Dissertation. Control of aluminium oxide deposition by variable biasing

Transcription

1 Control of aluminium oxide deposition by variable biasing Dissertation zur Erlangung des Grades Doktor der Naturwissenschaften an der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum vorgelegt von Marina Prenzel aus Dortmund Bochum 2013

2 1. Gutachter: Prof. Dr. Achim von Keudell 2. Gutachter: PD Dr. Teresa de los Arcos Datum der Disputation:

3 Contents 1 Introduction 5 2 Magnetron Plasmas Theoretical description of the deposition process Sputter process Target poisoning Plasma characteristic numbers Tailoring the energy distribution function Ion fluxes Determination and tailoring of the ion energy distribution Mean energy per deposited atom Calculation of the average energy E i of the biasing signal Connection between the average energy E i and the mean energy per deposited atom < E > Aluminium oxide - deposition techniques and material properties Crystalline phases Material parameters of γ-aluminium oxide Deposition techniques Experimental set-up Configuration of the deposition chamber Feedback loop Temperature measurement Substrate biasing parameter Film analysis methods Profilometry Ellipsometry X-ray diffraction

4 Contents Fourier-Transform Infrared Spectroscopy X-ray Photoelectron Spectroscopy Stress determination Results and Discussion Film thickness evolution Crystalline film formation enhanced by variations in maximum ion energy Displacement per atom defining γ-crystalline phase formation Determination of displacement per atom Determination of crystalline state Displacement per atom by rectangular biasing signals Triangular Biasing signal «Structural» analysis by XPS Stoichiometry of Al 2 O 3 films Argon within amorphous and crystalline structures Angle-resolved measurements on the Ar2p peak Destroying crystallinity by ion bombardment Connection between Ar2p peak position and stress External stress load to the Al 2 O 3 films on stress cantilever arrays Conclusion 119 Bibliography 123 Appendix 129 4

5 1 Introduction Thin film plasma deposition processes have a broad application spectrum. By depositing a thin film onto a basic material, the chemical surface of the material as well as its physical properties can be modified. To illustrate, anti reflecting properties of glasses are created by thin films on the glass surface. Barrier coatings on PET bottles which are containing soft drinks can enhance the storage time of these drinks because of an optimized entrapment of the carbon dioxide and oxygen within the bottle. Physical properties may be enhanced by depositing scratch resistant layers onto these objects or by coatings of dielectric barriers. Further, water-repelling layers on objects are demanded. A high requirement on these physical properties is realised by the deposition of aluminium oxide (Al 2 O 3 ) onto an object. Aluminium oxide is used within the microelectronic industry because of its dielectric characteristic. A further use of Al 2 O 3 depends on the crystalline structure of this material which exhibits different physical properties. One can distinguish between different crystalline phases and the amorphous phase of aluminium oxide. The only thermodynamic stable crystalline phase of Al 2 O 3 is the α phase. Another very popular phase is the γ phase. Further states of crystallinity are named by Θ, δ, λ, η phase. The most important physical property of the α phase, also known as sapphire, is its hardness. γ-crystalline Al 2 O 3 is used within catalytic processes because of its low surface energy and porosity. Generation of these phases take place at different temperatures, which is for the γ phase of aluminium oxide 700 C to 800 C, according to Brandon et al. [1]. By heating any of the thermodynamic unstable phases up to a temperature of approximately 1,000 C, a transition to the thermodynamic stable α-al 2 O 3 occurs. Deposition of aluminium oxide is realised by different techniques such as chemical vapour deposition (CVD) or plasma-enhanced vapour deposition (PECVD). Further 5

6 1 Introduction distinction within these fields is the hot-wall deposition of Al 2 O 3 via a CVD process [2]. Moreover, physical deposition processes by filtered arc deposition systems [3] or magnetron sputtering [4] are reported on. During a magnetron sputter process, aluminium atoms are vaporized within a deposition chamber and transported to the substrate. Traditionally, crystalline films are formed through a defined substrate temperature. This substrate temperature enhances the atom mobility of the growing film. However, energy impact to the atoms of the growing film is realised by a substrate biasing. The substrate biasing has the potential to transfer kinetic energy to ions in front of the substrate which are accelerated to the film. The collisional energy impact to the surface of the film may lower the needed substrate temperature to establish crystallinity, which is desired for temperature sensitive materials. Moreover, studies on the impact of temperature and mean energy per deposited atom < E >were performed by several researchers [1, 5, 6, 7, 8]. Petrov et al. [5] showed that beside the ion energy E ions, also the ratio between ion and neutral flux during a plasma deposition process effects the film properties. Investigation of the interplay between ion bombardment and material properties were realised in the past, resulting in the common belief that an ion-induced enhancement of the adatom mobility promotes crystallinity and/or a certain crystalline orientation. Description of the parameter enhancing the ion-induced evolution of crystallinity is done by the energy per deposited atom < E >. This energy per deposited atom is linked with the ion energy E ions induced by the biasing and the ion-to-neutral ratio of the growth flux J ions /J neutr., resulting in < E >= E ions J ions /J neutr.. This relation consists of the ion flux to the substrate, J ions, mainly determined by Argon ions and the growth flux, J neutr., including the neutrals contributing the film growth. Petrov et al. [5, 9] also concluded that the average energy per deposited atom is clearly not a universal growth parameter. In more detail, two different series of measurements were done. The crystal orientation of titanium nitride, TiN, was analysed when varying the ion energy and keeping the ion-to-neutral ratio constant. In a second experiment, the ion energy was kept constant and the ion-to-neutral ratio was varied. In both cases, the energy per deposited atom was varied. So, a small ion-to-neutral ratio and an ion energy of 85 ev resulted in a preferred orientation of the deposited TiN films. Petrov et al. concluded that it is essential that ions are stopped within the first monolayers to efficiently promote adatom mobility. This 6

7 sets boundaries not only on the ion-to neutral ratio, but also on the absolute energy of the ions. Studies on the connection between ion bombardment and structure evolution for physical vapour deposition systems already exist. Andersson et al. [10] showed that a variation of the oxygen partial pressure leads to a change of the DC self bias at the target, thus to a different ion bombardment and finally to a different crystallinity of the films. However, plasma chemistry, surface coverages of oxygen etc. influencing the evolution of the microstructure are changed by more than the ion energy per deposited atom. Using pulsed plasmas and/or pulsed bias concepts, the structure evolution is affected by the sequence of adsorption of neutral species and of ion-induced densification of the film may occur simultaneously or sequentially. A new technique is represented by HPPMS (High Power Pulsed Magnetron Sputtering) plasmas [11], where a high power plasma pulse interacts with a surface for a short time, followed by a long off-period, where relaxation may occur and/or neutral species may still adsorb. Establishment of a correlation between binding energy shifts in X-ray Photoelectron Spectroscopy (XPS) measurements and structural characteristics of thin films are reported by several authors [12, 13]. Commonly used thin film deposition methods such as sputtering or PECVD deposition employ noble gases. As a consequence, some amount of gas is often implanted within the deposited thin film. The very nature of the noble gas electronic structure prevents it from sharing electrons in chemical bonds with atoms from the host matrix. Therefore, the precise determination and correct interpretation of the binding energy levels of core electrons from the naturally implanted gas atoms has the potential of providing information about their local environment. In the case of noble gas embedded in metals, the observed binding energy shifts are dominated by final state effects, which allows to extract information about the situation of the foreign gas in the matrix. For example, the noble gas may exist in the form of bubbles, whose sizes can be inferred from the magnitude of the binding energy shift of the noble gas [14, 15, 16, 17, 18, 19]. Although, phase formation mechanism of aluminium oxide is well-known, no systematic determination of the evolution of its microstructure using a biasing scheme has been reported on. Moreover, no report on the correlation between ion impact 7

8 1 Introduction tailored within the plasma sheath is reported. The exact details of these ion-induced surface processes remain unclear. Although, one can devise an experiment providing a unique energy per deposited atom and a constant ion-to-neutral ratio, film growth may still depend on more subtle effects such as the particular ion energy distribution (IED) and/or the temporal sequence of the incident species. Additionally, a connection to the resulting material properties such as stress measurements is not reported on. Specifically, final state effects on embedded noble gases within a matrix measuring dielectric thin films can not be found. The objective of this work is to determine the dependence of material properties on the plasma parameter. In detail, when using a substrate biasing scheme during a plasma depositing system, the ion energy distribution of the impinging ions is tailored. Therefore, the mechanism which connects the ion energy distribution function with the mobility of the surface atoms of the growing film needs to be understood. So, ion energy distribution is determined and compared with the crystalline structure of the thin film. Finally, by using Argon which is embedded to the films during the deposition process, the Ar2p peak position within XPS measurements correlates with stress measurements on these films. The present work deals with the development of the evolution of crystallinity by variable substrate biasing at the representative material example aluminium oxide. This thesis is divided into six chapters. The second chapter deals with the theoretical description of the sputter system and a first characterization of the plasma. Within the experimental set-up part, chapter 3, the depositing system as well as the principle in tailoring the ion energy distribution by a substrate biasing is presented. Then, the results of the deposition system will be discussed. Within this part, beside the evolution in crystallinity, the analysis of the stress within the film using a surface sensitive measurement technique, X-ray Photoelectron Spectroscopy, is shown. Finally, the discussion and the conclusions and outlook complete this thesis. 8

