification. By these mechanisms the centers of the two particles move closer to each other reducing the surface area. However, evaporation-condensation and diffusion from the surface to the neck area do not move the centers toward each other, hence they only result in coarsening. In thin films, where the thickness of the films is comparable to the grain size, these two mechanisms can also cause densification if they transport vacancies all the way to the surface of the film [136]. The densification by viscous sintering is faster than densification by solid state sintering which relies on diffusion. This is because, in viscous sintering there is a volume flow of material through a relatively low viscosity matrix, whereas in diffusion the material moves due to local concentration gradients through impinging crystals with high viscosity [137, 138]. This enhanced material transport and particle rearrangement results in higher densification. The densification rate for viscous sintering is approximately given by [136], d dt SV n 1 3 SV r Eq. (2.32) 72

89 where is the viscosity, n is the number of pores per unit volume of solid, and r is the particle size. According to this equation the densification rate depends on viscosity, surface tension, and the pore size. Hence, precursor chemistry, deposition conditions, and the heat treatment schedule can be used to control the densification behavior. Crystallization in amorphous pyrolyzed films occurs by nucleation and growth processes. Nucleation of a new phase requires energy to create a new interface and undercooling provides the driving force for this process as shown in Figure It is observed from the figure that the free energy of the amorphous gel phase is larger than the supercooled liquid. This is due to the large surface area, residual hydroxyl, and excess free volume [130]. At low temperatures, even though the gel is unstable and the degree of undercooling is large, crystallization is inhibited by low atomic mobility [128]. Figure 2.19 Schematic plot of an amorphous CSD film, the supercooled liquid, and the crystalline perovskite phase (taken from Schwartz [130]). 73

90 From the classical nucleation theory, the thermodynamic barriers for homogeneous and heterogeneous nucleation are given by, * G homo = ( G V ) 2 Eq. (2.33) * G hetero = 16 3 f ( ) Eq. (2.34) 2 3( G V ) f ( ) = 2 3cos + cos3 4 Eq. (2.35) where is the surface tension, G V is the driving force for nucleation, and is the dihedral angle between the nucleus and the heterogeneous site. These equations implicate that the difference in the thermodynamic barriers depend on the driving force and the dihedral angle. Therefore, the values of these terms have important consequences in the transformation and the microstructure. For example, at low temperatures the driving force is very large (Figure 2.19) and the G V term dominates in the equations, making both homogeneous and heterogeneous nucleation possible. On the other hand if crystallization starts at higher temperatures, then the driving force will be small and the difference in the barriers will be determined by the f( ) term favoring heterogeneous nucleation. The crystallization temperatures can be shifted due to the changes in transformation pathways, precursor 74

91 chemistry and heating rates [130]. Typically, barium titanate thin films form the perovskite phase via an oxycarbonate phase and lead zirconate titanate (PZT) films form the perovskite via the pyrochlore phase which delay the perovskite crystallization temperature. While PZT mostly forms a columnar microstructure, barium titanate results in equiaxed grains. The pyrochlore phase in PZT does not act as nucleation sites for the perovskite formation, hence heterogeneous nucleation takes place at the substrate interface resulting in a columnar microstructure [139]. However, in barium titanate it was suggested that the perovskite phase crystallizes from the oxycarbonate which nucleates at low temperatures where the driving force is large resulting in an equiaxed grain structure [75, 130]. The altering of precursor chemistry through utilizing various alkyl chain lengths and using chelating agents was also shown to change the transformation pathways and the microstructure [117]. Once the material crystallizes densification occurs by solid state sintering which is much slower than the viscous sintering [128, 130, 136]. Thus, it would be beneficial to delay the crystallization to higher temperatures until a high density is achieved or the densification is completed. This is in fact possible, because the driving forces for the two processes are different. While crystallization is driven by the amount of undercooling, i.e. temperature dependent, it weakly depends on the surface energy, which is the driving force for sintering. Therefore, by controlling the thermal treatment it is possible to favor one process over the other. This can be analyzed by using time-temperature transformation (TTT) diagrams which show the effect of thermal history on phase transformation. Volume fraction of the crystallized material is given by the Avrami s equation, 75

92 V c = 1 exp( 3 I v u3 t 4 ) Eq. (2.36) where I v is the nucleation rate, u is the growth rate, and t is time. Using these to construct the TTT diagram and superimposing the densification curves it is possible to analyze the competition between sintering and crystallization as shown in Figure As seen from the figure, slow heating rates will result in incomplete densification. However, if the heating rate is fast enough, then it is possible to completely densify the material before the crystallization starts. Figure 2.20 TTT and sintering curves for an amorphous material (adapted from Uhlmann et al. [128]). 76

93 The effect of heating rate can also be visualized by considering the nucleation and the growth rates separately. The growth rate (u) increases with undercooling below the melting point as the free energy difference between the crystal and the amorphous gel, reaches a maximum and begins to decrease due to the rising viscosity (or low mobility). The nucleation rate (I v ) rises at a relatively large undercooling, because of the thermodynamic barrier to form a nucleus and then decreases at lower temperatures due to the increasing viscosity. By using faster heating rates to pass quickly the temperature range where the nucleation rate is high, so that there is not enough time for many nuclei to form, it is possible to densify the material before an appreciable amount of crystallization occurs (Figure 2.21). Figure 2.21 Nucleation (I v ) and growth (u) rate data for anorthite-cao Al 2 O 3 2SiO 2 (taken from Scherer [136]). 77

94 Another way to decouple the rates of crystallization and sintering is controlling the microstructure. While the crystallization rate does not depend on microstructure, the sintering rate strongly depends on the pore size. Therefore, by controlling the microstructure and the pore size through precursor chemistry, it is possible to obtain small pore size to increase the surface energy and the densification rate Solution Processing of BaTiO 3 and (Ba,Sr)TiO 3 Conventional processing of barium titanate involves the solid state reactions between the raw materials BaCO 3 and TiO 2 which requires temperatures in excess of 1200 C to decompose the carbonate and accelerate the diffusion between the species to complete the reaction. However, this process results in coarse inhomogeneous particles with impurities and secondary phases [140]. To overcome these problems solution routes were utilized to obtain powders with small particle size, high purity, and homogeneity with reduced processing temperatures. Then, the benefits of sol-gel processing in thin films were realized as the thin films were integrated into microelectronic devices. The first cited report on the sol-gel processing of barium titanate was from Yanovskaya et al. [141]. The authors deposited alcoholic solutions of barium and titanium ethylate on platinum and quartz substrates, which were then fired at temperatures between C. Even though the samples had secondary phases from the BaO-TiO 2 system, they were able to measure the temperature dependence of the dielectric constant with a distinct transition at ~120 C. Tuchiya et al. was able to synthesize dense and single phase 78

95 barium titanate films on platinum substrates via hybrid routes [142]. The authors demonstrated the enhancement in the dielectric properties with increased firing temperatures. The room temperature permittivity data showed almost an order magnitude increase as the processing temperature was increased from 700 to 1000 C. A room temperature permittivity of 1000 with a loss tangent of was obtained with a sharp ferroelectric/paraelectric transition in the r -T curve. This report clearly shows the advantage of the film-on-foil process where high processing temperatures can be used to enhance the dielectric properties without facing cracking or delamination problems that are commonly observed in rigid substrates. Hayashi et al. deposited barium titanate films via metal alkoxides [143]. They demonstrated that sol-gel films that show ferroelectric behavior could be deposited on various substrates including platinized silicon, MgO, and sapphire. By controlling the precursor chemistry and the deposition parameters Hoffmann et al. were able to tailor the film morphology [75]. The authors deposited BST films on platinized silicon using hybrid routes. Diluting the short chain Ba-carboxylate solutions from 0.3 M to 0.1 M changed the microstructure from equiaxed to columnar. This was attributed to the high crystallization temperature which decreased the driving force for nucleation resulting in heterogeneous nucleation. Later, Schwartz et al. demonstrated that crystallization of a dilute seed layer is sufficient to achieve columnar microstructure [118]. Chemical solution deposition of thin films directly on base metal substrates (Ni and Cu) were demonstrated by Dawley et al. and Ihlefeld et al. in an attempt to fabricate inexpensive base metal electrode capacitors [76, 88]. Both groups were able to achieve 79

96 permittivities larger than 1500 by crystallizing their films in a reduced atmosphere to avoid base metal oxidation. Phase evolution in solution processed barium titanate differs from conventionally processed bulk ceramics. Generally, decomposition of the precursors results in the formation of an intermediate oxycarbonate phase in all of the sol-gel, metalorganic, and hybrid routes [75, 117, ]. Hasenkox et al. studied the effects of precursor chemistry on the phase formation of barium titanate thin films. For the hybrid routes, which involve the reaction of Ba-carboxylate and Ti-alkoxide, the authors made the following observations. The titanium precursor decomposes before the barium precursor around C [117]. At that point the structure is a Ti-O gel network with adsorbed Ba-carboxylate species [130]. The barium precursor decomposition occurs in the range C depending on the chain length. Transformation pathway is also determined by the Ba-carboxylate chain length. For a long chain length precursor (2-ethylhexanoate) decomposition occurs at lower temperatures and BaTiO 3 forms via, BaCO 3 + TiO 2 BaTiO 3 + CO 2 On the other hand, if the precursor is an acetate or a propionate it decomposes at higher temperatures and forms the oxycarbonate phase through reacting with titania. Then the BaTiO 3 formation occurs via, Ba 2 Ti 2 O 5 CO 3 2BaTiO 3 + CO 2 Hence, the transformation pathway depends only on the barium precursor. Oxycarbonate phase formation shifts the crystallization temperatures resulting in higher densities [117]. 80

97 2.6.3 Firing of Thin Films on Base Metal Substrates Multilayer ceramic capacitors (MLCC) based on BaTiO 3 have been manufactured using palladium or silver palladium alloys as the electrode material until the Pd price increased dramatically [147]. This necessitated finding less expensive electrode materials which can be co-fired with the ceramic. In 1963, Herbert suggested that any metal with a sufficiently high melting point (>1300 C) could be used unless its oxygen affinity causes the reduction of barium titanate (e.g. Ti and Zr) [148]. By using nickel electrodes, cost savings of a factor of five compared to the noble electrodes were achieved [147]. However, these capacitors need to be fired in reducing atmospheres (N 2 /H 2 or CO/CO 2 ) to avoid metal electrode oxidation which also reduces the barium titanate creating oxygen vacancies. For the forming gas atmosphere the reaction can be written as [147] BaTiO 3 + xh 2 BaTiO 3 x [ V o ] x + xh 2 O The reduction creates free electrons which decrease the insulation resistance of the material. This reaction for barium titanate can be written using the Kröger-Vink notation as [149], O o 1 2 O 2 + V o + 2e Herbert also suggested the use of metal cations which can substitute for Ti 4+ with lower valence (i.e. acceptors) such as Mn, Co, Cr, and Fe. These could compensate for the free electrons and increase the insulation resistance [148]. Burn and Maher demonstrated this by doping the barium titanate based thick films with Mn, Co, and Mg [150]. The authors measured a three orders of magnitude increase in the resistivity, from 10 9 to cm, with the addition of these dopants. As a result of acceptor doping the free electrons are annihilated 81

98 by the acceptor states or by positively charged carriers, i.e. holes [149]. Nevertheless, the insulation resistances of the doped-materials were observed to degrade when they were under electrical field for long periods of time due to the electromigration of charged oxygen vacancies [151]. This could be overcome by using donor-acceptor complexes or amphoteric rare-earth ions such as Y 3+, Dy 3+, and Ho 3+ [ ]. The amphoteric dopants can occupy both A and B sites in barium titanate limiting second phase formation and also segregate to grain boundaries limiting the ionic transport of oxygen vacancies [156]. Furthermore, the insulation resistance of base metal electrode capacitors can be also improved by a reoxidation treatment. This typically involves annealing the capacitor at C in an N 2 atmosphere containing ppm O 2. The aim here is to decrease the oxygen vacancy concentration in the material while kinetically limiting the base metal oxidation. Especially in the presence of multivalent acceptor ions such as Mn and Fe, the reoxidation changes the cation valency (e.g. Mn 2+ to Mn 3+, Mn 4+ ) which further decreases the number of oxygen vacancies [147]. Thermodynamics of processing oxide ceramics without oxidizing the base metal electrodes can be understood by analyzing the free energies of the oxidation-reduction reactions of the constituent materials. Considering a simple oxidation reaction for a metal M, 2M (s) + O 2 (g) = 2MO (s) The standard Gibbs free energy change for the reaction is given by, G o = RT ln K and K = a MO 2 a M 2 po 2 Eq. (2.37) 82