9 2 Magnetron Plasmas Deposition of the aluminium oxide (Al 2 O 3 ) films was realised using a magnetron sputter system. A description and characterisation of the magnetron plasma will be presented within the next chapter. The theoretical description of the deposition process will be given, including effects such as target poisoning and regulation of the oxygen partial pressure. Characterisation of the electron temperature by the plasma absorption probe is presented. The determination of ion fluxes and ion energy distribution function were realised using a retarding field analyser. The biasing signal and characterisation of the waveform are shown. Finally, the key words for the ion bombardment impact, namely mean energy per deposited atom and maximum ion energy, will be presented in the context of the used biasing signals. 2.1 Theoretical description of the deposition process Thin film deposition can be realised by using different techniques. In general, one has to distinguish between CVD (Chemical Vapour Deposition) processes and PVD (Physical Vapour Deposition) processes. In a CVD process, reaction of liquid or gaseous compounds is realised by mixing the components and heating them, for example. The chemical reaction of gas components in the non-thermal equilibrium within a plasma enhanced chemical vapour deposition (PECVD) is a more specified deposition techniques. In a PVD process, atoms are extracted physically from a solid target. The addition of a reactive gas component characterises this process as reactive sputtering [20]. Deposition of aluminium oxide was realised by sputtering aluminium atoms from a solid target and by adding oxygen to the deposition chamber aluminium oxide was formed. 9

10 2 Magnetron Plasmas Sputter process Using plasma for thin film deposition, one has to remind oneself that a plasma consists of charged particles, such as electrons and ions, and of neutral particles. The term «plasma» was established by Irving Langmuir in 1927 [21]. Within further studies, Langmuir worked on the description of plasma discharges, which made him one of the famous people from the plasma research field. Specifically, a plasma is a quasineutral, ionised gas which shows collective behaviour. In case of a depositing plasma, ignited within a capacitively set-up, the ionisation degree of the gas is lower than 1%. Therefore, the majority of atoms stays uncharged within the plasma. In order to obtain higher ionisation degrees of the gas atoms, the power applied to the plasma system has to be increased. This is reached within a HPPMS (High Power Pulsed Magnetron Sputtering) plasma, for example, where a nearly fully ionised plasma is generated by applying pulses with peak voltages of several kv to the system [22]. The basic principle of the PVD deposition within this thesis is the sputter process. During a sputter process, ions from the plasma are accelerated to a so-called «target» by an electrical field. Collisions of the ions from the plasma with the target surface result in extractions (sputtering) of target atoms. The sputtered atoms are, then, transported to the substrate. By increasing either the ion flux or the energy of the ions, the sputter process can be enhanced. This leads to a higher flux of target atoms to the substrate electrode. The acceleration of ions from the plasma to the target takes place within the plasma sheath. The kinetic energy of a charged particle within an electric field is directly proportional to the distance and the electric field strength. One has to provide long mean free paths (long distances) of the ions within the plasma sheath and a high electric field strength to ensure optimal sputter conditions. Long mean free paths can be realised by pressures below 1 Pa inside the reaction chamber. In contrast, high pressures would mean short mean free paths, under which the sputter yield would decrease. A maximum in electric field strength is also demanded, which is defined by the voltage drop within the plasma sheath. Both conditions are required in order to guarantee optimal high kinetic energies of the ions when colliding with the target. 10

11 2.1 Theoretical description of the deposition process After extraction from the target surface, the sputtered atoms are moving freely within the plasma chamber. This free movement is stopped with the adsorption at a surface. By placing a silicon wafer in the deposition chamber, the growing film can be extracted and analysed after deposition. Collision mechanism of ions with the bounded target atoms may also result in other effects, such as photon emission or secondary electron emission, and accelerated ions may be implanted at the surface of the target as well. The deposition process is not affected by these by-products, so that they are not specifically discussed at this point. Enhancement of the sputtering yield by a magnetic field configuration To enhance the sputter process, a magnetic configuration above the target is generated. A schematic illustration of such a configuration is shown in Figure 2.1, where the magnetic components are indicated. One can observe a circular configuration of cylindrical magnets at an outer circle and one centre magnet. The magnetic field is symmetrically pointing from the centre to the outer parts of the target. Figure 2.1: Enhancing the sputter rate by using a magnetron set-up, copied and modified from [23]. Magnetic configuration within the experimental set-up was measured by a Hall probe. Hall probe measurements have shown that the inner magnetic field density is 60% higher than the outer magnets, which indicates an unbalanced magnetron. A detailed analysis of the magnetic field configuration are shown in a previous work [24]. According to Window et al. [25], this magnetic configuration refers to a magnetic configuration from type I. The additional magnetic field results in an attraction of free electrons in the environment of the target. The electrons are forced onto circle like paths, so-called 11

12 2 Magnetron Plasmas gyration paths, which lead to a high density of electrons within the magnetic field region. With the higher density of electrons, more ionisation processes of gas atoms take place and more ions from the plasma are accelerated to the target and drive the sputter process. In short, the magnetic field is used to raise the electron density in front of the target. These electrons enhance the ion density in front of the target which leads to a higher sputter rate of target atoms. The magnetic field enforces charged particles onto gyration paths, which are defined by the Larmor radius. Small Larmor radii of electrons are required due to the ionisation processes within the plasma sheath. The Larmor radius should be lower than the plasma sheath thickness, so the electrons are considered to be magnetised. Within the plasma sheath, ions are accelerated to the target. Magnetisation of ions would lead to a decrease of the sputter yield because of a deviation in movement to the target surface. Therefore, the Larmor radius for ions needs to be larger than the plasma sheath thickness. This is equivalent to the description that the ions are not magnetised within the plasma. In the following, the effect of the magnetic field configuration on the two kinds of charged particles is evaluated. The calculation of the Larmor radius for electrons and argon ions can be determined for the given plasma parameter and magnetic field strength. In general, the Larmor radius is given by r L = m v q B (2.1) The gyration radius for electrons and ions is calculated in order to determine the species driving the sputter mechanism. First, electrons entering the plasma sheath are assumed to have a temperature of T e = 4 ev, measured by a Langmuir probe (see section 2.1.2, page 18). Also high energetic electrons may be accelerated over the plasma sheath by the cathode voltage of 300 V (extrapolated from Semmler et al. [26]). The magnetic field strength has its maximum with B= 180 mt directly below the target and a magnetic field strength of B= 85 mt in a distance of 1 cm to the target. The calculated Larmor radii are shown in Table 2.1 (a). Second, the Larmor radii for low energetic ions and high energetic ions for the given magnetic field strengths of B= 180 mt and B= 85 mt are calculated. Low energetic ions are assumed to have a thermal energy of T i = ev, while high 12

13 2.1 Theoretical description of the deposition process energetic ions are accelerated by the voltage drop over the plasma sheath resulting in T i = 70 V. The Larmor radii for ions are shown in Table 2.1 (b). (a) bbbbbbi Electrons B [mt] T e [ev] r L,e [mm] (b)bbbbbbbb Ions B [mt] T i [ev] r L,i [mm] Table 2.1: Larmor radii for electrons (a) and ions (b) with different ion energies are shown. The magnetic field strength is assumed as the maximum magnetic field strength of 180 mt directly below the target or as the magnetic field strength of 85 mt in 1cm distance to the target. In order to determine the magnetisation of the regarded particles, the sheath thickness of the plasma sheath has to be determined. According to Liebermann et al. [27], the sheath thickness for a collisionless sheath is given as s = ( λ 2eV 0 Debye kt e ) 3 4 (2.2) ( ɛ Using a Debye length of λ Debye = 62 µm λ Debye = 0 k B T e e 2 n e ), a plasma sheath thickness of s = 1.70 mm is calculated. Assuming that charged particles are affected by the magnetic field within the plasma sheath and participate within the sputter process, the plasma sheath thickness is the comparing parameter to determine the magnetisation within the plasma. Comparing the plasma sheath thickness with the calculated Larmor radii, one obtains that electrons with any kinetic energy have Larmor radii smaller than the plasma sheath thickness, see Table 2.1 (a). Therefore, one can conclude that electrons are the magnetised species within the plasma and promote the sputter process. Although low energetic ions are characteristic as magnetised, their kinetic energies are too small in order to extract atoms from the target surface anyway. High energetic ions are not affected by the magnetic field, which means that the sputtering process through ions is untouched by the magnetic field (Table 2.1 (b)). 13