99 Figure 2.22 po 2 versus temperature diagram for the oxidation of metals. where R is the gas constant, T is temperature, K is the equilibrium constant, and a is the activity. Assuming the activities of pure solids to be unity, the free energy change can be written as, G o = RT ln 1 po 2 Eq. (2.38) The variation of G or po 2 with temperature can be plotted using the thermodynamical data in the literature for the oxidation of metals [157]. Hence, by plotting 83

100 the oxidation curves it is possible to find the processing window in which the base metal is thermodynamically stable with the constituent oxides. Figure 2.22 illustrates the curves for barium, titanium, and the base metals nickel and copper. In this diagram, which is called an Ellingham diagram, the oxides are stable above the lines and metals are stable below the lines. The reason for avoiding the metal oxidation is that even though the base metals are thermodynamically stable with barium titanate, their oxides will react to form second phases that would degrade the capacitor properties [158]. Adapting the MLCC firing technology Dawley et al. demonstrated the fabrication of BST thin films capacitors on nickel tapes using chelate chemistry [88, 159]. Chemical solution deposited BST thin films were annealed at 900 C in an atmosphere of 3% H 2 /N 2 bubbled through room temperature water which gave a po 2 of ~10-18 atm. As it can be seen in Figure 2.22, these conditions are within the processing window of barium titanate on nickel. The authors were able to obtain a permittivity of 500 for random orinted grains and 1500 for their textured films. The dielectric losses were between 1-3%. Ihlefeld et al. expanded this work to copper foils using a similar chemistry approach [76, 160]. By annealing at 900 C at a po 2 of atm, permittivities in excess of 2500 were achieved with grain sizes up to 0.3 μm. This large grain size was believed to be the reason for bulk-like permittivities [76]. Furthermore, the r -T curves showed a clear hysteresis and the X-Ray diffraction patterns confirmed the tetragonal structure which is rarely seen in thin films. Laughlin et al. synthesized BST thin films on copper by rf magnetron sputtering [89]. By 84

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120 CHAPTER 3. EXPERIMENTAL PROCEDURES 3.1 Barium Strontium Titanate Sputtering on Base Metal Foils Copper and nickel foils were used as the substrates and the bottom electrodes for the BST capacitors fabricated in this study. Copper foils were Oak-Mitsui PLSP foils with 18 μm thickness. The nickel foils were obtained from Alfa Aesar (Nickel Thinfoil, %) and had a thickness of 10 μm. The root mean square (rms) surface roughnesses of the copper and nickel foils were measured to be 100 and 270 nm respectively on an 8 μm 8 μm area. The atomic force microscopy images are shown in Figure 3.1. It is important to note that these roughness values are between two and three orders of magnitude higher than values for single crystal substrates such as silicon and sapphire. 104

121 Copper Nickel Figure 3.1 Atomic force microscopy images of Cu and Ni foils. (Ba 0.6 Sr 0.4 )TiO 3 films were sputtered using rf magnetron sputtering from a 4" stoichiometric target (Super Conductor Materials, Inc., NY). The magnetron gun was oriented 30 off-axis to reduce the plasma damage caused by the bombardment of oxygen anions. The substrates were mounted on a heated and rotating manipulator for optimum stoichiometry and uniform thickness. The manipulator consisted of a stage with BN coated graphite heating element and a motor feedthrough for stage rotation. The manipulator was designed so that the stage was able to rotate around the fixed heater. The stage was rotated using a 12V dc motor at a speed of ~5 rpm. An S-type thermocouple was used to monitor 105

122 substrate temperature. The thermocouple was positioned equidistant to the heating element and the substrate. The schematic depiction of the system is given in Figure 3.2a. The copper and nickel foils were put on a 3" quartz plate side-by-side and held down by 0.836" diameter copper gaskets as shown in Figure 3.2b. The samples were heated via the radiation of the heater through the quartz plate. The as-received foils were cut into square peaces of 1" 1" and placed into the chamber. The chamber was pumped down to a base pressure of ~ Torr. Then, UHP argon (99.999%) was introduced to the system at a flow rate of 20 sccm using an MKS Instruments (Andover, MA) mass flow controller. The depositions were performed at 3.7 W/cm 2 using an Advanced Energy RFX-600 rf power supply and an RF Plasma Products MN 500-E matching box. The sputter gun was a Kurt J. Lesker Torus 4 magnetron gun with Figure 3.2 (a) Schematic illustration of the sputtering system and (b) nickel and copper samples on a quartz plate. 106

123 the flex mount capability. A one-hour deposition at 10 mtorr with an 8 cm target-substrate distance resulted in a film thickness of 0.8 μm. The thicknesses were measured using a Sloan-Dektak-2 profilometer. The films were deposited at manipulator temperatures ranging from 100 to 500 C. Before cofiring the samples, to complete the metal-insulator-metal stack Pt top electrodes were sputtered via dc sputtering using a 2" AJA ST-20 magnetron gun. The target was a 2" Pt foil (99.9% Alfa Aesar). An Advanced Energy MDX 1.5K power supply was used to obtain a power of 3.7 W/cm 2. Circular electrodes with a 0.5 mm diameter were defined sputtering through shadow masks. The depositions were performed at 30 mtorr argon pressure for 3.5 min. which resulted in 0.25 μm thick electrodes. The top electrodes had a relatively large thickness to minimize the de-wetting effects that result from firing at elevated temperatures [1]. 3.2 Chemical Solution Deposition of Barium Titanate Chemical solutions were prepared using the methods of Ihlefled et al. developed at North Carolina State University. The methods are based on the original works of Hoffmann and Schwartz [2-4]. A glove box was used to provide a low humidity environment during solution preparation. Before each preparation, the glove box was purged with desiccated nitrogen to obtain relative humidity levels consistently less than 15%. This enabled handling of the reactive titanium isopropoxide. To prepare the barium precursor, grams of barium acetate (99% Sigma-Aldrich) was put in a 50 ml screw top Erlenmeyer flask 107

124 (Kimble Kimax). Then, grams of glacial acetic acid ( 99.99% Sigma-Aldrich) was added to the powder using syringes and eyedroppers. The masses were measured using a Mettler-Toledo AT201 5-decimal analytical balance. To prepare the titanium precursor, first, grams (0.08 mol) of acetylacetone ( 99% Sigma-Aldrich) was put in an Erlenmeyer flask and then grams (0.02 mol) of titanium isopropoxide (99.999% Sigma-Aldrich) was added. The masses of all the chemicals were carefully recorded for the precise calculation of the barium precursor amount which would be added to the titanium precursor to yield 1:1 stoichiometric ratio. Both solutions were stirred at room temperature for 2 hours at 200 rpm using 0.625" Teflon coated magnetic stirring bars. Next, the calculated amount of barium precursor was added to the titanium precursor, again using syringes and eyedroppers for high precision. The mass measurements suggested a stoichiometric ratio accuracy within 100 ppm. Finally, grams of diethanolamine (99% Sigma-Aldrich) was added to increase the viscosity. The resulting solution was ca. 0.3 M. This solution was stirred for 12 hours to obtain the barium titanate precursor. The following steps were applied for solution deposition and drying. The as-received copper foils were cut into 2" 1" pieces. The copper foil was taped on two edges to a 3" quartz plate. Then, the quartz plate was placed on the vacuum spin chuck. A syringe with a 0.2 μm filter was used to flood the copper substrate with excess barium titanate solution until all the area was covered. The films were spun at 3000 rpm for 30 s. using a Cookson Electronics P-6000 spin coater. After that, the films were dried on a hot plate at 250 C for 5 min. This procedure was repeated until the desired film thickness was achieved. Each layer 108

125 had a thickness of ~0.1 μm. The films were then ready for high temperature firing. The process flow for the film preparation is shown in Figure 3.3. Figure 3.3 Process flow for barium titanate chemical solution deposition. 3.3 Low po 2 Processing of Thin Films Firing of Sputtered BST Thin Films The films need to be fired at elevated temperatures for complete phase formation, densification and crystallization. Firing barium titanate thin films on base metal substrates requires reducing atmospheres to avoid metal oxidation, as discussed in Section Firing at temperatures in excess of 700 C requires a po 2 less than atm [5]. This cannot be 109

126 achieved by using for example UHP nitrogen gas which typically gives po 2 values on the order of 10-6 atm. To overcome this problem, generally, H 2 O-H 2 gas mixtures are used when the oxygen partial pressure is required to be fixed at a low value [6]. For example, from Figure 2.22 it can be seen that at 900 C a po 2 of ~10-13 atm is required. It is possible to obtain this value by establishing the equilibrium H 2(g) O 2(g) = H 2 O (g) for which the free energy change of the reaction is given by, G o = 247, T Eq. (3.1) Using Equation 2.37 and 3.1, the equilibrium constant K is calculated to be at 1173 K. The equilibrium constant for the reaction is given by the expression, K = P H 2 O 1/2 P H 2 P O2 Eq. (3.2) so, for a po 2 of atm, the ratio of water vapor pressure to hydrogen partial pressure is about 40. If we flow forming gas (1% H 2 balanced with nitrogen) at a flow rate of 20 sccm and flow UHP nitrogen at a flow rate of 400 sccm, by assuming the partial pressure of nitrogen to be 1 atm we get a hydrogen partial pressure of atm. This would require a 110

127 water vapor pressure of 0.02 atm. Using the equation for the saturated vapor pressure of water as a function of temperature [6], viz. log P = 2900 T 4.65 logt Eq. (3.3) for a vapor pressure of 0.02 atm, the temperature is calculated to be 291 K, i.e. 18 C. Therefore, a po 2 of atm can be achieved by bubbling the above gas mixture through liquid water at 18 C. A Lindberg-Blue M glowbar tube furnace was used for heat treatments. For controlled atmosphere processing, a 2" diameter fused silica tube was used with CVD end caps and Viton o-ring seals. The furnace had an approximately 10 cm hot zone capable of reaching 1400 C. The samples were placed on a quartz plate and held on the plate using copper chunks cut from used copper conflat flange gaskets The above gas mixture, i.e. 400 sccm N 2 and 20 sccm forming gas (1% H 2 balanced with nitrogen), was passed through a water bubbler using MKS mass flow controllers. The exhaust was connected to another bubbler to avoid back streaming and to observe the gas flow. The po 2 was monitored in-situ by a solid-state oxygen sensor (Australian Oxycontrol Systems DS-Series). The schematic of the furnace is depicted in Figure 3.4. The sensor was located in the hot zone and also had a thermocouple, thus the po 2 and the temperature near the sample was monitored with high accuracy. The samples were fired at 900 C for 30 min with a ramp rate of 30 C/min. After 111

128 the anneals, the samples were furnace cooled to 150 C, and then removed from the furnace to avoid copper oxidation. Figure 3.4 Illustration of the system used for low po 2 firing Firing and Probing the Phase Evolution of CSD Barium Titanate Thin Films The phase formation steps of chemical solution deposited barium titanate thin films involve decomposition reactions which result in carbon dioxide emission. During the organic removal step, the gelated barium titanate precursor forms an intermediate oxycarbonate phase and at elevated temperatures (>600 C) this intermediate phase crystallizes into barium titanate [7, 8]. These process steps as a function of time/temperature are summarized with the pertinent chemical and physical processes in Figure 3.5. These processes are interdependent and participate in determining the phase evolution and the final microstructure. For instance, incomplete organic removal can slow down crystallization or a low crystallization 112

129 temperature can result in porous films as discussed in the previous sections. Therefore, being able to monitor the changes during these process steps would be a valuable means to achieve the optimum microstructure and dielectric properties. Figure 3.5 Physical and chemical processes that occur during firing of a chemical solution deposited thin film. A system was constructed for in-situ probing the effects of firing parameters such as po 2 and heat rate on the phase formation and microstructural development of chemical solution deposited barium titanate thin films. The changes in the partial pressure of gases in the firing atmosphere, especially carbon dioxide, were monitored using an SRS-200 residual gas analyzer (RGA). A Thermco Mini-Brute (MB-71) 3-zone furnace with a 2" diameter fused silica tube was used for firing the samples. The long hot zone (~80 cm) enabled firing of many samples at a time to enhance the resolution of the RGA data. Similar to the system used for sputtered films, nitrogen and forming gas were bubbled through liquid water using 113

130 mass flow controllers. The end of the furnace was connected to the RGA system to monitor the gases. The exhaust gases were leaked into the RGA using a leak valve. The illustration of the experimental system is shown in Figure 3.6. Figure 3.6 Schematic illustration of the system used for in-situ experiments. The end of the tube furnace was connected to the RGA via stainless steel tubing which was wrapped by heating tape kept at temperatures >120 C to avoid condensation. A k-type thermocouple was passed through the end cap and placed in the furnace near the samples for accurate temperature monitoring. An Omega DPi32 temperature reader was connected to the thermocouple. A LabVIEW program was written to interface the RGA and the temperature reader with the computer and record the changes in the partial pressures of gases as a function of time and temperature. A residual gas analyzer is a small size mass spectrometer in which the ionized gas molecules are detected and measured according to their mass-to-charge ratios. The RGA used in the experiments, i.e. SRS-200, consisted of an ionizer, a quadrupole mass filter, and 114