14 2 Magnetron Plasmas Enhancement of the sputtering yield by an optimised powering of the plasma Further, enhancement of the sputter rate is realised by an increase of the electric field strength, which leads to higher ion energies. Under an ohmic heating of the plasma, the coupled power is related to the applied signals as following: P ohmic ω 2 V rf (2.3) Using frequency of 71 MHz, a high plasma density through the excitation of electrons is supported. This higher plasma density leads to a higher production of more ions in front of the target. A low frequency of MHz adjusts the bias potential at the target and thereby the energy of the sputtering ions by a large voltage drop, through which more energy is transferred to the ions. Both frequencies supply the target electrode via two matchboxes. The sputtering of target atoms is enhanced because of a higher energy impact to the target atoms through collisions. This results in a greater amount of sputtered target atoms. All in all, a combination of a higher ion density in front of the target plus higher ion energies are used to obtain a maximum sputter yield Target poisoning Formation of aluminium oxide is realised by the addition of oxygen to the sputter chamber when using a pure aluminium target. However, the addition of a reactive gas to the deposition chamber, forming, for example, metal-oxide or metal-nitride, gives a challenge to the control of the deposition process. A chemical reaction of the additional gas with the metal atoms on the substrate is required, but the same reaction takes also place at the target. A decrease in sputter rate and change in composition of the deposited film are the results of the addition of any reactive gas to the deposition process [28]. Thus, the behaviour of the aluminium deposition to the addition of oxygen to the deposition process will be discussed representatively. Besides the formation of aluminium oxide at the substrate, a chemical reaction of the oxygen atoms with the target atoms is observed. A thin layer of aluminium oxide is generated at the target surface. Having a thin oxide layer at the target surface, 14

15 2.1 Theoretical description of the deposition process the sputtering mechanism of the plasma ions at the target is redirected to the extraction of oxygen atoms from the target. The oxygen atoms forming a metal-oxygen compound at the target surface constrain the sputtering of metal atoms and powering of the plasma is redirected to the sputtering of the oxygen from the aluminium target. The sputter rate decreases with increasing oxygen partial pressure within the deposition chamber. More and more oxygen atoms cover the aluminium target, which has to be relieved from the oxygen layer on top within the sputter process. Under a continuous increase in oxygen flow to the chamber, an overfill of reactive gas atoms at the target is reached at some point, where the deposition rate is minimised and no sputter process is detected. This process is called target poisoning. A decrease in oxygen partial pressure could increase the sputter rate again. After the complete removal of the oxygen atoms from the target, a sputtering of metal atoms is possible again. Formation of a desired film stoichiometry may be located in the intermediate regime between the target poisoning modus and the metallic sputtering. Hysteresis effect The addition of a small oxygen flow to the deposition chamber forms a certain stoichiometric film at the substrate and decreases the sputter rate slightly. At a certain amount of oxygen within the deposition chamber, the sputter rate hardly drops to zero because of a full covering of the oxygen atoms on the target surface. Intuitively, one may think that the sputter rate increases immediately after decreasing the oxygen flow below the critical value at which the sputter rate dropped to zero. This behaviour is not observed, instead a hysteresis effect can be found. By decreasing the oxygen flow below the critical value where no sputter rate was observed any more, the complete removal of the oxygen atoms takes a long time. Of course, sputter rate could be increased again by waiting for several hours until all oxygen atoms at the target surface are removed, which would result in an increase in the sputter rate of metal atoms, but taking some seconds as response time, the sputter rate only increases if the reactive gas species is decreased below another critical value. In this case, the ratio of the reactive gas component within the deposition chamber is small enough that the oxygen is vanished from the target and the sputtering process of metal atoms is provided again. 15

16 2 Magnetron Plasmas D e p o s itio n R a te [n m /s ] IV III O 2 I F lo w [s c c m ] II Figure 2.2: Hysteresis of the sputter rate in aluminium through the addition of oxygen to the plasma process, copied and modified from a previous work [24]. The above described effect can be observed by different measurement methods, such as quartz microbalance measuring the growth rate, see Figure 2.2 (showing results from a previous work [24]). The figure represents the sputter rate depending on the oxygen flow to the chamber. The sputter conditions were similar to the deposition conditions for the film growth of aluminium oxide, which will be described in the following section 4.1, page 45. Within the figure, one can see that the sputter rate is slightly decreasing with an increase in oxygen flow, region I (filled squares). At an oxygen flow of 1.7 sccm, the sputter rate abruptly goes to zero (region II), which is the point where almost no sputtering is possible any more. A decrease in oxygen flow down to 0.3 sccm is necessary in region III (open triangles) to increase the sputter rate to the previous value of approximately 0.9 nms 1 (region IV). Within a previous work [24], pressure and power variations were realised while observing the sputter rate using a quartz microbalance. The sputter rate had a maximum under the used parameters without any addition of oxygen of 0.9 nms 1. Addition of oxygen (to around 20% of the maximum aluminium intensity) decreases the sputter rate to approximately 0.02 nms 1. This value is not constant for all sputter conditions because also the biasing signals applied to the substrate electrode influences the sputter rate by effects such as resputtering of the film atoms through high energetic ions. 16

17 2.2 Plasma characteristic numbers The described hysteresis effect is well-known and illustrated within the Berg model [29]. It can also be observed in the self-biasing voltage of the target electrode, within mass spectrometry when measuring the oxygen and aluminium concentrations and within the optical emission line of aluminium. Avoiding hysteresis effect by a feedback loop The above described hysteresis curve can be divided into two regions. We can distinguish between the high sputter rate regime, which is called metallic mode, and the low sputter rate regime, which is called poisoned mode. The desired stoichiometry and deposition conditions may be located in between both modes, which is represented by an unstable transition region. A feedback loop regulating the oxygen flow to the chamber is required. With this feedback loop, any point in between both modes can be achieved. Basically the feedback loop consists of a measurable value which represents the amount of oxygen within the sputter process. The aluminium (Al I) emission line at 396 nm represents the hysteresis behaviour of the sputter target. A detail description of the set-up and application can be found in the experimental set-up part, chapter 4.1.1, page 48. The most challenging task is the response time of the feedback loop system on changes in the sputter conditions. The sputter system used for this experimental approach showed response times of tens of µs, which had to be undercut by the feedback loop. 2.2 Plasma characteristic numbers Characterisation of the plasma by probes or analysers is presented in the next section. The plasma background provides the system with a given number of aluminium atoms, sputtered from the target. Electron density is a well-known parameter to quantitatively evaluate the plasma and, therefore, defines the sputter conditions through the amount of ionising noble gas atoms. 17

18 2 Magnetron Plasmas Electron density Measurements of the electron density under deposition conditions, were performed with a Plasma Absorption Probe (PAP) invented by Scharwitz et al. [30]. The working principle of the PAP is an antenna covered by a glas tube, producing rf signals with variable frequency. Measurement of the power reflection spectrum shows characteristic resonance from which the electron density can be determined [30]. In general, the electron density is proportional to the square of the resonance frequency. The tip of the probe was mounted at 23 mm distance to the target, which is the middle between the two electrodes. The radial distribution of the plasma density can be seen in Figure 2.3. A maximum electron density is observed in the middle of the target and decreases to the sides. However, a bimodal electron density distribution due to the impact of the magnetic field is not expected because the distance between the tip of the probe and the target surface exceeds the range of influence of the magnetic field. On the symmetry axes of the target, an electron density of n e = m 3 was determined. Measurements of the electron density for this position were performed three times, the average of this values results in the mentioned value n e. A drop in the plasma density to the outer part of the target is observed. Regardless of this drop, a constant electron density of n e = m 3 is assumed, although measurement with the PAP also at the outer parts (measured distance d measure = 120 mm, while the target aperture was d target = 140 mm) of the plasma were performed. Absolute errors within the PAP measurements are around 50%. The radial distribution fits very well to the averaged value for the electron density. Because the sample was aligned to the centre of the target, the given value of n e = m 3 is assumed. Further parameters The electron temperature was determined by Semmler et al. [26], using a Langmuir probe. An extrapolation of their data under slightly different conditions, reveals an electron temperature of T e = 4 ev for the used parameter. The plasma potential was determined to Φ plasma = 18 ev and the floating potential to Φ float = 4 ev [31]. 18

19 2.3 Tailoring the energy distribution function ] -3 P la s m a D e n s ity n e [ m S a m p le p o s itio n / 0.5 C e n tre o f ta rg e t P o s itio n [m m ] Figure 2.3: The plasma density was measured in 23 mm distance to the target at different positions. The plasma was driven under deposition parameters, but with a high oxygen flow avoiding deposition of the probe tip. 2.3 Tailoring the energy distribution function The energy impact to the film surface can be tailored by the energy distribution function of the incoming ions. By tailoring the ion energy distribution function of a constant ion flux to the substrate surface, the energy impact to the substrate surface is modified. The mean energy per deposited atom < E > is defined by this process. The first subsection deals with the measurement of the total ion flux to the substrate. Measurements of the ion flux by a retarding field analyser are described in this subsection as well as the calculation of the ion velocity distribution function. In the second subsection the tailoring of the ion energy distribution function by a rectangular and triangular biasing signal is explained Ion fluxes Ion fluxes to the substrate were measured using a retarding field analyser (RFA). The RFA was mounted on the substrate electrode at the same position as the silicon substrate when depositing thin films. Therefore, the exact ion flux to the substrate surface during the deposition process can be determined. 19