131 an ion detector. In the basic operation, positive ions are produced by bombarding the gas molecules with electrons emitted from a heated filament. These ions are then driven to the quadrupole mass filter which is formed of four cylindrical electrodes. A combination of rf and dc voltages is used to separate the ions based on their mass-to-charge ratio. The ions are then directed to the ion detector where the ion currents are measured. The operating pressure of the SRS-200 was from UHV to 10-4 Torr. The minimum resolution was Torr. For each furnace run, 4 samples with dimensions of 2" 1" were used. For the po 2 experiments, a po 2 of atm was obtained by flowing a mixture of 400 sccm N 2 and 20 sccm forming gas (1% H 2 balanced with nitrogen), a po 2 of atm was obtained by flowing a mixture of 400 sccm N 2 and 5 sccm forming gas, and a po 2 of atm was obtained by flowing 100 sccm forming gas through a water bubbler using MKS mass flow controllers. For the heat rate experiments, the samples were heated up to 900 C with 1 C/min, 3 C/min, and 20 C/min. The rapid heat-up experiments were conducted by sliding the samples into the hot zone at 900 C via a transfer arm. The dwell times were 30 min. for all the experiments. Furthermore, the effects of a two-step processing were also investigated. The samples were baked at 450 C for 15 min. under a po 2 of atm after each drying step and then fired at 900 C. The total gas pressure in the RGA was set at Torr via the leak valve. The changes in the water, nitrogen, carbondioxide, oxygen, and hydrogen partial pressures were monitored as a function of time and temperature. Specifically, carbon dioxide was important since it is emitted during the decomposition reactions. A rough calculation shows that it is possible to detect the carbon dioxide given off during firing of the thin film samples using the residual gas analyzer. The partial pressure of carbon dioxide in 115

132 the mixture can be very roughly calculated as follows. Four 2" 1" samples result in an area of 50 cm 2. If we assume a shrinkage of 40% [9], we can calculate the decrease in thickness as ~0.4 μm since we know the final thickness is 0.6 μm. This corresponds to a cm 3 loss in the solid volume. Assuming a gel density of 2 g/cm 3 and assuming most of the emitted gas will be carbondioxide with a density of g/cm 3, the samples will give off ~2 cm 3 of gas. The volume of the furnace tube is ~2400 cm 3. When the total pressure in the RGA system is Torr, carbon dioxide will have a pressure on the order of 10-8 Torr which is within the sensitivity range of the RGA. When preparing the samples for dielectric measurements, each sample set for the ramp rate and po 2 experiments were cut from the same 2" 1" sample to be able to make sensible comparisons. These were then fired at varying ramp rates or oxygen partial pressures. Finally, Pt top electrodes were sputtered on the films following the same procedure explained in Section Reoxidation Anneals There are several possible mechanisms that control the oxygen vacancy concentration in barium titanate. The most important ones are the po 2 dependence, presence of acceptor impurities, and the Ba:Ti ratio in the material. As discussed in Section 2.6.3, the firing under reducing conditions result in the formation of oxygen vacancies in the material via the reaction, O o 1 O V o + 2e 116

133 for which the mass action expression is given by, [ V o ]n 2 1 = K n po 2 2 = K n exp RT H n 1 po 2 2 Eq. (3.4) where K n is a constant which accounts for the change in the number of occupied sites and H n ~568 kj/mol is the enthalpy of reduction [10, 11]. The approximate electroneutrality condition for the reaction is given by, 2[ V o ] n + A [ ] Eq. (3.5) where [ A ] is the concentration of acceptor impurities. Acceptor impurities such as Fe, Mg, Al are unavoidably present in all barium titanate samples due to their natural abundance compared to the donor impurities as La, Nb, Ta, etc [10]. Depending on the relative concentrations of electrons n (introduced by reduction) and the acceptor impurities [ A ], the oxygen vacancy concentration is controlled by intrinsically or extrinsically. Smyth plotted the defect concentrations as a function of oxygen partial pressure for barium titanate using Equation 3.4 and assuming an acceptor concentration on the order of 100 ppm as shown in Figure 3.7. As seen from the figure, for the firing conditions used in this thesis, 900 C and po 2 of atm~10-14 MPa, and assuming similar amounts of acceptor impurities, the po 2 has a comparable effect to the acceptor impurities. Therefore, the low po 2 can result in 117

134 the decrease of the insulation resistance. This was observed in the dielectric loss measurements with high loss tangents. Figure 3.7 Defect concentrations in undoped-batio 3 as a function of po 2 (taken from Chan et al. [10]). The insulation resistance of the samples were improved by a low temperature higher po 2 anneal. The aim here was to decrease the number of oxygen vacancies in the barium titanate while kinetically limiting the substrate oxidation. A vacuum furnace was used for this purpose. The furnace was pumped down do a base pressure of ~ Torr. Then, it was ramped up to 500 C and the sample was slid in the furnace via a transfer arm passed through an Ultra-Torr fitting while maintaining the vacuum. The pressure was increased to Torr by leaking UHP oxygen (99.999%) to the chamber using a leak valve. The samples were annealed for 30 min., then moved away from hot zone and cooled down to

135 C without breaking the vacuum. This process is called reoxidation, since it oxidizes the reduced film decreasing the number of oxygen vacancies created by firing in reduced atmospheres Physical Characterization of the Thin Films X-Ray diffraction (XRD) was used to confirm phase formation and crystallinity. The measurements were made by a Bruker AXS D-5000 diffractometer equipped with a HighStar area detector. A 0.8 mm collimated Cu-K ( =1.54 Å) X-Ray beam was used for measurements. The foils were attached to a glass slide using double sided tape and then mounted on the aluminum stage. An area map of diffraction intensity was collected in which the horizontal axis was the 2 and the vertical axis was the tilt in the sample plane. Then, the intensity versus 2 plots were obtained by integrating counts over the -circle. The planar and cross-sectional microstructure characterizations were performed using scanning electron microscopy (SEM). The electron de-wetting in co-fired BST thin films was characterized using the backscattered mode of a Hitachi S3200 electron microscope equipped with a Robinson BSE detector. The electrode area mapping was conducted using the ImageJ software. The surface characterization of the chemical solution deposited barium titanate films were made by an Ultra-High Resolution Hitachi S-5500 SEM using the secondary electron mode. The grain sizes of the samples were calculated from the secondary electron images using the linear intercept method. The cross-sections were analyzed by a JEOL 6400F Field emission SEM using the secondary electron mode. The cross-section images were used 119

136 to identify the grain morphology and to calculate the film thickness. For accurate thickness measurements and avoiding the curling of the copper foils, the samples were prepared by sandwiching the foil samples between silicon pieces. Each sample was adhered in between two silicon pieces using Vishay 600 M-bond. Then, the stack was placed in a small vice and cured on a hot plate at 200 C for 45 min. After that, the cross-section was ground using 600- grit SiC paper and then fine polished via 1 μm and 0.05 μm alumina slurries. Microstructural characterization of the sputtered films, which had smaller grain size compared to the solution deposited films, was performed using a Nanosurf Easyscan 2 atomic force microscope (AFM) in the contact mode. The root mean square roughness values of the foils and the films were calculated using the AFM software. Again, the grain sizes were calculated using the linear intercept method Electrical Characterization of The Thin Films The thin film dielectric properties, i.e. capacitance and loss tangent as functions of voltage, frequency, and temperature, were measured using an HP 4192A (Agilent Technologies, CA) impedance analyzer. The electrical connection between the impedance analyzer and the thin film capacitors were made using HP 16048A test leads and Signatone micromanipulators with tungsten probes. One of the probes was pierced through one of the capacitors to make contact with the bottom Cu electrode and the other one was contacted to the top electrode of each capacitor. Through-the-thickness capacitance measurements such as in a parallel plate capacitor were performed this way. The data were recorded using a 120

137 LabVIEW program. Room temperature capacitance-voltage measurements were made using an oscillating voltage of 0.05 V at 10 khz with a superimposed dc bias sweep from 35 to 35 V (in 1 V steps) for the sputtered films and 10 to 10 V (in 0.5 V steps) for the solution deposited films. The temperature dependence of capacitance and loss tangent was measured via an MMR Technologies cryogenic temperature stage. The working principle of the stage relies on the Joule-Thomson effect, in which the adiabatic expansion of gas results in cooling. The cooling stage consists of a quartz arm with capillary channels and a resistively heated stage on the tip. High pressure gas (>1800 psi) is passed through these microchannels and then allowed to expand in the tip (10 psi) decreasing the temperature. Capacitance and loss tangents were measured with an oscillating voltage of 0.05 V at 10 khz using this stage while cooling from 500 to 100 K. The contact to the samples was made using micromanipulators which were connected to the impedance analyzer. Temperature was controlled using a K-20 programmable temperature controller (MMR Technologies, Inc, CA) and the data were recorded using a LabVIEW program. Room temperature leakage current measurements of the sputtered films were performed by using a Keithley 617 programmable electrometer with a sweep from 25 to 25 V with 1 V steps. A prerelaxation and a delay time of 3 s each were used. 121

138 References 1. Daniels, P., et al., Smart electrodes for ultralarge-area thin film capacitors. Journal of Materials Research, (7): p Schwartz, R.W., et al., Control of thin film processing behavior through precursor structural modifications. Ceramic Engineering Science Proceedings, : p Hoffmann, S. and R. Waser, Control of the morphology of CSD-prepared (Ba,Sr)TiO3 thin films. Journal of the European Ceramic Society, (6-7): p Schwartz, R.W., Chemical solution deposition of perovskite thin films. Chemistry of Materials, (11): p Barin, I., Thermochemical data of pure substances. 1989, Weinheim, Federal Republic of Germany; New York, NY, USA: VCH. v. 6. Gaskell, D.R. and D.R. Gaskell, Introduction to the thermodynamics of materials. 3rd ed. 1995, Washington, D.C.: Taylor & Francis. xxi, 568 p. 7. Gopalakrishnamurthy, H.S., M.S. Rao, and T.R.N. Kutty, Thermal-Decomposition of Titanyl Oxalates.1. Barium Titanyl Oxalate. Journal of Inorganic & Nuclear Chemistry, (4): p Frey, M.H. and D.a. Payne, Synthesis and Processing of Barium-Titanate Ceramics from Alkoxide Solutions and Monolithic Gels. Chemistry of Materials, (1): p

139 9. Keddie, J.L. and E.P. Giannelis, Effect of Heating Rate on the Sintering of Titanium- Dioxide Thin-Films - Competition between Densification and Crystallization. Journal of the American Ceramic Society, (10): p Chan, N.H., R.K. Sharma, and D.M. Smyth, Non-Stoichiometry in Undoped Batio3. Journal of the American Ceramic Society, (9): p Smyth, D.M., The defect chemistry of metal oxides. 2000, New York: Oxford University Press. x, 294 p. 123

140 CHAPTER 4. HOT SPUTTERING OF BARIUM STRONTIUM TITANATE ON BASE METAL FOILS 4.1 Hot Sputtering of Barium Strontium Titanate on Nickel Foils Section 4.1 corresponds to a manuscript published in Journal of Applied Physics: Volume 103, , April 2008 Seymen M. Aygün, Patrick Daniels, and Jon-Paul Maria North Carolina State University, Department of Materials Science and Engineering, Raleigh, NC William Borland DuPont Electronic Technologies, Research Triangle Park, NC Abstract The relationships linking temperature and voltage-dependent dielectric response, grain size, and thermal budget during synthesis are illustrated. In so doing, it was found that maximizing thermal budgets within experimental bounds leads to electrical properties comparable to the best literature reports irrespective of processing technique or microstructure. Optimal film properties include a bulk transition temperature, a room temperature permittivity of 1800, a voltage tuning ratio of 10:1 at 450 kv/cm, and loss tangent less than 1.5% at 450 kv/cm. The sample set illustrates the well-known relationship between permittivity and crystal dimension, and the onset of a transition temperature shift at 124

141 very fine grain sizes. A brick wall model incorporating a high permittivity grain and a low permittivity grain boundary is used to interpret the dielectric data. The data show, however, that high permittivity and tunability values can be achieved at grain sizes or film thicknesses that many reports associate with dramatic reductions in the dielectric response. These differences are discussed in terms of crystal quality and maximum processing temperature. The results collectively suggest that scaling effects in ferroelectric thin films are in many cases the result of low thermal budgets and the consequently high degree of structural imperfection and are not from the existence of low permittivity phases at the dielectricelectrode interface. Keywords: ferroelectric thin films, barium strontium titanate, nickel Introduction Compositions of the BaTiO 3 -SrTiO 3 binary solid solution system allow a wide range of application possibilities with systematically variable dielectric constants and Curie points. Through modification of the composition, the Curie temperature can be tuned for the required application temperature and optimal values of permittivity can be obtained [1]. Thin films of the paraelectric phase (Ba,Sr)TiO 3 (BST) are particularly attractive for applications in embedded memories, frequency-agile devices, IR detection, and embedded capacitance layers [2, 3]. High quality BST thin films have been deposited via various techniques including chemical vapor deposition, chemical solution deposition and radio frequency (RF) magnetron sputtering [2, 4-6]. Most of the work on BST has employed single crystalline 125