20 2 Magnetron Plasmas A detailed description of the RFA is given by Baloniak et al. [32, 33, 34]. The used retarding field analyser consists of four grids (each grid has a diameter of 0.5 ) and a collector plate measuring an ion current. Ions are guided through the grids and measured at the collector, which attracts positively charged particles. The resulting collector current is directly proportional to the amount of ions reaching the substrate electrode. The incoming ions are discriminated as a function of their energies by biasing the grid in front of the collector. Collisions of ions within the plasma sheath and inside the RFA have to be evaluated because these collisions deform the ion energy distribution. In this case, a broadening of the ion energy distribution function may be observed, but under deposition conditions a narrow ion energy distribution function is required. Collisions within the RFA are more obstructive because the measured ion energy at the collector would have changed through the collisions. One has to distinguish between three different kinds of collisions: neutral particles colliding with neutral particles, neutral particle and ion collision, and ion-ion collisions. The neutral particle density has the highest value within the plasma. Regardless this fact, ions are not created through this collision process, so it is negligible for the evaluation of variations in the ion energy. The collision probability of ions with ions is low enough at this working conditions, so this collision process is negligible as well. Therefore, the only interesting process which has to be considered, is the collision between ions and neutral particles. The worst result of such a collision is the charge transfer from a fast ion to a slow neutral particle, which would, then, be detected at the collector. In general the expression of the mean free path is given by: λ i = k BT g. (2.4) 2pσ In case of the argon plasma, a gas temperature of T g = 300 K, a pressure of p = 0.1 Pa, and a cross section of σ = cm 2 [27] are given, which result in a mean free path of λ = 4.14 cm. This path is longer than the plasma sheath ( s = cm) and the dimension of the retarding field analyser (L = 0.24 cm). Assuming that, statistically, argon neutrals will not collide with ions in the plasma sheath or in the RFA, the error of the RFA measurement is considerably reduced. 20

21 2.3 Tailoring the energy distribution function The given plasma conditions reveal that the mean free path is long enough to satisfy the Bohm criterion. The Bohm criterion is based on Maxwellian distributed electrons at a certain temperature T e within the plasma. Only cold ions are assumed, and the ion and electron densities are equal at the surface of the electrodes. If both, an ion energy conservation and continuity of the ion flux are assumed, the ion flux to the substrate is given by the Bohm flux. The relation to calculate the ion flux can be written by the ion density n 0 and Bohm velocity v B Γ ions = n 0 v B = n 0 kb T e M i. (2.5) Calculation of the Bohm flux from equation 2.5 assumes a floating wall, for which the RFA is operated under floating grids and the ion current to the collector is measured. The Bohm flux Γ i to the electrode for a RFA measurement is defined by the ion current I i and the size of the aperture A B : Γ ions = I i A B e. (2.6) Here, I i is the ion current measured by the RFA. A B is the size of the aperture (here A B = 7.04 mm 2 ) and e the elementary charge. The unknown variable within equation 2.6 is the ion current I i, which has to be determined separately. By operating the RFA without any bias at the energy filtering grid, the incoming ion current can be used to calculate the complete ion flux to the substrate. The total ion flux to the substrate is needed for the calculation of the mean energy per incorporated atom when using the depositing set-up with different biasing waveforms and frequencies. The advantage of this measurement method is the independence from the ion species reaching the collector, which is not that critical in this case because emission spectroscopic measurements have shown that the only ionised species within the plasma is argon. Nevertheless, a direct measurement of the ion current at the collector I c does not reveal the total ion flux, which is obtained at the surface of the silicon substrate during the deposition process. Because ions have already passed four grids when reaching the collector, a loss of ions at the grid as well as a loss because of collisions 21

22 2 Magnetron Plasmas is possible. A correction of the measured ion current is necessary, which is given by I i = I c P g P c. (2.7) Equation 2.7 indicates that the ion current I i is reduced by the geometrical transparency P g and the collisional transparency P c. The collisional transparency only depends on the mean free path of the ions, namely P c = exp( L/λ i ) = 0.94 with L = 0.24 cm as the effective distance of the ions within the RFA. This shows that the influence of collisions within the RFA is more or less negligible. Geometric transparency is determined by the collector current and the current at the electrode, which results in an expression for the geometrical transparency of P g = A E P 0 A B P c A B Ic I E, (2.8) where I E is the electrode current, A E the electrode surface, and P 0 the ideal geometric transparency with P 0 = Due to reasons of precision during the installation of the grids of the retarding field analyser, the grids are not absolutely parallel. Therefore, by measuring a collector current I c = 1370 na with the current at the substrate electrode (d electrode = 140 mm) being I E = ma, the determination of the desired relation I c /I E is possible in order to solve equation 2.8. A geometrical transparency for this RFA of P g = is determined. Inserting this values into equation 2.7, an ion current of I i = I c is resolved. The collector current I i is determined within the measurements as I i = µa, which results in a Bohm flux of Γ ions = m 2 s Determination and tailoring of the ion energy distribution Until now, the plasma background providing a constant ion and neutral flux to the substrate electrode was described. Now, the modulation of the ion energy distribution function tailored by the biasing signal at the substrate electrode will be described. 22

23 2.3 Tailoring the energy distribution function In literature, one can find different terms to the very same situation when dealing with the ion velocity distribution (IVD) and ion energy distribution (IED), respectively. An explanation of both terms is necessary at this point in order to make the differences and similarities of both functions clear. The ion velocity distribution is mathematically described as [35]: Γ i = 0 v f(v) dv. (2.9) The IVD is easily connected to the ion flux and provided by RFA measurements. Connection with the ion energy is given by M i v dv = de. Because the velocity within the distribution of f(v) is connected to the energy, it can be converted to a energy depending distribution f(e), which results in: Γ i M i = 0 f(e) de (2.10) The ion velocity distribution is the convolution of the ion energy over the ion velocity. In contrast, an ion energy distribution function represents the ion energy convoluted by the ion energy. Measurements and simulations of the distribution function within the plasma sheath will be represented by the ion velocity distribution in this work. Because the effect of the ion energy on the film surface is required, the ion energy distribution (IED) at this point is the most common phrase describing the effect of the substrate biasing to the film. The valuable difference of both distribution functions is the normalisation of these functions. It is necessary to emphasise that the calculation of the mean ion energy per deposited atom < E >, which is necessary for the evaluation of the ion impact, is equal for both distribution functions. Calculation of the mean energy per incorporated atom < E > is independent from the y-axes of the distribution function which reflects the flux of ions with different velocities or energies, respectively. The applied waveforms at the substrate electrode can be chosen arbitrarily, which can be distinguished by the waveform of the signal (sinusoidal, rectangular...), the amplitude (U max ), and the frequency (f). By changing one of these parameters, almost any shape of the IED can be achieved. The obtained waveforms within this 23

24 2 Magnetron Plasmas work are reduced to two different types of waveforms. First, a rectangular biasing signal was applied during the measurements. This leads to an ion energy distribution only containing two different peaks at different energy values. Further, a triangular biasing signal was applied, which leads to a constant ion flux to the surface over a large interval of different ion energies (constant ion flux of ions with different ion energies between 18 ev and 80 ev, for example). Tailoring of the IEDF by rectangular biasing signals The most simple way to perform defined changes within the ion energy distribution is a rectangular biasing signal. The resulting ion energy distribution function is a bimodal distribution, including one low energetic peak and one high energetic peak. It is possible to change separately the frequency f and the maximum voltage U max of the signal in order to vary the position of the two peaks or to change the ion fluxes. By varying U max, the ratio between the high energetic and low energetic peak is modified. By determining the type of waveform, one more boundary condition can be already isolated for the applied biasing signals. The signal is divided into an on- and offtime (τ on, τ off ), respectively, see Figure 2.4. The on-time τ on is set constantly for all biasing signals (τ on = 500 ns), which includes a variation in on- and off-time when changing the frequency. Figure 2.4 shows an ideal biasing signal of a frequency of f = 1 MHz (continuous line), which can be easily identified by a period duration of 1 µs of the signal. In general, the biasing frequency is varied between 0.80 MHz and 1.60 MHz because within this frequency interval, the ions can still follow the modulation of the sheath voltage so that ions entering the sheath experience the full potential drop between sheath edge and surface. The bias signal at the substrate electrode is recorded by a VI probe in the rf-feed line. By a variation of the frequency f to other values, the off-time τ off has to be aligned in order to maintain the boundary conditions (constant value of τ on = 500 ns, randomly chosen). The maximum voltage U max is modified so that the energy of the maximum energy of the ions impinging the substrate is tailored to the desired value. 24