142 semiconductor or oxide substrates for making BST decoupling capacitors, microwave filters, and phase shifters. The use of base metal foils as substrates for ferroelectric thin films provides a viable solution for integrating embedded passive components in a printed wiring board (PWB). Base metal foils have several advantages including flexibility, low cost and compatibility with processing temperatures in excess of 700 o C [7-9]. In addition, the flexible nature of film-on-foil capacitors holds interest for applications where non-planar geometries hold advantage like conformable antennae, electronic textiles, and energy storage. Ni foils are of interest for these applications, but in addition, Ni foils enable BST synthesis over a wide firing window under reducing atmospheres which encompasses temperatures in excess of 1300 C. These temperatures approach the sintering temperatures of bulk BST ceramics thus provide the means to study the impact of thermal budget on the dielectric response. As has been shown for the case of Cu and Ni, there is an inconspicuous advantage to foil substrates - the small thickness and highly compliant mechanical properties (as compared to Si, SrTiO 3, or sapphire crystals) make possible film annealing to temperatures in excess of 1000 C without the thermomechanical instabilities routinely encountered by thermal expansion mismatch in rigid substrate-film systems. Consequently, a range of temperatures that promote film densification, grain growth, and structural refinement are experimentally viable: this presents the possibility for better exploring the crystal dimension - crystal quality - electrical property relations that regulate ferroelectricity. The authors utilize this expanded processing window to study sputtered barium strontium titanate thin films, to better understand scaling effects, and to improve the ability to engineer the dielectric response. 126

143 In this work, (Ba,Sr)TiO 3 was RF magnetron sputtered directly on Ni foils. The effects of sputtering temperature on the final film structure and electrical properties were investigated. We demonstrate that deposition temperature influences grain size, crystal quality, and extrinsic permittivity. Ultimately through comparisons of literature reports, we show that dielectric properties are best optimized through high thermal budgets while grain size (the 10s of nm range) is of secondary importance. This finding ultimately impacts the manner in which scaling effects are viewed in thin ferroelectric layers Experimental Procedure (Ba 0.6 Sr 0.4 )TiO 3 thin films were RF magnetron sputtered on 10 m thick nickel foils (Alfa Aesar, 99.95%) from a cm diameter stoichiometric (Ba 0.6 Sr 0.4 )TiO 3 target (Super Conductor Materials Inc., NY). The magnetron gun was oriented at 30 o off-axis to reduce the plasma damage caused by the bombardment of oxygen anions. The substrates were mounted on a heated and rotating manipulator for optimum stoichiometry and uniform thickness. X- ray fluorescence measurements revealed an A:B ratio of 1 with a ±3% uncertainty. Depositions were made at 3.7 W/cm 2 target power density for 1 h with a target to substrate separation distance of 8 cm, which resulted in 0.8 μm thick films. Pure argon was used as the sputtering gas with a deposition pressure of 10 mtorr. The films were sputtered at sample manipulator temperatures between o C. After BST deposition, 0.25 μm thick Pt top electrodes were DC magnetron sputtered to complete the metal-insulator-metal stack. Depositions were performed at 3.7 W/cm 2 in Ar pressure of 30 mtorr, through a shadow- 127

144 mask to define 0.5 mm diameter capacitors, which were ready for high temperature annealing. The high temperature processing of Ni should be carried out under reducing atmospheres to avoid oxidation. The required partial pressure of oxygen at an equilibrium temperature can be calculated by plotting po 2 vs. T diagram using reference thermochemical data [10, 11]. Figure 4.1 shows the equilibrium oxygen partial pressure curves for Ba, Sr, Ti, Ni and their respective oxides as a function of temperature. These curves clearly identify the equilibrium conditions for stability between metallic Ni, (Ba,Sr)TiO 3, and O 2 (g). From the figure, po 2 ~10-12 at 900 o C are within this range of stability. The required oxygen partial pressure was obtained by flowing a mixture of 400 sccm N 2 and 20 sccm forming gas (1% H 2 balanced with N 2 ) through a water bubbler at 25 o C. The po 2 was monitored in-situ using a Figure 4.1 po 2 vs. temperature diagram showing the processing window in which the oxides of Ba, Sr, and Ti are stable with metallic Ni. 128

145 zirconia electrolyte oxygen sensor. The samples were co-fired at 900 o C for 30 min. under atmospheric pressure. To compensate for the oxygen non-stoichiometry established by equilibration with the low po 2 annealing atmosphere, a reoxidation anneal was performed at 500 o C in a high vacuum tube furnace for 30 min. under a background oxygen pressure of 10-8 atm. X-Ray diffraction was used to confirm phase formation and crystallinity with a Bruker AXS D-5000 Diffractometer equipped with a GADDS area detector. The surface and the microstructural characterizations were performed with a Hitachi S3200 scanning electron microscope (SEM) and a Nanosurf easyscan 2 atomic force microscope (AFM) using contact mode. The dielectric measurements were made using a Hewlett-Packard 4192A Impedance Analyzer and an MMR Technologies Inc. Joule-Thomson cooler. Capacitance-voltage measurements were made under a DC bias sweep (-35 to 35 V) with steps of 1 V and an oscillation voltage of 0.05 V at 10 khz. Temperature dependence was measured while cooling from 450 to 100 K at zero bias with the same ac signal. Room temperature leakage current measurements were conducted using a Keithley 617 programmable electrometer with a sweep from 25 to 25 V and 1 V steps. A pre-relaxation and a delay time of 3 s each were used. 129

146 4.1.3 Results and Discussion The X-Ray diffraction patterns of the as-deposited and fired BST deposition temperature series are shown in Figures 4.2a and 4.2b respectively. Diffraction patterns show Figure 4.2 at 900 o C. X-Ray diffraction patterns of the samples for (a) as-deposited and (b) fired 130

147 the increasing crystallinity with increasing sputtering temperature as evidenced by narrower peaks with higher relative intensities. It is important to note that NiO formation was not observed by XRD in the deposition temperature range between 100 and 400 o C. At 450 o C, the high relative intensity peaks of NiO, (111) and (200), appeared. These peaks were no longer discernable after high temperature annealing indicating that NiO was either reduced back to metallic Ni or dissolved into the BST, or a combination thereof. Analysis of the X- Ray patterns show that the as-deposited samples are incompletely crystallized thus unable to develop the nonlinear dielectric response and high permittivity associated with ferroelectric oxides. For example, though some peaks attributed to BST are present in the as-deposited case, the {200} reflections can only be seen after the 900 C anneal. Figure 4.3 shows the capacitance vs. field curves for the as-deposited films, which were sputtered at 100 o C and Figure 4.3 Capacitance and loss tangent vs. field curves for the as-deposited samples sputtered at 100 o C and 400 o C. 131

148 400 o C. The capacitance values were very low and the films showed no tunability. Similar dielectric responses for low thermal budget BST films was reported by Baniecki et al [12]. For that reason, the films were fired at 900 o C to increase the crystal quality and to develop the desired dielectric properties. Figure 4.4a shows the room temperature capacitance vs. field curves for the entire sample set measured at 10 khz. The curves exhibit typical paraelectric C-V behavior with maxima at zero bias and saturation to a minimum high-field value. The zero bias capacitance increases with increasing sputtering temperature, while the saturation values remain relatively constant. This is similar to the trends observed in several literature reports of BST prepared on platinized silicon [12, 13]. The asymmetry in the curves may be attributed to the different top and bottom electrode materials. The sputtering temperature dependence of tunability is illustrated in Figure 4.4b. The tunability is given as the ratio of C max (capacitance at 0 V) to C min (capacitance at 35 V). The tunability showed a roughly parabolic increase with increasing deposition temperature and a tunability of 10:1 was obtained from the sample sputtered at 400 o C. The fugitive nature of the as-deposited NiO interface layer causes microstructural instability and local delamination of the BST. Consequently, the capacitors processed at 450 o C showed very high dielectric losses and could withstand very little electric field. 132

149 Figure 4.4 (a) Capacitance and loss tangent vs. field curves for the samples sputtered in the range o C (b) Tunability vs. sputtering temperature plot. 133

150 Due to the high surface roughness of Ni foils (30 nm rms on a 1 μm 1 μm area), the BST layer was co-fired with the top Pt electrode to increase capacitor yield. As reported previously, this co-firing approach persuades Pt top metallization to retreat from regions of high curvature (like crack edges or sharp asperities on the Ni surface) to minimize its interfacial energy, and hence decreasing the possibility of through-the-thickness short circuit pathways [14]. However, a consequence of co-firing is partial local de-wetting of the Pt film, which precludes the use of simple capacitor area calculations using the measured electrode diameter. To calculate the accurate area, fraction mapping of the Pt was conducted using the SEM images taken at various magnifications. In this manner, the actual contact area, hence capacitor dimensions could be computed with high confidence. The area ratio of Pt to the BST film was calculated using the secondary electron contrast between the Pt electrode and BST. Figure 4.5 shows an SEM image of one capacitor used for this study (sputtered at 400 Figure 4.5 SEM surface image of the sample, which was sputtered at 400 o C (dewetted light colored areas are Pt). 134

151 o C). The de-wetting of Pt can be easily seen from the image. The Pt area was calculated by averaging the values from the images taken at multiple magnifications and it was consistently found to be ~70% of the nominal electrode area. Field dependence of permittivity and leakage current density was plotted using this value. Figure 4.6 presents the dielectric properties of this sample, with a maximum permittivity of 1800 and a loss tangent of at 10 khz. This permittivity value with a 10:1 tunability is remarkably high for a sputtered BST thin film [2, 15-17]. The permittivity saturates at a value of ~180 which is typical for Ba-based ferroelectric materials at fields approaching 0.5 MV/cm. The leakage current density was measured and is also shown in Figure 4.6. The permittivities of all other samples were estimated using this calculation. SEM analysis and constant platinum thickness confirmed that the area fraction was similar in all cases. Figure 4.6 Field dependency of (a) Dielectric constant and (b) Leakage current density of the sample sputtered at 400 o C. 135

152 Figure 4.7 shows the AFM images taken using the contact mode of the samples sputtered at temperatures between 100 C and 400 o C and subsequently fired at 900 C. The images were taken on 1 μm 1 μm areas. Using linear stereology, the average grain size was Figure 4.7 Atomic force microscopy images of the samples sputtered at (a) 100 o C, (b) 200 o C, (c) 300 o C, and (d) 400 o C. 136

153 calculated to be 50 nm for the sample sputtered at 100 o C and it increased to 81 nm when sputtering temperature was elevated to 400 o C. The grain size values and the rms roughnesses are summarized in Table 4.1. TABLE 4.1 Summary of the atomic force microscopy results. T sputtering ( o C) Grain Size (nm) rms roughness (nm) The dielectric properties of BST thin films strongly depend on microstructure and grain size. There have been numerous investigations of grain size effects on BaTiO 3 and a combination of these reports for bulk ceramic and thin film embodiments can be used to interpret the present data and to evaluate existing models for size-induced property dependencies. Frey et al. explained the change in permittivity with grain size in bulk ceramics with a mixing model where grains (with high permittivity) and grain boundaries (with low permittivity) are connected in series [18]. Therefore, with decreasing grain size, the contribution of the low permittivity grain boundaries increases and the composite permittivity falls. The Frey model is of particular interest as it does not require an intrinsic size effect, but an extrinsic dependency imparted by the existence of grain boundaries and their finite thickness, at least for grain sizes down to 70 nm. The Frey data is an important 137

154 benchmark as it exhibits the highest permittivities for nano-grained ceramic BaTiO 3, and bulk transition temperatures (i.e., T C ~ 130 C) down to the smallest grain sizes. The AFM images in Figure 4.7 and the temperature dependent permittivity data in Figure 4.8 illustrate a similar trend. With higher final processing temperature, the BST grain size increases with a concomitant increase in permittivity. The dielectric maxima at the phase transition temperature also become substantially sharper. We note that when comparing Frey's 40 nm and 70 nm data points the permittivities agree favorably, though the phase transition in Frey's work are substantially sharper [19]. Note that this comparison uses Frey's permittivity values at 35 C above T C. This provides a sensible comparison since the room temperature values of permittivity for the current BST sample set are approximately 35 C above their T max value. Figure 4.8 Temperature dependency of dielectric constant and loss tangent for the samples sputtered at o C. 138

155 There is one exception to the data set, the 400 C sputtered sample shows the sharpest phase transition, but the Curie temperature is substantially suppressed. Recall from Figure 2a however, that the deposition at 450 o C resulted in formation of NiO. Therefore, even though it was not detected by X-Ray diffraction, a small amount of NiO is likely to be present in the sample sputtered at 400 o C. This NiO layer will react and dissolve into BST during annealing, and the compositional modification would influence the temperature dependent dielectric properties. Hafid et al. have studied the effects of Ni doping on the electrical properties of (Ba 0.6 Sr 0.4 )TiO 3 ceramics [20]. They reported that doping BST with 1.5% Ni results in a 25 o C decrease in T max. The temperature shift that was observed in our sample is likely due to the same effect. The X-Ray area detector used for characterization is sensitive to layers between 5 nm and 10 nm. Thus, a 5 nm NiO interface layer would be invisible to diffraction, but when dissolved into an 800 nm BST film would produce ~1% Ni doping and a temperature depression consistent with experimental observations. This data set shares a similarity with numerous other papers on size effects: the magnitude of the permittivity scales with crystalline dimension, and that at very low dimensions, in the present case ~ 50 nm, the ferroelectric transition temperature shifts to lower values. The size onset of a T C shift is comparable to the reports of Ihlefeld, Frey, and McCauley, and the permittivity magnitudes are comparable when grain sizes are similar [18, 21, 22]. The data set, however, is distinctly different from many thin film studies, especially those produced by PVD. For instance, Parker et al. studied crystal dimension dependency of permittivity and transition temperature for BST 70/30 thin films prepared by MOCVD [5]. Bulk values of transition temperature were achieved in films with 600 nm columnar grains, 139

156 and at this thickness, permittivity saturated at about 700. Similarly, Sinnamon et al. reported size dependent dielectric properties for BST 50/50 thin films [23]. In their work, permittivity values saturated at about 500 for films with columnar grains 1500 nm tall and greater than 100 nm in average diameter. Shaw et al. reviewed the size-dependent properties of ferroelectric crystals which included the efforts of IBM to prepare thin film BST in the late 1990s [24]. Again, permittivity values for BST 70/30 films saturated as a function of thickness at around 600 for films 150 nm thick with columnar grains. Finally, Hwang et al, and Chen et al., reported nearly identical findings, permittivities saturating near 600, for sputtered BST 60/40 films [25, 26]. Though the rate of permittivity decrease with thickness, and the value of film thickness or grain diameter may change between these authors, one commonality links all reports: regardless of deposition method or electrode composition, permittivity saturates at values near 600. In the present case, films with comparatively small grain sizes, ~ 80 nm, show room temperature permittivities of In Sinnamon's and Parker's work, a comparable sample exhibited permittivities of ~ 150 and 200 respectively [5, 23]. There is an additional commonality between these reports, in all cases, the maximum processing temperature lies between 600 C and 700 C. In this work, films are prepared at sputtering temperatures that are low compared to traditional oxide film processing. The ~ 400 C limit stems from the need to avoid metal foil oxidation. As such, the grain size is largely fixed at the time of deposition. The high nucleation rate for low temperature sputtering of polycrystalline films results in the fine nodular microstructure, and since the BST system is highly refractory with scant solubility, 140

157 extensive grain growth beyond the as-deposited microstructure does not occur unless temperatures above 1200 C are used. However, after deposition, all films are exposed to a 900 C anneal. The aforementioned references and a collection of additional reports of BST thin film processing are plotted in Fig. 4.9 [2, 4, 5, 21, 23, 25-35]. In this graph, permittivity is plotted against grain size for a number of BST films in the technologically interesting 50 nm to 200 nm thickness range. Two populations become evident: a population with permittivity values greater than 1000, and a population with permittivity values less than 700. For both populations, grain sizes span the same range, the critical difference lies in the thermal budgets used during synthesis. Without exception, thermal budgets which incorporate temperatures in excess of 900 C are associated with high permittivity. Figure 4.9 Comparison of dielectric constant values as a function of crystal dimension taken from several reports (data points are numbered according to their reference numbers). 141

158 We hypothesize that this comparatively high temperature heat treatment produces large permittivity in grain sizes which are typically associated with strong suppression of the dielectric response. Though the reason for this increase is not perfectly understood, we propose that a 900 C anneal improves the crystallinity within each grain, reducing structural defects and effectively thinning the grain boundaries. Ihlefeld et al. has demonstrated this effect using synchrotron x-ray scattering and we believe the same processes are occurring in these films [21]. As a consequence of this work, the ability to observe large permittivity in fine grain ceramic films brings into question the use of interfacial capacitance models to describe dimensionally dependent dielectric properties. Sinnamon et al. demonstrated that with equal effectiveness low permittivity layers perpendicular or parallel to the film thickness can be used to model experimental data sets showing a thickness dependent dielectric response [23]. The present data set brings further into question the interfacial dead layer model. This is not to say that low permittivity layers at the interface do not exist. Clearly electrostatic models prove that these effects are finite, however, the present results illustrate that microstructural aspects of ferroelectric crystals have a dramatic effect on the dielectric response, and for the purpose of reproducing bulk-like properties in thin films, efforts to optimize microstructure and crystal structure should receive maximum attention. 142

159 4.1.4 Summary (Ba 0.6 Sr 0.4 )TiO 3 thin films have been deposited on Ni foils. Metal-insulator-metal capacitors were fabricated by co-firing the BST thin films with Pt top electrodes. The dielectric properties were shown to improve substantially by increasing the sputtering temperature up to 400 o C. The increase in the permittivity and the tunability was attributed to the increase in grain size. The ferroelectric anomaly also became sharper with the increased grain size. The best sample of this work exhibited a room temperature permittivity of 1800, a tunability ratio of 10:1, and a loss tangent less than 1.5% at 10 khz. This work shows that Ni can be a strong candidate as a flexible substrate for embedded capacitors in printed wiring boards. The permittivity of BST on Ni can likely be further improved by increasing the annealing temperature closer to bulk sintering temperatures of BaTiO 3. Acknowledgements The authors would like to acknowledge the support of DuPont Electronic Technologies, Research Triangle Park, North Carolina. 4.2 Hot Sputtering of Barium Strontium Titanate on Copper Foils Even though the processing temperatures on copper are lower than that of nickel s, copper still has a few advantages. It is inexpensive, widely available, easier to process due to its smooth surface, and has lower resistivity. Therefore, to compare with the nickel data 143

160 (Ba 0.6 Sr 0.4 )TiO 3 films were also sputtered on bare copper foils at manipulator temperatures ranging from 100 to 400 C. The films were subsequently fired at 900 C for 30 min. at a po 2 of atm for densification and crystallization. XRD patterns of the as-deposited and fired films are shown in Figure The intensities were plotted using a logarithmic scale for easy identification of any second phases. The as-deposited films are partially crystalline and become completely crystallized after the firing. Figure 4.10a shows that copper oxide-cu 2 O forms above 300 C. It is important to note that the (111) Cu 2 O peak observed in the sample deposited at 350 C disappears after the annealing at 900 C under reducing atmosphere. This indicates that copper oxide reduces back to copper and/or dissolves into the BST. 144

161 Figure 4.10 XRD patterns of the (a) as-deposited samples and (b) those fired at 900 C. After firing, Pt top electrodes were dc magnetron sputtered through shadow masks. Figure 4.11 shows an optical microscope image of a 0.5 mm diameter Pt electrode on a BST film. All films were subsequently exposed to a reoxidation anneal at 500 C for 30 min. under a po 2 of 10-8 atm. 145

162 Figure 4.11 Optical microscope image of a 0.5 mm diameter Pt electrode. The room temperature permittivity-field curves for the films deposited at temperatures ranging from C are shown in Figure The measurements were made at 10 khz. Typical paraelectric field dependent permittivity curves were observed, with permittivity maxima at zero and falling to saturation at high fields. 146

163 Figure 4.12 Permittivity and loss tangent vs. field curves for the samples sputtered in the range of C. The maximum permittivity values increased from 900 to 1050 with the increase in sputtering temperature from 100 to 300 C. The highest tunability, which is given as the ratio of max (permittivity at zero bias) to min (permittivity at 35 V), was obtained from the sample sputtered at 300 C with a value of 6:1. The samples sputtered at above 300 C showed high dielectric loss values could not stand to applied dc bias. This was attributed to the presence of 147

164 the as-deposited Cu 2 O interface layer as observed by XRD and the microstructural instabilities that are expected during its reduction to Cu metal. Ultimately, the oxidation of copper limits the temperature at which BST can be deposited which limits the ultimate crystal quality and microstructure of the final film after post-annealing. Nickel, has much slower oxidation rate compared to copper in the processing temperature range of BST thin films [36, 37]. Therefore, higher deposition temperatures can be achieved by using nickel foils. Consequently, the benefits of hot sputtering observed in the Ni system could not be appreciated with Cu. References 1. Jaffe, B., W.R. Cook, and H.L.C. Jaffe, Piezoelectric Ceramics. 1971, London, New York: Academic Press. ix, 317 p. 2. Padmini, P., et al., Realization of high tunability barium strontium titanate thin films by rf magnetron sputtering. Applied Physics Letters, (20): p Ezhilvalavan, S. and T.Y. Tseng, Progress in the developments of (Ba,Sr)TiO3 (BST) thin films for Gigabit era DRAMs. Materials Chemistry and Physics, (3): p Basceri, C., et al., The dielectric response as a function of temperature and film thickness of fiber-textured (Ba,Sr)TiO3 thin films grown by chemical vapor deposition. Journal of Applied Physics, (5): p

165 5. Parker, C.B., J.P. Maria, and A.I. Kingon, Temperature and thickness dependent permittivity of (Ba,Sr)TiO3 thin films. Applied Physics Letters, (2): p Pontes, F.M., et al., Study of the dielectric and ferroelectric properties of chemically processed BaxSr1-xTiO3 thin films. Thin Solid Films, (1): p Borland, W.J. and S. Ferguson, Embedded Passive Components in Printed Wiring Boards, a Technology Review. Circuitree, March: p Maria, J.P., et al., Lead zirconate titanate thin films on base-metal foils: An approach for embedded high-permittivity passive components. Journal of the American Ceramic Society, (10): p Balaraman, D., et al., Exploring the Limits of Low Cost, Organics-Compatible High- K Ceramic Thin-Films for Embedded Decoupling Applications. Proceedings - 55th Electronic Components and Technology Conference, v 2: p Gaskell, D.R. and D.R. Gaskell, Introduction to the thermodynamics of materials. 3rd ed. 1995, Washington, D.C.: Taylor & Francis. xxi, 568 p. 11. Barin, I., Thermochemical data of pure substances. 1989, Weinheim, Federal Republic of Germany; New York, NY, USA: VCH. v. 12. Baniecki, J.D., T. Shioga, and K. Kurihara, Microstructural and electrical properties of (BaxSr1-x)Ti1+yO3+z thin films prepared by RF magnetron sputtering. Integrated Ferroelectrics, : p

166 13. Tsai, M.S., S.C. Sun, and T.Y. Tseng, Effect of oxygen to argon ratio on properties of (Ba,Sr)TiO3 thin films prepared by radio-frequency magnetron sputtering. Journal of Applied Physics, (7): p Daniels, P., et al., Smart electrodes for ultralarge-area thin film capacitors. Journal of Materials Research, (7): p Auciello, O., et al., Science and technology of high dielectric constant thin films and materials integration for application to high frequency devices. Journal of Electroceramics, (1-2): p Laughlin, B., J. Ihlefeld, and J.P. Maria, Preparation of sputtered (Ba-x,Sr1-x)TiO3 thin films directly on copper. Journal of the American Ceramic Society, (9): p Pervez, N.K., P.J. Hansen, and R.A. York, High tunability barium strontium titanate thin films for rf circuit applications. Applied Physics Letters, (19): p Frey, M.H., et al., The role of interfaces on an apparent grain size effect on the dielectric properties for ferroelectric barium titanate ceramics. Ferroelectrics, (1-4): p Frey, M.H., Grain Size Effect on Structure and Properties for Chemically Prepared Barium Titanate, in Materials Science and Engineering. 1996, University of Illinois at Urbana-Champaign. p