25 Electrode Voltage [V] 2.3 Tailoring the energy distribution function off Biasing Signal Plasma - float Plasma Plasma -U max Time [µs] Figure 2.4: Biasing scheme for a 1 MHz signal (continuous) and the ideal response of the plasma sheath Φ P lasma (dashed). Indicated are the on- and off-time τ on and τ off, as well as the difference between shifted plasma potential Φ P lasma Φ float and Φ P lasma U max. on The biasing signal does not only influence the energy of the ions, but also the plasma potential in front of the substrate electrode. The ion energy is modified by applying a negative voltage to the substrate electrode, which does not influence the plasma potential. However, by applying a positive voltage to the substrate electrode, the plasma potential is also pushed upwards (see Figure 2.4, dashed curve). Therefore, a distinction between two cases has to be performed: (i) if the voltage becomes too positive, it pushes the plasma potential even higher. In this case, the voltage drop remains constant and it corresponds to only the difference between plasma potential and floating potential, yielding a constant voltage drop of 14 V (Φ P lasma = 18 V; Φ float = 4 V); (ii) if the bias voltage is lower than the plasma potential, the sheath voltage corresponds to the difference between the bias voltage measured by the VI probe and the plasma potential (Φ plasma U max ). The resulting plasma sheath voltage is shown in Figure 2.5. The ions are accelerated by the shown voltage scheme, which is aligned to the ground of the lab. The above described behaviour of the plasma sheath to the applied biasing signal is the key parameter which defines the IEDF. By applying any biasing signal, the plasma sheath is deformed in the way indicated above, which leads to an acceleration of the ions through the plasma sheath according to its shape. 25

26 Sheath Voltage [V] 2 Magnetron Plasmas Plasma - float Plasma -U max Time [µs] Figure 2.5: The calculated plasma sheath is tailored by the biasing signal, which is shown in Figure 2.4. During one period, ions are accelerated by two different voltages to the substrate: during the low energetic phase, ions are accelerated with 14 ev and during the high energetic phase by -118 ev, in this case. The time ratio between both phases determines the energies of high and low energetic ions at the substrate. E le c tro d e V o lta g e [V ] 6 0 A d ju s te d S ig n a l A p p lie d S ig n a l T im e [µ s ] Figure 2.6: Resulting (continuous) and applied (dotted) biasing signal measured at the substrate electrode at 1.01 MHz. A p p lie d S ig n a l [V ] Until now, calculation of the mean energy of an ideal biasing signal at the substrate electrode was described. The «real» biasing signal adjusted at the substrate electrode is shown in Figure 2.6 (continuous line). The signal itself is measured using a VI probe and displaced by an oscilloscope. The generated signal applied to the substrate electrode by the waveform generator (amplified by a broadband amplifier) is shown as dotted curve in Figure 2.6. Comparing the ideal biasing signal with the measured signal, one observes a deformation of the biasing signal, please compose Figure 2.4 and Figure 2.6. It is not possible to divide the biasing signal into a constant positive phase and a constant defined negative phase for the real biasing situation like it was done with the ideal biasing signal (Figure 2.4). 26

27 2.3 Tailoring the energy distribution function Because of the capacity of the cable connected to the substrate electrode and because plasma behaves as a capacitor, the biasing signal is not adjusted 1:1 to the electrode voltage. Especially fast changes in voltage deform the biasing signal. Ions which are located directly in front of the substrate electrode, are not rapid enough to follow the very fast change in voltage immediately after applying the steep edge to the system. The response time is approximately 0.1 µs. Thus, a deformation of the falling edge of the biasing signal is detected. A noise is overlaid to the constant positive phase of the biasing signal. This effect is already visible in the applied signal. A direct comparison of the plasma sheath of a rectangular biasing signal with a frequency of 1.01 MHz and the resulting IVDF can be found in Figure 2.7. In Figure 2.7 (a), the plasma sheath calculated from the applied biasing signal is shown. The signal can be divided into the off- (L, left part) and on-time (H, right part) of the biasing signal. Within the left part, only low energetic ions are accelerated by the biasing signal, which leads to a low energetic peak (L) in the IVDF, see Figure 2.7 (b). The higher energetic peak within the IVDF is produced during the on-time of the biasing signal (H) in Figure 2.7 (b). The low energetic peak (L) of the IVDF in Figure 2.7 (b) is a very defined peak with a small width. In contrast, the high energetic part of the IVDF (H) is much more broadened. The reason for the broadening of the high energetic peak is the absence of a steep falling edge of the biasing signal, shown in Figure 2.7 (a). An ideal rectangular biasing consists of a vertically falling edge, representing the δ function. When applying the signal to the substrate electrode, the falling edge, connecting the low voltage phase with the high voltage phase, is not reached instantaneously. A finite time is necessary until the maximum voltage U max is applied to the system. Therefore, during this short time, ions are neither accelerated by the low voltage nor by the high voltage U max, but with some voltages in-between. Observing the rectangular biasing signal within Figure 2.7 (a), one has the possibility to modify the ion velocity distribution function in amplitude and frequency. Because the on-time within this set-up is kept constant to τ on = 500 ns, a defined off-time when changing the frequency is given. A more detailed description of the above mentioned tuning knobs the IVDFs should be discussed at this point. 27

28 2 Magnetron Plasmas E le c tro d e V o lta g e [V ] L U m a x H (a ) T im e [µ s ] Io n E n e rg y [e V ] L H (b ) Io n F lu x [ e V -1 m -2 s -1 ] Figure 2.7: Rectangular biasing signal at 1.01 MHz (a) and resulting ion velocity distribution (b). The lower energetic region (L) within the biasing signal results in the low energetic peak within the IVDF. The high energetic region (H) of the biasing signal is connected to the high energetic peak (H) of the IVDF. The results of the variation of frequency and maximum negative voltage of the biasing signal on the IEDF are shown in Figure 2.8 (a) and 2.8 (b). By changing the frequency of the biasing signal, the off-time of the biasing signal is varied because of the fixed on-time of the signal. This variation is indicated by the horizontal arrow in Figure 2.8 (a). The ratio of high and low energetic ions will be defined by the change of frequency (see vertical arrows in Figure 2.8 (b)). A higher frequency within the biasing signal results in a relatively long on-time compared to the offtime. Therefore, the high energetic peak within the IEDF raises. However, the total amount of ions stays always the same, namely Γ ions = m 2 s 1. The high energetic ions are accelerated by the voltage drop between plasma potential and biasing voltage. By changing the voltage U max of the biasing signal, the high energetic peak within the IEDF is shifted on the ion energy scale (vertical arrows in Figure 2.8 (a) and (b)). Instead, keeping the frequency constant and changing the maximum value of the biasing signal, the position of the high energetic peak will be defined (horizontal arrow in Figure 2.8 (b)). With this tuning knobs, any bimodal ion velocity distribution can be applied to the substrate electrode and evolution of film crystallinity can be analysed with different biasing schemes. Measurements of the resulting ion velocity distribution function with different biasing signals were performed. However, the RFA measurements are limited to a small range of power. This is due to the fact, that with the biasing signal an rf signal is coupled to the electronic of the measurement unit, which distorts the measured 28

29 2.3 Tailoring the energy distribution function E le c tro d e V o lta g e [V ] (a ) V m a x T im e [µ s ] f s -1 ] -2 Io n F lu x [ e V -1 m (b ) f V m a x Io n E n e rg y [e V ] f Figure 2.8: Rectangular biasing signal (a) with adjustable parameters. Figure (b) shows an example of a 1.01 MHz IEDF simulated by M. Shihab. Possible variations in peak height and peak position within the IEDF are shown. signal. Only RFA measurements with low power in order to calibrate simulations can be realised. No further measurements are shown because they would not represent the measurement range. Simulations were realised at the Institute for Theoretical Electrical Engineering at the Ruhr-Universität Bochum and compared with the measured distribution functions. Very good agreement to the measurements were shown by Shihab et al. Simulations were carried out using an EST (ensemble-in-spacetime) code, which is a fast and accurate at the same time, see Shihab et al. [36]. IVDFs result from the data of one period of the biasing signal, saved from the oscilloscope. Integration of the IVDFs reflect the value of the total ion flux to the substrate. The IEDF for rectangular biasing signals using various biasing frequencies is given in Figure 2.9. From left to right, Figure 2.9 (a) to (e), the frequency is raised from 0.80 MHz to 1.6 MHz in 0.20 MHz steps. The mean energy within these IEDFs is the same for all cases, namely approximately 13 ev. 29