167 20. Hafid, M., et al., Dielectric and conduction properties in nickel doped barium strontium titanate ceramics. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, (6A): p Ihlefeld, J.F., et al., Extrinsic Scaling Effects on the Dielectric Response of Ferroelectric Thin Films. submitted to Physical Review B, McCauley, D., R.E. Newnham, and C.A. Randall, Intrinsic size effects in a barium titanate glass-ceramic. Journal of the American Ceramic Society, (4): p Sinnamon, L.J., et al., Exploring grain size as a cause for "dead-layer" effects in thin film capacitors. Applied Physics Letters, (4): p Shaw, T.M., S. Trolier-McKinstry, and P.C. McIntyre, The properties of ferroelectric films at small dimensions. Annual Review of Materials Science, : p Hwang, C.S., et al., Depletion layer thickness and Schottky type carrier injection at the interface between Pt electrodes and (Ba, Sr)TiO3 thin films. Journal of Applied Physics, (1): p Chen, H.W., et al., The size effect of Ba0.6Sr0.4TiO3 thin films on the ferroelectric properties. Applied Surface Science, (12): p Dawley, J.T. and P.G. Clem, Dielectric properties of random and < 100 > oriented SrTiO3 and (Ba,Sr)TiO3 thin films fabricated on < 100 > nickel tapes. Applied Physics Letters, (16): p Nagata, H., et al., Microcontact printed BaTiO3 and LaNiO3 thin films for capacitors. Journal of the American Ceramic Society, (9): p

168 29. Lee, W.J., H.G. Kim, and S.G. Yoon, Microstructure dependence of electrical properties of (Ba0.5Sr0.5)TiO3 thin films deposited on Pt/SiO2/Si. Journal of Applied Physics, (10): p Ihlefeld, J.F., J.P. Maria, and W. Borland, Dielectric and microstructural properties of barium titanate zirconate thin films on copper substrates. Journal of Materials Research, (10): p Kim, W.J., et al., Structural and microwave properties of (Ba, Sr)TiO3 films grown by pulsed laser deposition. Applied Physics a-materials Science & Processing, (3): p Ellerkmann, U., et al., Interface-related thickness dependence of the tunability in BaSrTiO3 thin films. Applied Physics Letters, (20): p Takeshima, Y., K. Tanaka, and Y. Sakabe, Thickness dependence of characteristics for (Ba, Sr)TiO3 thin films prepared by metalorganic chemical vapor deposition. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers, (9B): p Zhu, X.H., et al., Effects of growth temperature and film thickness on the electrical properties of Ba0.7Sr0.3TiO3 thin films grown on platinized silicon substrates by pulsed laser deposition. Thin Solid Films, (2): p Panda, B., et al., Thickness and temperature dependent electrical characteristics of crystalline BaxSr1-xTiO3 thin films. Journal of Applied Physics, (6): p

169 36. Aniekwe, U.V. and T.a. Utigard, High-temperature oxidation of nickel-plated copper vs pure copper. Canadian Metallurgical Quarterly, (4): p Haugsrud, R., On the influence of sol-gel derived CeO2 coatings on high-temperature oxidation of Co, Ni and Cu. Corrosion Science, (7): p

170 CHAPTER 5. PROCESS-PROPERTY RELATIONSHIPS IN CHEMICAL SOLUTION DEPOSITED BARIUM TITANATE THIN FILMS Chapter 5 corresponds to a manuscript that was submitted to Acta Materialia Seymen M. Aygün 1, Patrick Daniels 1, William Borland 2 and Jon-Paul Maria 1 1 North Carolina State University, Department of Materials Science and Engineering, Raleigh, NC DuPont Electronic Technologies, Research Triangle Park, NC Abstract Residual gas analyzer (RGA) techniques were used to analyze furnace gas atmospheres in real time during the thermal processing of chemically solution deposited BaTiO 3 films. This in situ probe enabled quantitative investigation of firing parameters including ramp rate, time, and oxygen partial pressure, and their relationship to crystal structure and microstructure development in complex oxides formed from metalorganic precursor solutions. The ability to monitor organic removal and barium titanate phase formation using an RGA was instrumental in identifying heat treatments that optimized structure and properties. Very slow ramp rates resulted in higher porosity, larger grain size, and a dramatic drop in the capacitor yield. Very fast ramp rates produced similar trends, however, the mechanisms were distinct. These observations are understood by considering 154

171 the profiles of organic removal and perovskite nucleation as measured by residual gas analysis. The effects of oxygen partial pressure on barium titanate formation and microstructure development were also explored. Grain size increased with increasing po 2 while there was no appreciable influence on density and capacitor yield. Optimal firing parameters, i.e., 20 C/min ramp rate at a po 2 of atm maximized permittivity, minimized loss tangents, and produced dramatic improvements in microstructure uniformity and density. Downstream analysis of furnace gas is a generically applicable means to better understand synthesis methods that are complicated by simultaneous mechanisms of precursor decomposition, extraction of volatile components, and crystallization. 5.2 Introduction Chemical solution deposition (CSD) of barium titanate is an attractive low cost synthesis method suitable for large-scale production. CSD has many advantages including high purity, compositional homogeneity, straight-forward variation of stoichiometry, and control over phase formation and microstructure development. Initial investigations of solution based barium titanate processing were intended to decrease the processing temperatures and obtain fine sized high purity powders [1-4]. Analogous methods were first applied to synthesize barium titanate thin films by Yanovskaya et al. [5]. Since these pioneering reports, solution based barium titanate powders and thin films have been prepared using multiple precursor chemistries. The most popular ones include sol-gel approaches with alkoxide solutions [6-9], metalorganic and oxalate salt decomposition [10-13], and hybrid routes utilizing carboxylates and alkoxides [14-17]. These studies revealed the importance of 155

172 solution chemistry and firing parameters on the phase evolution and the microstructural development of barium titanate. In conventional bulk synthesis, the transformation pathway of barium titanate involves diffusion and reactions between micron-sized BaCO 3 and TiO 2 powders. These processes require temperatures in excess of 1100 C, whereas in thin films, the temperatures are lowered due to the mixing on the nanometer scale [4]. Additionally, there are other transformation pathways for barium titanate formation depending on the solution chemistry, which also affect the crystallization temperature. Gopalakrishnamurthy et al. were the first to report the crystallization of barium titanate through an intermediate oxycarbonate phase with the chemical formula Ba 2 Ti 2 O 5 CO 3 [10]. The authors identified this phase using TGA/DTA and chemical analysis for the decomposition of barium titanyl oxalate tetrahydrate. Kumar et al. also observed the presence of a weakly crystalline phase for the decomposition of their citrate based organic precursors [11]. Based on the TGA, XRD, and Raman data it was concluded that the compound had again a stoichiometry close to Ba 2 Ti 2 O 5 CO 3. In addition to the metalorganic and oxalate routes, this oxycarbonate phase was also formed during the processing of both sol-gel and hybrid chemistries [6, 14, 15]. Hasenkox et al. studied the role of precursor chemistry in the transformation pathway for barium titanate formation. Utilizing various chain length Ba-carboxylates and Ti-alkoxide precursors it was demonstrated that the formation of the intermediate oxycarbonate depends on the barium precursor, and this phase shifts the crystallization to higher temperatures. The higher density and permittivity obtained in these films were attributed to the elevated crystallization temperature. 156

173 The heat treatments applied to metalorganic layers are similarly important in determining structure since in the course of firing a number of physical and chemical processes are required to extract organics, crystallize, and densify. After the drying step, which in principle removes only residual solvent, a xerogel is formed. Subsequent heat treatments promote organic removal, which involves thermolysis, condensation reactions, and the formation of carbonate species. These reactions and structural relaxation consolidate the xerogel [18, 19]. With increasing temperatures, densification occurs by viscous sintering until crystallization. After crystallization solid-state sintering becomes the predominant densification mechanism. The final microstructure and the dielectric properties are influenced by each of these processes which are interdependent. For instance, incomplete organic removal prior to crystallization can interfere with nucleation, while over aggressive drying can produce brittle xerogels which crack upon organic removal and crystallization. As such, these processes must be fundamentally understood and purposefully engineered in order to optimize physical and electrical properties. Recently, the film-on-foil approach, which started with platinum substrates [20], was applied to base metal foils by firing the films in reducing atmospheres to avoid substrate oxidation [21-23]. The higher thermal budget allowed by the thin and compliant foils compared to rigid substrates were shown to enhance the crystal quality and the dielectric properties of barium titanate thin films [24, 25]. The present work investigates the effects of firing parameters on the dielectric properties of these solution deposited barium titanate films on copper foils. The larger processing temperature window afforded by these substrates is ideally suited to in situ monitoring of furnace gases by mass spectroscopy, which can be used 157

174 to quantitatively study the organic extraction and barium titanate formation reactions as a function of temperature and time. It is the hypothesis of this investigation that in situ analysis of furnace gasses can be used to monitor the processes of organic removal and BaTiO 3 formation as a function of time, temperature, and heating rate, and that this information will provide a better understanding of the mechanisms that regulate structure evolution. This information will in turn improve our ability to optimize materials properties and performance, and the approach is generically applicable to many materials systems. The authors note that other researchers have used mass spectrometry and thermal gravimetric analysis to monitor phase formation in metalorganic precursors, however, the current study offers a unique improvement. The present results analyze the heat treatment process in the exact samples used for electrical and structural analysis. Most importantly, the high surfaceto-volume ratio of the thin film embodiment is conserved. This is in contrast to conventional studies where a crucible of precursor with much smaller surface area (thus access to the gas phase) is subject to heat treatment. As such, a unique insight is available regarding the relationships between organic extraction and property development. 5.3 Experimental Procedure Barium titanate precursor solutions were prepared using a process developed by Ihlefeld et al. which utilizes hybrid-chelate chemistries [22]. The barium precursor was prepared by dissolving barium acetate (99% Sigma-Aldrich) in glacial acetic acid ( 99.99% Sigma-Aldrich) and the titanium precursor was prepared by mixing titanium isopropoxide 158

175 (99.999% Sigma-Aldrich) with acetylacetone ( 99% Sigma-Aldrich). The precursors were mixed in Ba:Ti ratio of 1:1 and diethanolamine was added to obtain a molarity of ~0.3 M. The films were spin coated on 18 μm thick copper foils (Oak-Mitsui PLSP) at 3000 rpm for 30 s and then dried on a hotplate at 250 C for 5 min. The process was repeated 6 times to get the desired final film thickness of ~0.6 μm. Then the films were fired in a 3-zone tube furnace for organic removal and crystallization under reducing atmospheres. The po 2 was adjusted by flowing nitrogen and forming gas (1% H 2 balanced with nitrogen) and ranged from to atm by varying the gas flow rates which were flown through a water bubbler at room temperature. A po 2 of atm was obtained by flowing 400 sccm nitrogen and 5 sccm forming gas, a po 2 of atm was obtained by flowing 400 sccm nitrogen and 20 sccm forming gas, and a po 2 of atm was obtained by flowing 100 sccm forming gas. The po 2 was monitored using a solid-state oxygen sensor located in the hot zone. The films were heated to 900 C with various ramp rates and held at that temperature for 30 min. The rapid heat-up experiments were performed by sliding the samples into the hot zone at 900 C using an o-ring sealed transfer arm. The exhaust line of the furnace was connected to an SRS-RGA200 residual gas analyzer (RGA) system using stainless steel tubing and a leak valve. The line was kept at >120 C to minimize gas condensation. The total pressure in the RGA was Torr. The exhaust gas partial pressures of nitrogen, water, carbon dioxide, oxygen, and hydrogen were monitored as a function of time and temperature. The large and uniform hot zone of the 3-zone tube furnace enabled simultaneous firing of four 5 cm 2.5 cm thin film samples in order to achieve suitable signal-to-noise ratios from the RGA. The 159

176 RGA data were fit using the software IGOR Pro (WaveMetrics, Inc) such that peak areas could be calculated and quantitatively compared. X-Ray diffraction (XRD) was used to confirm phase formation using a Bruker AXS D-5000 diffractometer equipped with a HighStar area detector. The local probing was performed by Raman spectroscopy (Renishaw Ramascope) using an Ar laser with a 514 nm wavelength. The planar and cross-sectional microstructural characterizations were performed with a Hitachi S-5500 scanning electron microscope (SEM) and a JEOL 6400F Field emission SEM, respectively. For accurate film thickness calculations, the samples for crosssectional characterization were prepared by sandwiching the films in between silicon pieces and polishing down to 0.05 μm using alumina slurries. Grain sizes were calculated via the linear intercept method using the film surface images. Dielectric measurements were used to evaluate electrical properties. To do so, test capacitors were made by depositing platinum top electrodes by dc magnetron sputtering through shadow masks to complete the metal-insulator-metal capacitor stack. Reoxidation anneals were conducted to reduce oxygen vacancy populations produced by the highly reducing crystallization anneals, as is customary for base metal electrode capacitor processing [26]. The anneals were performed in a controlled atmosphere furnace at 500 C for 30 min. under a po 2 of 10-8 atm. Dielectric properties including capacitance and loss tangent as a function of dc bias and temperature were measured using an HP 4192A Impedance Analyzer and an MMR Technologies, Inc. Joule-Thomson thermal stage. Capacitance-voltage measurements were made by doing forward and backward sweeps between 10 and 10 V with 0.5 V steps using an oscillating voltage of 0.05 V at 10 khz. 160

177 Temperature dependence measurements were made by cooling the sample from 500 K down to 100 K with a 5 K/min rate using the same ac signal. 5.4 Results and Discussion Our preliminary experiment was designed to assess feasibility and to ensure the absence of artifacts with potential to obfuscate the measurements, to do so, three sets of hot plate dried barium titanate thin films were fired at 900 C under a po 2 of atm with a ramp rate of 20 C/min. Organic extraction and barium titanate phase formation was monitored in situ by recording the changes in the partial pressures of the exhaust gases, specifically carbon dioxide, since it is emitted in substantial quantities during both processes of interest. The total gas flow passed through the furnace was doubled and tripled with respect to our standard flow of 400 sccm. The partial pressure profile of CO 2 vs. time and temperature for all three experiments is shown in Figure 5.1. The data show that the temperatures at which pco 2 reach a maxima are the same, thus we can be confident that issues associated with gas residence time in the furnace or condensation during the path between sample and RGA do not interfere with our analysis. To further ensure that these measurements are free from artifacts, the peaks were curve fit and the total areas under the carbon dioxide curves were calculated, i.e. the total signals obtained during each heat treatment. The calculated area for the doubled and tripled flow rate was 1/2 and 1/3 of that calculated for the standard flow rate respectively. This is consistent with the expectation that 161

178 increasing the flow rate will reduce the partial pressure of CO 2, which is determined by sample volume thus fixed. Figure 5.1 Changes in the partial pressure of carbon dioxide as a function of time and temperature for different flow rates. Examining the general curve shapes reveals two features, pressure maxima at 510 C and 810 C. The former is attributed to the organic removal process and the latter is attributed to the barium titanate formation [6, 10, 11, 13]. Previous researchers have observed similar temperatures for organic thermolysis and BaTiO 3 formation reaction, however the reported temperatures were lower. This observation can be understood by recognizing that in these reducing atmospheres the absence of oxygen slows the volatilization of carbon containing species. The data are not shown, but reference measurements were made for precursor gels fired in flowing air and pure forming gas, in the former, BaTiO 3 formation 162

179 reactions occurred at lower temperatures while in the latter, reactions shifted to higher temperatures, These data alone are valuable as they enable us to identify the thermal budget needed to fully remove residual carbon and complete the BaTiO 3 solid-state reaction. Fig. 5.1 clearly shows that at ramp rates of 20 C/min temperatures > 800 C need to be achieved before the BaTiO 3 formation reactions are complete. This persistance of carbon was also observed in chemical solution deposited barium titanate films on nickel foils which were fired at temperatures as high as 1000 C in reducing atmospheres [27]. Temperature-dependent phase formation and film crystallinity were analyzed by ex situ X-Ray and Raman analyses as shown in Figure 5.2. To make a meaningful comparison with the RGA data, samples were extracted directly from the hot zone (via transfer arm) of the furnace thus quenched from temperatures between C in 50 C intervals. A different sample was used for each temperature. The X-ray data in Fig. 5.2 identifies the intermediate oxycarbonate phase (Ba 2 Ti 2 O 5 CO 3 ) above 600 C. This phase precedes the onset of barium titanate crystallization which initiates at temperatures above 750 C. It can be seen from the narrowing of the diffraction lines in Fig. 5.2 with temperature that the crystallinity of barium titanate improves, which is consistent with the RGA data showing a steady decrease in carbon content. The temperature-dependent Raman analysis also supports these results. With increased annealing temperature, an increasing peak intensity and the appearance of the bands near 305 and 715 cm -1 indicate crystallographic refinement via the appearance of a tetragonally distorted structure [28]. This combination of RGA and structural characterization enables us to make an important observation - the property improvements seen in solution-deposited oxides with increasing annealing temperature result not only from 163

180 an increased thermal budget and it s ability to reduce crystal mosaicity, the improvements are also associated with the removal of residual carbon which persist in measurable quantity to temperatures higher than often used in thin film processing. 164

181 Figure 5.2 (a) X-Ray diffraction patterns and (b) Raman spectra of the barium titanate thin films. The effects of ramp rate on the phase formation, microstructure, and the dielectric properties were similarly investigated by monitoring furnace gasses for 900 C anneals using 1 C, and 3 C/minute ramp rates. Figure 5.3 shows the plots as a function of time and temperature. Decreasing the ramp rate decreased the temperatures at which the CO 2 maxima were observed. This result is expected from a kinetic perspective since the reactions which produce CO 2 require diffusion within the film. To quantitatively validate this interpretation, the total area under the carbon dioxide curves, i.e. the signals obtained from each ramp rate were calculated. The total area under the peaks for each firing condition remained constant suggesting that the same final chemical assembly results despite the changes in furnace ramping rate. 165

182 Figure 5.3 Changes in the carbon dioxide partial pressure as a function of time and temperature for the ramp rates of (a) 3 C/min and (b) 1 C/min. 166

183 The impact of ramp rate on film microstructures was studied using SEM. For this experiment, an additional sample was introduced, one in which the dried 6-layer precursor film was inserted directly into a hot furnace - for this sample we estimate the ramp rate to be ~ 100 C/minute. The surface and the cross-sectional images of the films fired using 20 C/min, 1 C/min, and direct insertion are depicted in Figures 5.4 and 5.5. All films exhibited equiaxed grain morphology, which is typical for barium titanate [7, 15]. Reducing the ramp rate from 20 to 1 C/min, increased the grain size from 85 nm to 105 nm, this increase in grain size however, was accompanied by a decrease in the density. Additional grain growth can be attributed to a larger thermal budget, while the density decrease can be understood by comparing the RGA plots shown in Fig There is substantially more time during which the organic components are exposed to elevated temperatures at low heating rates. This provides for more extensive condensation reactions within the precursor gel which stiffen the network [18]. Consequently, the stiff gel cannot consolidate uniformly as the organic is removed and a porous final microstructure results. Furthermore, the lower crystallization temperatures observed at low ramp rates present detrimental effects on density. Early crystallization leads to incomplete densification, since solid state sintering which relies on diffusion of crystallized BaTiO 3 is much slower than viscous sintering which can occur in the xerogel prior to complete BaTiO 3 formation [29, 30]. For these reasons, the shift of both RGA CO 2 peaks to lower temperatures contributed to a lower final density. 167

184 Figure 5.4 Plane view images of the samples fired with (a) 20 C/min, (b) 1 C/min, and (c) rapid ramp rates. The sample which was fired using a rapid ramp, i.e. direct insertion into the hot zone at 900 C, also had a lower density than the sample fired using a 20 C/min ramp. This is contrary to both of the organic removal and crystallization arguments discussed above. However, it is important to note that there are intrinsic limits to these synthesis trends. A large gas volume must be evolved during the thermal decomposition stages regardless of the ramp rate. When ramp rates are rapid, and the total film thickness is ~ 1 m, gasses become trapped internally within the films, which frustrates gel consolidation and creates porosity after firing. SEM analysis in Fig. 5.4 also reveals an increase in the grain size from 85 to

185 nm for samples prepared by direct insertion. We attribute this to the relative rates of nucleation and growth as a function of temperature. That is, larger grains can be obtained by quickly passing the lower temperature range where the nucleation rate is high, thus reaching the higher temperature range where growth processes dominate with a smaller number of crystal nuclei [31]. Figure 5.5 Cross-sectional images of the samples fired with (a) 20 C/min, (b) 1 C/min, and (c) rapid ramp rates. 169

186 The permittivity versus applied bias curves for the samples fired using this series of ramp rates are shown in Figure 5.6. The sample set was measured at room temperature and 10 khz. Typical nonlinear curves were obtained with hysteretic behavior expected for ferroelectric barium titanate. Two general trends are observed from the data. First, the permittivity is lowest for samples fired at 1 C/min and 3 C/min, and second, the loss Figure 5.6 Permittivity versus applied bias curves for the samples fired with a ramp rate of (a) rapid, (b) 20 C/min, (c) 3 C/min, and (d) 1 C/min. 170

187 tangent is highest for the slowest ramp rates. Low field permittivity reduces from 1500 to less than 1200 when the ramp rate is changed from rapid to 1 C/min. The importance of the ramp rate is further illustrated by capacitor yield analysis. Large numbers of dot capacitors for statistical dielectric measurements were prepared as follows. A 5 cm 2.5 cm foil was spin coated with 6 layers and dried. This sample was subdivided into quarters, each fired at one of the previously discussed thermal profiles mm capacitor dots were prepared and measured for each firing schedule and the number of working capacitors was determined. Functionality was defined as a capacitor loss tangent less than 0.1 at 2 V dc bias. Table 5.1 summarizes this yield data and the microstructural properties. It can be seen that the yield was reduced dramatically with decreasing ramp rate. Whereas the higher ramp rates resulted in about 90 % yield, this was reduced to 70% and 27% when the ramp rate was reduced to 3 C/min and 1 C/min respectively. Additionally, it is important to note that while the direct insertion sample resulted in a similar yield as the 20 C/min ramp rate, with many measurements it became apparent that the loss tangents were substantially higher for samples processed using the direct insertion method. Average loss tangents at 2V were 0.05 and for samples processed by direct insertion and 20 C/min ramping respectively. The trends linking yield, loss tangent, and temperature profiles are understood via a density argument. During slow ramp-up, extensive condensation reactions causes the gel to lose its viscoelastic nature, which promotes cracking during consolidation, and the yield decreases sharply. During direct insertion, the rapid process of thermolysis results in trapped gasses ultimately producing microstructural defects which promote 171

188 conductive pathways and elevate loss tangent values. Table 5.1. Summary of the SEM and yield studies. Firing Condition Grain Size (nm) Thickness (nm) Yield (%) rapid C/min C/min C/min po 2 ~ po 2 ~ An additional parameter of importance during heat treatment of BaTiO 3 on base metal foils is the firing atmosphere, especially for nickel, which requires a much lower po 2 than copper to avoid oxidation. For those reasons the effects of po 2 on the phase development were investigated. Changing firing atmosphere during the entire heat treatment is difficult to interpret since there will be consequence on organic removal as well as the BaTiO 3 defect equilibrium. To minimize this, firing atmosphere was varied for a set of samples after the organic removal had been completed. For a 20 C ramp rate, this condition occurs at ~700 C, which was verified by RGA. To investigate the impact of atmosphere on crystallization and microstructural development, a set of samples were fired (after identical organic removal) at a po 2 of and atm in addition to the atm po 2, which was used in the initial ramp rate experiments. The RGA data for the experiments are shown in Figure

189 Figure 5.7 Changes in the carbon dioxide partial pressure as a function of time and temperature for the oxygen partial pressures of (a) atm and (b) atm above 700 C. 173

190 The higher po 2 firing resulted in a similar carbon dioxide profile as the standard po 2 of atm. The maximum for the barium titanate formation peak was observed at 810 C. Alternatively, for the low po 2 experiment, the peak maximum shifted to 910 C. For the BaTiO 3 crystallized at atm po 2, there is a substantial (~ 4X) increase in the total carbon dioxide partial pressure reported in Fig This is only an apparent increase attributed to the relative gas flow rates. A po 2 of atm is obtained using 100 sccm forming gas, while po 2 is obtained with 400 sccm of N 2 and 20 sccm of forming gas. As such, the CO 2 produced is measured in the context of total gas flow. At this point, we cannot explain the shift of barium titanate formation to higher temperatures, however, the shift is consistent with literature observations when BaTiO 3 is processed in atmospheres with low oxygen partial pressures. The plane view and cross sectional images of the po 2 -variable sample set are shown in Figures 5.8 and 5.9. While the grain size and the thickness values were similar for the po 2 of atm and po 2 of atm, the high po 2 sample exhibited a larger average grain diameter. The grain size increased from 75 to 120 nm, when the po 2 was increased from to atm above 700 C. However, it is important to note that the X-Ray analysis for this sample revealed trace quantities of Cu 2 O. Therefore, the change in grain size cannot be attributed solely to oxygen partial pressure at this point. 174

191 Figure 5.8 Plane view images of the samples fired at a po 2 of (a) atm and (b) atm above 700 C. Figure 5.9 Cross-sectional images of the samples fired at a po 2 of (a) atm and (b) atm above 700 C. 175

192 Voltage dependent permittivity data for the po 2 series are shown in Figure It is seen from Figure 5.10a that the high po 2 resulted in a low permittivity and a high loss tangent rapidly increasing at high fields. This was attributed to the presence of Cu 2 O as a second phase which degrades the dielectric properties. The sample, which was fired at atm po 2 resulted in similar permittivity and loss tangent values to the sample fired at atm po 2. As it can be seen in Table 5.1, changing the po 2 did not have a noticeable effect on the capacitor yield. In all cases a yield of ~90 % was achieved. Figure 5.10 Permittivity versus applied bias of the samples fired at a po 2 of (a) atm and (b) atm above 700 C. 5.5 Summary Barium titanate thin films have been chemical solution deposited on copper foils utilizing hybrid-chelate precursors. It was shown that a combination of in situ analysis of furnace gasses and ex situ structural and electrical characterization can be used to monitor the 176