30 2 Magnetron Plasmas s -1 ] (a ) M H z (b ) 4 0 % d u ty -c y c le M H z 5 0 % d u ty -c y c le (c ) M H z 6 0 % d u ty -c y c le (d ) M H z 7 0 % d u ty -c y c le (e ) M H z 8 0 % d u ty -c y c le s -1 ] -2 Io n F lu x [ e V -1 m Io n F lu x [ e V -1 m Io n E n e rg y [e V ] Io n E n e rg y [e V ] Io n E n e rg y [e V ] Io n E n e rg y [e V ] Io n E n e rg y [e V ] Figure 2.9: Ion velocity distributions for all used frequencies. From left to right (from (a) to (e)), frequencies between 0.80 MHz and 1.60 MHz are applied. One can clearly see that with low frequencies, the low energetic peak at 18 ev is more dominant than for high frequencies, except for a biasing frequency of 0.80 MHz. This exception is created because of the transition time between on phase and off phase of the biasing signal. In general, with low biasing frequencies, the off-time τ off of the biasing signal is longer than for frequencies. In order to achieve the same mean energy per deposited atom < E > for all biasing situations, the higher energetic peak has to be shifted to higher values on the x-axes by a lower maximum negative voltage U max. This can be also seen within the different IEDFs, shown in Figure 2.9 (a) to (e). The situation of 1.20 MHz, Figure 2.9 (c), already shows a smoother low energetic peak than the high energetic peak, while the low energetic peak for 1.01 MHz has more or less the same amount of low and high energetic ions, see Figure 2.9 (b). The ratio does not fit perfectly because the biasing signal itself has no clear falling edge, which is the reason that ions with energies between the low and high energetic part are detected. However, there is still one confinement due to the ion behaviour to the applied biasing signal within the off-phase of the signal. The ion transit time through the sheath is relatively low compared to the rf signal. In a positive phase of the biasing signal, the ion s inertia will prevent the ions from complete modulation with the instantaneous field. These ions will only see the plasma potential or the drop between plasma potential and ground, respectively. Therefore, the minimum ion energy is higher than the minimum sheath potential, which could be explained as ion inertial effects. 30

31 2.3 Tailoring the energy distribution function For the calculations of the mean energy per deposited atom < E > within this thesis, a peak of the low energetic ions was set to 14 ev and not to 18 ev, which is represented by the low energetic peak within the calculated IEDF. The calculation of the mean energy per deposited atom < E > from the oscilloscope data described in section 2.4.2, page 36 were done with a low ion energy of 14 ev. The validation for both cases with which energy ions during the off phase of the biasing signal are accelerated to the substrate electrode is still unclear. No measurements were applicable to our deposition system to justify one of these theories. Both methods show similar results, that one could neglect this fact. The resulting error for the correct determination of the mean energy per incorporated atom depends on the frequency of the applied signal. For biasing signals of 0.80 MHz, an error of 4% occurs, while for 1.6 MHz, only an error of 0.5% is calculated. Triangular biasing signal Further, triangular biasing signals were applied to the substrate electrode. The shape of the ion velocity distribution differs from the previous IVDFs, so that the impact to the crystal evolution of the aluminium oxide films can be observed. M e a s u re d V o lta g e D is trib u tio n Id e a l V o lta g e D is trib u tio n E le c tro d e V o lta g e [V ] T im e [µ s ] Figure 2.10: Triangular biasing signal, measured at the substrate electrode (continuous) and the ideal biasing signal (dashed). By using this type of waveform, the measured and the applied signal at the substrate electrode also differ from each other. In Figure 2.10, the ideal and the measured bi- 31

32 2 Magnetron Plasmas asing signal are compared. The continuous curve represents the measured signal at a frequency of 1.20 MHz, whereas the dashed curve indicates the ideal biasing signal at the same frequency. Within the positive phase of the biasing signal in Figure 2.10, the deformation due to the positive plasma potential is observed. The measured signal shows a compression in this region. The sharp edge at the maximum negative voltage of the biasing signal is deformed because the plasma sheath cannot follow the fast and abrupt change within the signal. No boundary conditions in on- and off-time of the biasing signal are applied for the triangular biasing signals. An ideal triangular biasing signal shown in Figure 2.11 would result in a homogeneous ion flux with different ion energies, which is shown in Figure 2.11, where the ion energies are normalized to the total ion flux of Γ ions = m 2 s 1. This IVDF represents an ideal situation of a constant ion flux to the substrate electrode with ion energies in an interval between 18 ev and 200 ev. Comparing the ideal situation with the expected shape of the IVDF, formation of a higher peak at 18 ev will be observed due to the necessarily positive phase within the signal. Moreover, the already mentioned deformation of the high energetic regime will also result in a deformation of the real IVDF at higher ion energies s -1 ] -2 Io n F lu x [ e V -1 m Io n E n e rg y [e V ] Figure 2.11: Ideal IVDF of a triangular biasing signal, normalized to the total ion flux. Figure 2.12 (a) to (c) represent simulations of three different triangular biasing signals. The left Figure, 2.12 (a), shows an IVDF produced by a 0.80 MHz signal with a maximum negative voltage of U max = -180 V. Figure 2.12 (b) shows a 1.20 MHz signal with U max = -200 V and Figure 2.12 (c) indicates the situation for 1.60 MHz with U max = -150 V. 32

33 2.4 Mean energy per deposited atom All shown IVDFs differ clearly from the before mentioned ideal situation for an ideal triangular biasing signal in Figure Beside a high energetic peak, also a low energetic peak is observed. It has to be emphasised that in contrast to a rectangular biasing signal, the IVDF of a triangular biasing signal implies ion energies between to the two peaks. For the rectangular biasing signals, less ions within this region could be found. The advantage of this biasing signal is a mixture of ions reaching the substrate with different ion energies and the effect of these three selected IVDFs applied to the substrate electrode during the deposition process was checked (a ) M H z, U m a x = V (b ) M H z, U m a x = V (c ) M H z, U m a x = V s -1 ] s -1 ] Io n F lu x [ e V -1 m Io n F lu x [ e V -1 m Io n E n e rg y [e V ] Io n E n e rg y [e V ] Io n E n e rg y [e V ] Figure 2.12: Ion velocity distributions for triangular biasing signals with different frequencies. From left to right (from (a) to (c)), frequencies between 0.80 MHz and 1.60 MHz are applied. 2.4 Mean energy per deposited atom The most important characteristic number for the quantification of the biasing impact to the depositing system is the mean energy per deposited atom. Different ion energy distribution functions may result in the same mean energy per deposited atom, but differ in the maximum energy which is transferred to the surface atoms and in the amount of ions of a certain ion energy. Therefore, the connection between the applied biasing scheme and the resulting energy distribution will be discussed, so that the connection of the variation in IEDF on the crystal growth may be established. 33

34 2 Magnetron Plasmas Distinction between the average energy of the biasing signal E i and the mean energy per deposited atom < E > has to be emphasized at this point. Energy transfer of the ions to the growing film has to be quantified by the mass and ratio of neutral and ionised particles, which will provide the strength of the energy impact of the ions to the surface atoms. Thus, the average energy of the biasing signal has to be discussed as well as the resulting energy transferred to the ions. The first named energy, the average energy of the biasing signal E i, is only an average in voltage, which is applied to the system during one period of the biasing signal. This energy is then transferred to the film atoms through collisions of the ions, which are accelerated over the plasma sheath, with the atoms on the film surface. The value of the mean energy per incorporated atom < E > is weighted by the ratio between ions and neutrals impinging the substrate surface during one period of the biasing signal Calculation of the average energy E i of the biasing signal The calculation of the average energy of the biasing signal will be representatively realised for a rectangular biasing scheme in this subsection. The equation to calculate the average energy of the biasing signal is a general equation which can be solved for the triangular biasing situation as well as for the rectangular biasing situation. The already calculated distribution of the plasma sheath can be used for the determination of the average energy of the biasing signal. The average energy of the biasing signal is transferred to the system during one period by the applied signal at the substrate electrode, shown in Figure 2.4 on page 25, representing the identical figure as already shown for the rectangular biasing signal. Calculation of the average energy E i of a rectangular biasing signal including steep falling and rising edges results in: E i = (Φ P lasma Φ float ) τ off τ on + τ off + (Φ P lasma U max ) τ on τ on + τ off. (2.11) Equation 2.11 can be divided into two parts: the first fraction describes the influence of the positive phase of the signal, and the second fraction represents the 34

35 2.4 Mean energy per deposited atom energy input of the biasing signal for a given negative voltage with the minimum value U max. Again, the dependence of the average energy on the variables of the rectangular waveform can be illustrated: the average energy of the biasing signal E i in equation 2.11 depends on τ off and U max. The other variables in equation 2.11 (Φ P lasma, Φ float, τ on ) are already defined by the plasma and boundary conditions, respectively. Variation of U max influences the acceleration of the ions and τ off defines the ratio in flux of low and high energetic ions. Manipulation of the shape of IEDF is mainly realised by only these two parameters. In order to determine the mean energy of the biasing signal E i for a real biasing situation, the above described method can be used. Due to the fact that the calculation of the mean energy of the biasing signal E i (see equation 2.11) is based on one period, measured signals are necessarily handled identically. One has to cut one period from the whole signal of the biasing signal (a ) (b ) E le c tro d e V o lta g e [V ] P la s m a S h e a th V o lta g e [V ] T im e [µ s ] T im e [µ s ] Figure 2.13: Real situation of biasing signal (a) and resulting plasma sheath (b), calculated from the original biasing signal (a). The frequency of the biasing signal is 1.01 MHz. Calculation of the average energy of the biasing signal E i of a real biasing situation is realised using an Excel [37] sheet. Within this sheet, identification of the positive and negative phase plus calculation of the plasma sheath is realised using the following relation given by Kushner et al. [38]: [ ] Φ sheath = MIN Φ P lasma + V signal, (Φ P lasma Φ float ) (2.12) 35

36 2 Magnetron Plasmas Equation 2.12 includes any variable value of the biasing signal V signal ; the maximal negative value is still reached with U max. Using this relation, any shape of biasing signal can be dealt with. The result of the operation in equation 2.12 is shown in Figure The original signal measured by the VI probe is represented by Figure 2.13 (a) for a rectangular biasing signal. Applying equation 2.12 to the data, the plasma sheath is calculated, see Figure 2.13 (b). The average energy of the biasing signal E i is determined from the plasma sheath which is then integrated over one period of the signal and divided by the duration of one period (τ on + τ off ): E i = 1 1/f Φ sheath dt (2.13) τ on + τ off 0 This method is applied to the measured signals in order to calculate the average energy of the biasing signal E i Connection between the average energy E i and the mean energy per deposited atom < E > Calculation of the mean energy per deposited atom < E > is already possible without determination of the IEDF in an extra work step. This is due to the fact that the IEDF is already represented by the calculated plasma sheath, see section 2.3, page 28. Moreover, an extra work step, which needs some hours in calculating each IEDF from the plasma sheath, would be necessary for the calculation of the mean energy per deposited atom < E > from the IEDF. Therefore, it is practicable to work with the given plasma sheath in order to calculate the mean energy per deposited atom. First, the mean energy per deposited atom < E > is determined by the energy transfer from the ions to the film surface. The ion average energy E i (see equation 2.11) is tailored by the biasing signal. The value of the average energy E i has to be weighted by the flux of ions to the substrate surface and by the ratio of ions and neutral particles reaching the film surface. Ions are accelerated by the plasma sheath which voltage distribution is controlled by the biasing signal. When these 36

37 2.4 Mean energy per deposited atom ions reach the surface with the average energy E i, the impact to the surface depends on the ratio of ions and neutral particles of the film. In short, the mean energy per deposited atom of the film < E > consists of the average energy of the biasing signal E i, weighted by the ion flux Γ ions and the neutral flux Γ neutr. [5]. Therefore, the correlation between the average energy of the biasing signal E i and the mean energy per deposited atom < E > derives as: < E >= Γ ions Γ neutr. E i. (2.14) The very obvious relation in equation 2.14 is that with a high ion flux compared to the neutral flux impinging to the substrate, the mean energy per deposited atom < E > is always increased compared to a smaller ratio between ion flux and neutral flux. For the following calculations, the ion flux is assumed to a constant value because a constant plasma background is applied to the system. Because the ion flux Γ i to the surface is known and also the average energy of the biasing is already determined, the only unknown variable is the neutral flux to the substrate surface. The neutral flux Γ neutr. consists of all particles reaching the substrate. However, not all particles reaching the substrate may also stick to it. It is not possible to measure the value of particles which leave the surface and do not contribute to the film growth. The only reasonable assumption is that all particles detected on the surface by measuring the film thickness have also reached it and stuck to it. This assumption is necessary because otherwise the number of the growth flux would be different and with a higher growth flux, the mean energy would change. The assumption is also reasonable because a constant number of leaving atoms is estimated for all processes and the mismatching of the mean energy would mean a constant shift in neutral flux Γ neutr.. The growth flux within equation 2.14 is given by: Γ neutr. = ρ g M Al2 O 3. (2.15) Taking this equation into account, the neutral flux Γ neutr. is determined by the ratio of the growth rate g times the density of the film ρ to the mass of the film particles M Al2 O 3. According to Brandon et al. [1], film density ρ for aluminium oxide is given as ρ = kg m 3. Furthermore, the neutral flux Γ neutr. depends on the growth rate g. It is calculated for each sample from deposition time t dep and film thickness d. 37

38 2 Magnetron Plasmas Finally, the mass of aluminium oxide M Al2 O 3 has to be taken into account. XPS measurements have shown that the mean stoichiometric distribution stays constant over the samples. It is determined to a value of 60% : 40% Al:O concentration, which results in a stoichiometry of Al 2 O 3. Under consideration of this stoichiometry, an average mass for the aluminium oxide of M Al2 O 3 = kg is calculated. With the help of this values, calculation of the mean energy per deposited atom < E > from equation 2.14 for each sample can be realised. Evaluation of the value of the mean energy per deposited atom < E > is realised by rating the error for the mean energy. Because determination of the deposition time is adequate good (assuming an error of 2 s, under a deposition time of 40 min, the error would be 0.08%, for 80 min 0.04%), the only error which needs to be taken into account is the error for film thickness d. The error of the mean energy per deposited atom results in: < E >= E i Γ ions M Al2 O 3 t dep ρ d 2 d (2.16) 38

39 3 Aluminium oxide - deposition techniques and material properties Aluminium oxide (Al 2 O 3 ) is a famous material used for many applications. In this chapter, the different crystalline phases of aluminium oxide are reported on. A short description of the most important material parameters and specific details about the phase transition of this material will be presented. The following chapter closes with an overview of different deposition techniques of Al 2 O Crystalline phases Aluminium is a reactive metal which can be found within the boron group. Due to the reactive character of oxygen, formation of aluminium oxide takes place naturally when both components are brought together. Aluminium oxide has the stoichiometric formula Al 2 O 3 and is known because of its excellent dielectric properties. The incident crystal structure depends on the crystal phase of aluminium oxide. One has to distinguish between an amorphous material and different crystalline phases. The only thermodynamic stable phase is the α phase. All other phases of aluminium oxide are thermodynamically unstable. The different metastable phases of Al 2 O 3 are named γ, κ, δ, η, θ or χ. Within this thesis, the transition from amorphous Al 2 O 3 to γ-al 2 O 3 is studied. The γ phase of aluminium oxide has an fcc structure, while the α phase has an hcp structure [1]. The importance of the α phase of aluminium oxide is due to its 39

40 3 Aluminium oxide - deposition techniques and material properties hardness and can be, therefore, used in the cutting tool industry [39] and as scratch resistant layer [40]. The γ phase of aluminium oxide can be found in catalysis processes. A representative scheme of the γ phase of aluminium oxide can be found in Figure 3.1. The lattice parameter for this crystalline phase is reported as a γ 7.9 Å by Brandon et al. [1]. According to Levin and Brandon et al. [1], the transition temperature for the phase formation from boehmite to γ-alumina is between C. At temperatures of C, the transition to the δ phase occurs. Further heating to approximately 1,000 C leads to the formation of the α phase. However, in literature one can find various temperatures for the phase formation of the different phases. This is due to the fact that the formation of crystalline films depends on the mobility of the sur- Figure 3.1: fcc structure of γ-aluminium oxide, where face atoms, which is related to the deposition aluminium atoms and process defined by the particle flux to the substrate and ion energies which enhance surface oxygen atoms are each indicated. atom mobility. Using a plasma based deposition technique a tailoring of the ion fluxes to the substrate and the ion energy distribution function is possible, which enhances collision cascades within the film and results in an advanced mobility of surface atoms. The broad range of transition temperatures reflects the fact that differences in the precursors used for alumina synthesis has an impact on the transition temperature. It is known that these thermodynamic transition temperatures can be lowered by applying an additional ion bombardment. Another example for the complexity of the transition temperature is given by the work of Edlmayer et al. [6]. They reported on film deposition of Al 2 O 3 at a substrate temperature of 640 C. After the deposition process, samples were heated to 700 C, 800 C or 1,000 C for several hours. The transition to the γ phase occurred at 800 C. Musil et al. [7] worked with nanocrystalline Al 2 O 3, reporting on a transition temperature from γ to α at 1,050 C. The explanation for the appearance of different transition temperatures may be given by McHale et al. [41] and Rosén et 40