193 processes of organic removal and BaTiO 3 formation as a function of time, temperature, and heating rate. This combination leads to better understanding of the mechanisms that regulate structure evolution and improves our ability to optimize materials properties and performance. The capacitor yield was improved from 27 % to 88 % with increasing the ramp rate from 1 C to 20 C/min. This also increased the permittivity and decreased loss tangents. A permittivity of 1450 and a loss tangent of was obtained with a 20 C/min ramp rate and a po 2 of atm. There was appreciable change in the dielectric properties with the variation of po 2 provided that the copper substrate was not oxidized. References 1. Clabaugh, W.S., E.M. Swiggard, and R. Gilchrist, Preparation of Barium Titanyl Oxalate Tetrahydrate for Conversion to Barium Titanate of High Purity. Journal of Research of the National Bureau of Standards, (5): p Mazdiyasni, K.S., R.T. Dolloff, and J.S. Smith, Preparation of High Purity Submicron Titanate Powder. American Ceramic Society Bulletin, (4): p. 509-&. 3. Pechini, M. July Phule, P.P. and S.H. Risbud, Low-Temperature Synthesis and Processing of Electronic Materials in the BaO-TiO2 System. Journal of Materials Science, (2B): p

194 5. Yanovskaya, M.I., et al., Preparation of Ferroelectric Barium-Titanate Films from Solutions of Metal Alcoholates. Inorganic Materials, (2): p Frey, M.H. and D.a. Payne, Synthesis and Processing of Barium-Titanate Ceramics from Alkoxide Solutions and Monolithic Gels. Chemistry of Materials, (1): p Gust, M.C., et al., In-situ transmission electron microscopy crystallization studies of sol-gel-derived barium titanate thin films. Journal of the American Ceramic Society, (11): p Jang, S.I., B.C. Choi, and H.M. Jang, Phase-formation kinetics of xerogel and electrical properties of sol-gel-derived Ba2Sr1-xTiO3 thin films. Journal of Materials Research, (5): p Kirby, K.W., Alkoxide Synthesis Techniques for Batio3. Materials Research Bulletin, (6): p Gopalakrishnamurthy, H.S., M.S. Rao, and T.R.N. Kutty, Thermal-Decomposition of Titanyl Oxalates.1. Barium Titanyl Oxalate. Journal of Inorganic & Nuclear Chemistry, (4): p Kumar, S., G.L. Messing, and W.B. White, Metal-Organic Resin Derived Barium- Titanate.1. Formation of Barium Titanium Oxycarbonate Intermediate. Journal of the American Ceramic Society, (3): p Shaikh, a.s. and G.M. Vest, Kinetics of Batio3 and Pbtio3 Formation from Metalloorganic Precursors. Journal of the American Ceramic Society, (9): p

195 13. Stockenhuber, M., H. Mayer, and J.a. Lercher, Preparation of Barium Titanates from Oxalates. Journal of the American Ceramic Society, (5): p Hasenkox, U., S. Hoffmann, and R. Waser, Influence of precursor chemistry on the formation of MTiO3 (M = Ba, Sr) ceramic thin films. Journal of Sol-Gel Science and Technology, (2): p Hoffmann, S. and R. Waser, Control of the morphology of CSD-prepared (Ba,Sr)TiO3 thin films. Journal of the European Ceramic Society, (6-7): p Phule, P.P. and S.H. Risbud, Sol-Gel Synthesis of Barium-Titanate Powders Using Barium Acetate and Titanium(Iv) Isopropoxide. Advanced Ceramic Materials, (2): p Schwartz, R.W., et al., Control of microstructure and orientation in solutiondeposited BaTiO3 and SrTiO3 thin films. Journal of the American Ceramic Society, (9): p Brinker, C.J. and G.W. Scherer, Sol-gel science: the physics and chemistry of sol-gel processing. 1990, Boston: Academic Press. xiv, 908 p. 19. Schwartz, R.W., T. Schneller, and R. Waser, Chemical solution deposition of electronic oxide films. Comptes Rendus Chimie, (5): p Tuchiya, T., et al., Preparation of Ferroelectric Batio3 Films by Sol-Gel Process and Dielectric-Properties. Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi-Journal of the Ceramic Society of Japan, (8): p

196 21. Dawley, J.T. and P.G. Clem, Dielectric properties of random and < 100 > oriented SrTiO3 and (Ba,Sr)TiO3 thin films fabricated on < 100 > nickel tapes. Applied Physics Letters, (16): p Ihlefeld, J., et al., Copper compatible barium titanate thin films for embedded passives. Journal of Electroceramics, (2): p Ihlefeld, J.F., J.P. Maria, and W. Borland, Dielectric and microstructural properties of barium titanate zirconate thin films on copper substrates. Journal of Materials Research, (10): p Aygun, S.M., et al., Hot sputtering of barium strontium titanate on nickel foils. Journal of Applied Physics, (8): p Ihlefeld, J.F., et al., Extrinsic scaling effects on the dielectric response of ferroelectric thin films. Journal of Applied Physics, (7): p Opitz, M.R., et al., Kinetic process of reoxidation of base metal technology BaTiO3- based multilayer capacitors. Journal of the American Ceramic Society, (11): p Dechakupt, T., et al., Chemical solution-deposited BaTiO3 thin films on Ni foils: Microstructure and interfaces. Journal of the American Ceramic Society, (6): p Frey, M.H., Grain Size Effect on Structure and Properties for Chemically Prepared Barium Titanate, in Materials Science and Engineering. 1996, University of Illinois at Urbana-Champaign. p

197 29. Keddie, J.L. and E.P. Giannelis, Effect of Heating Rate on the Sintering of Titanium- Dioxide Thin-Films - Competition between Densification and Crystallization. Journal of the American Ceramic Society, (10): p Keddie, J.L., P.V. Braun, and E.P. Giannelis, Interrelationship between Densification, Crystallization, and Chemical Evolution in Sol-Gel Titania Thin-Films. Journal of the American Ceramic Society, (6): p Scherer, G.W., Sintering of sol-gel films. Journal of Sol-Gel Science and Technology, (1-3): p

198 CHAPTER 6. HIGH DENSITY CHEMICAL SOLUTION DEPOSITED BARIUM TITANATE THIN FILMS Chapter 6 corresponds to a manuscript that is going to be submitted to Advanced Materials Seymen M. Aygün 1, William Borland 2 and Jon-Paul Maria 1 1 North Carolina State University, Department of Materials Science and Engineering, Raleigh, NC DuPont Electronic Technologies, Research Triangle Park, NC Materials scientists have struggled since the mid 1950s to achieve in a thin film embodiment the electromechanical response typical of a ferroelectric single crystal or a wellprepared ceramic. The deviations are observed in all thermodynamic properties, however, the most notable and most often characterized, is the suppression of radio frequency dielectric permittivity. Permittivity suppression is generally attributed to a set of phenomena termed scaling effects. These may be divided into two categories; the first is an intrinsic size effect, which describes the destabilization of ferroelectricity consequent only to reduced crystalline dimension. Since ferroelectricity is a cooperative phenomenon that involves the alignment of neighboring electrical dipoles, if the ensemble of dipoles is too small, the energy reduction for dipole-dipole coupling cannot stabilize the polar phase. The second category encompasses extrinsic size effects, which correspond to all practical deviations from the ideal crystalline state that occur due to the practical limits of material synthesis, and the physical 182

199 necessity of crystal interfaces and boundary conditions. The more important extrinsic effects include grain boundary volume and area; residual stress due to substrates, electrodes, and the spontaneous ferroelectric strain; point and line defects; density; stoichiometry control; and crystalline mosaicity [1, 2]. Scaling effects are particularly difficult to study because avoiding these extrinsic influences becomes more difficult as synthesis techniques are steered to produce increasingly small crystals in an embodiment that can be electrically and physically probed. Substantial progress in understanding scaling effects has been made. In ceramic systems for instance, the grain size effect in BaTiO 3 was explained by a brick-wall model, in which, permittivity is reduced due to the dilution of high permittivity grain interiors by structurally defective low permittivity grain boundaries [3]. In thin film systems, many authors observed a decrease in permittivity with decreasing thickness. Very often, an explanation involving low permittivity and potentially ferroelectrically inactive interfaces is used to explain these trends, however, it must be noted that models proposing geometries without parasitic interface layers can be used with equal success [4-9]. Furthermore, these simple interface layer approaches cannot explain the origin of transition temperature shifts and increased transition diffuseness that often accompany reduced film thickness [5]. With limited exceptions, the focus on interface-related effects has eclipsed the importance of rigorous physical characterization and optimization of microstructure and crystalline quality as a function of crystal dimension. Recently, a body of literature has evolved that demonstrates the importance of thin film crystalline quality and its role in extrinsic scaling effects. In most cases, these observations were enabled through novel synthesis methods 183

200 affording high temperature processing while maintaining small crystal size [10-14]. In summary, thin metal foil substrates enable crystallization anneals above 1200 C, which is approximately 2X higher than the processing temperature limits of Ba x Sr 1-x TiO 3 on silicon (~700 C). Permittivities larger than 1800 were obtained in both chemical solution deposited and sputtered films at grain sizes that were previously associated with intrinsic permittivity limitations. In this report we contribute to the scaling-effects knowledge base by demonstrating that understanding scaling-effects begins with fundamentally understanding oxide thin film processing science. Developing a sophisticated synthesis ability enables a self consistent parameterization of grain size, crystal quality, and microstructure effects and the observation of room temperature permittivity values above 3000 in chemical solution deposited barium titanate thin films. Barium titanate thin films were obtained by spin coating stoichiometric barium titanate precursor solutions on bare copper foils and 250 C hot plate drying after each layer. Each sample was coated with six layers. Precursor crystallization was performed using three different firing approaches. In the first approach, all six layers were fired at the same time at 900 C under a po 2 of atm. In the second approach, a two-step firing process was used which included a 450 C bake-out step after each hot plate dry and one final 900 C anneal. The third approach used a 900 C anneal after the deposition and hot plate drying of each layer. Figure 6.1 shows the plane view scanning electron microscope (SEM) images for BaTiO 3 film surfaces produced by the three different firing approaches. From these images grain sizes are calculated to be 100 nm, 120 nm, and 185 nm. The increase in grain size can be attributed to two factors: an overall increase in thermal budget with increased firing time 184

201 and/or a more effective removal of organic precursor components. To better understand the origins of grain growth a fourth sample was prepared in which 6 layers were deposited and hot plate dried, and fired. In this case, however, the standard firing schedule was repeated 6 times to replicate the thermal budget of the third approach. In this sample, an intermediate grain size of 140 was measured, which indicates that for the each-layer-fired sample, grain growth can be roughly equally attributed to an increased thermal budget and more effective organic removal. The SEM images in Fig. 6.1 also indicate a substantial narrowing of grain size distribution for the material produced with high temperature firing steps after each spinon layer. Figure 6.1 samples. Plane view images of (a) one-step, (b) two-step, and (c) each-layer-fired 185

202 Polished cross-sectional samples were used to examine the film density and to measure the film thickness. Since density measurement is difficult to assess from surface imaging alone, film thickness was used as a comparative measure of density: the identical amount of precursor was used in each sample and BaTiO 3 is not volatile at the temperatures used, thus differences in film thickness can be solely attributed to porosity. Accurate thickness was evaluated by numerous SEM measurements and averaging for each sample. The irregularity of copper foil substrates necessitates this approach. Figure 6.2 shows SEM Figure 6.2 samples. Cross-sectional images of (a) one-step, (b) two-step, and (c) each-layer-fired 186

203 cross-sectional images that compare the three deposition and annealing approaches. Incorporating the 450 C annealing step reduced film thickness from 570 nm to 550 nm, while firing each spun-on layer provided an additional reduction to 520 nm. Fracture surface cross section images were also taken to examine the change in density and microstructure, these data are shown in Fig Reduced porosity is apparent from the images as is a fully dense film for the each-layer-fired approach. Though difficult to quantify, a similar increase in grain size is reflected in the fracture cross sections. These images also reveal no evidence of columnar microstructure, in all cases, multiple grains can be identified through the thickness. A summary of the grain size and the thickness values for the films are given in Table 6.1. TABLE 6.1 Summary of the scanning electron microscopy results. Firing Schedule Grain Size (nm) Thickness (nm) One-step Two-step Each-layer-fired

204 Figure 6.3 samples. Fracture images of (a) one-step, (b) two-step, and (c) each-layer-fired 188