41 3.2 Material parameters of γ-aluminium oxide al. [8]. Considering the γ phase, it has a lower surface energy compared to the thermodynamic stable α phase, which stabilizes the γ phase while annealing. Musil et al. were dealing with nanocrystalline material, so the smaller grain size is able to thermodynamically stabilize the γ-aluminium oxide. It is not possible to give a specific transition temperature when dealing with the transition of different phases. Other deposition parameters such as the ion flux or the ion energy distribution function are able to influence the phase formation of Al 2 O 3 and may, therefore, serve as an excellent monitor signal for the ion-induced effects plasma deposition. The ratio of neutral particles and ions impinging to the film surface defines the effect of ion impact to the evolution crystallinity in the film. The incident ion energy distribution function defines the energy impact to the film surface. Within this work, formation of γ-alumina is investigated depending on the impact of substrate temperature and ion bombardment to the film surface. The transition temperature from amorphous to γ-crystalline aluminium oxide without any extra ion bombardment was found in the conducted experiments at 600 C substrate temperature. 3.2 Material parameters of γ-aluminium oxide Material parameters characterise the properties of the film and reveal a certain application environment. A material parameter such as film density of aluminium oxide was studied by Brandon et al. [1], given as ρ = gcm 3, which was already indicated in the previous section. The density of the deposited films was determined in this work by measuring the volume and its weight. A film density of ρ = 2.49±0.29 gcm 3 was calculated. This value strongly differs from the literature value of gcm 3 for alumina. The deviation of the density measurements is attributed to the limited accuracy of the weighing method. Because the XRD analysis of the films exhibits good quality alumina films, the film density is also assumed to agree with the literature value. Therefore, a literature value of ρ = 3.66 gcm 3 is taken for further discussion. 41

42 3 Aluminium oxide - deposition techniques and material properties Koski et al. [42] showed that the residual stress of amorphous Al 2 O 3 on silicon wafers depends on the pressure within the deposition chamber. They recognized a decrease in stress from a tensile stress of 180 MPa at a pressure of 1 Pa to a compressive stress of -250 MPa at a pressure of 0.3 Pa. Therefore, one would expect high negative values in the range of -250 MPa for amorphous aluminium oxide. 3.3 Deposition techniques Three different techniques for the deposition of aluminium oxide will be shown. Studies on the chemical vapour deposition (CVD) of α-al 2 O 3 are presented. Deposition of Al 2 O 3 with a PVD method, the filtered arc deposition, and the here used magnetron sputtering will be discussed. Chemical vapour deposition The first mentioned deposition technique is chemical vapour deposition which was already described in 1853 by Bunsen [43]. A more detailed classification was established in the 1960s by Blocher et al. [44]. The common deposition technique is the so-called hot-wall CVD deposition. By this deposition technique, a chemical reaction of a gas at a heated substrate surface takes place. An advantage of this technique is its independence of the surface profile onto which the film is deposited. Fallqvist et al. [2] report on the deposition of Al 2 O 3 on TiCN substrates using a CVD process. The substrate maintains at a temperature of 1,000 C while the gas composition AlCl 3 -H 2 -CO 2 is admitted to the deposition chamber at a pressure of Pa. The chemical reaction forming Al 2 O 3 is described as 2AlCl 3 (g) + 3CO 2 (g) + 3H 2 (g) Al 2 O 3 (s) + 3CO (g) + 6HCl (g). However, the nucleation of the α phase of Al 2 O 3 depends on the used substrate material [45], which requires an interlayer for the formation of α-al 2 O 3 in some deposition systems. In general, CVD processes of aluminium oxide are necessarily 42

43 3.3 Deposition techniques driven under high temperatures if the α phase is required. It is not possible to deposit an α-al 2 O 3 thin film by CVD onto temperature sensitive substrates. Vacuum arc deposition Deposition of α-al 2 O 3 was realised by Yamada-Takamura et al. [46] using a filtered vacuum arc. The working principle is based on the evaporation of the deposition material from a target. A voltage is applied between a metal target and the deposition chamber resulting in an arc current of approximately 100 A. Using a cathodic arc deposition system, sputtered target atoms are nearly fully ionised. Furthermore, an electromagnetic field is applied around the deposition system which increases ion energies. The mobility of surface atoms on the substrate is then enhanced by the high energetic ion bombardment. By using this deposition technique, the substrate temperature for the deposition of α-alumina is below 500 C at a working pressure of Pa according to Yamada-Takamura et al. The ionised target atoms were guided to the substrate, resulting in a deposition rate of 2 nm s 1 when adding oxygen to the substrate region. Because of the large distance between target and gas inlet, no reaction of the oxygen with the target surface is observed. Therefore, the inhibition of the sputtering process by a thin layer of dielectric aluminium oxide at the target is avoided. Magnetron Sputtering High deposition rates are achieved by magnetron sputtering systems. Different sputter set-ups are described in literature. One can distinguish between DC magnetron sputtering [47], rf magnetron sputtering [29], and HPPMS (high power pulsed magnetron sputtering) [48]. The principle of the DC magnetron sputter technique is based on a direct current between the target (cathode) and the substrate electrode (anode), which results in the evaporation of target material. With this technique, high sputter rates can be achieved. A DC sputter system would not be suitable for Al 2 O 3 because a charging of the target due to the dielectric character of aluminium oxide would occur, which inhibits the coupling of the driving power and enables arcing. Therefore, an oscillating signal at the target is necessary, which is achieved by RF magnetron sputtering. This technique is based on signals which imply positive 43

44 3 Aluminium oxide - deposition techniques and material properties voltages through which electrons are attracted and create a charge neutralisation of the target surface. The classic RF magnetron sputtering is based on relative low powers, where the sputter gas is ionised while most of the sputtered target atoms remain neutral. The feature of uncharged evaporated target atoms is changed within the HPPMS technique. This technique is based on applying high voltage peaks of a few kv to the target electrode [22]. An avalanche of ionised gas particles plus ionised target atoms is produced. This deposition technique is relatively new, so that the sputter and deposition mechanisms within the plasma are not so well-understood. Because of the RF magnetron sputter system is better understood, this system was used within this thesis in order to study the growth mechanism of aluminium oxide. 44

45 4 Experimental set-up In the previous chapter, the ion energy distribution function was the tailored parameter regarding the energy impact to the growing film surface by using a substrate biasing. The experimental set-up which was used to deposit the Al 2 O 3 films is described in the first section of the following chapter. The deposition chamber and the oxygen feedback loop will be presented and an overview over the different biasing parameters will be given. Techniques to investigate film properties will be focussed on in the second section of this chapter. Film thickness was determined by profilometry, whereas the evolution of the film thickness was measured by ellipsometry during the deposition process. Moreover, crystallinity was determined using X-ray diffraction patterns, which was supplemented by Fourier-Transform Infrared Spectroscopy. Finally, X- ray Photoelectron Spectroscopy measurements and stress measurements yielded chemical and mechanical properties of the deposited samples. 4.1 Configuration of the deposition chamber The experimental set-up consists of a two frequency rf-magnetron sputter experiment. The plasma is a capacitively coupled plasma (CCP), which is generated by two sinusoidal signals, coupled to the target electrode. A schematic of the experimental set-up is given within Figure 4.1, for more details see [24, 49]. Two electrodes electrodes, the target electrode (upper electrode) and the substrate electrode (lower electrode) build the main part of the chamber. Both electrodes had a diameter of 140 mm and were installed parallel to each other at a distance of 5 cm. The target electrode is composed by four elements. Below a magnet configuration (see 45

46 4 Experimental set-up Figure 4.1), an aluminium target was mounted. The target consisted of 99.99% aluminium and had a diameter of 140 mm. Besides, two connection units for the rf coupling coupling were installed as well as a cooling adapter. 300 W 200 W Broadband- Amplifier MHz Matchbox A 71 MHz Matchbox B MHz rf-generator MHz rf-generator 71 MHz Gas supply Photomultiplier S N S Sample Arbritary Signal Generator Pump System Heating Supply up to 700 C C Broadband- Amplifier MHz Figure 4.1: The experimental set-up for the deposition of Al 2 O 3 is shown. The plasma was driven by two frequencies, 71 MHz and MHz, coupled to the target electrode (upper electrode). At the opposite side, the substrate electrode was located, including a sample holder. Samples could be heated up to 700 C. Additionally, arbitrary biasing signals were applied to the substrate electrode. The plasma was powered with 300 W at 71 MHz and with 200 W at MHz. A 71 MHz sinusoidal signal was generated by a waveform generator and amplified by a broadband amplifier. Finally, the signal was matched by a matchbox from Aurion. The second frequency was delivered by a Dressler Cesar power supply (Model 136) plus matchbox at MHz to the very same electrode. Around the target electrode, a circular gas line with several inlet holes was installed. A constant argon flow of 9 sccm was applied to the deposition system through this gas line. Oxygen flow was regulated through the below described feedback loop, resulting in an average oxygen partial pressure of p O2 = Pa. A working pressure of 0.1 Pa was used under full working load of a turbopump. The base pressure of the chamber was p = Pa, which led to a water adsorption rate below 0.01 nm s 1. A low water adsorption rate was necessary because evolution of crystallinity and elastic properties can be interrupted by a high water vapour 46

47 4.1 Configuration of the deposition chamber pressure [50]. However, the critical value for the incorporated oxygen-hydrogen component from the water vapour within the film of 2 at% [51] was undercut within the experiments. Opposite to the target electrode the substrate electrode was located. Thin films were deposited onto cm 2 Silicon (Si) wafers, which were mounted to the substrate electrode within a substrate holder. A halogen lamp was used to heat samples from the bottom side. Due to the low pressure within the discharge chamber, convection through gas atoms did not influence heating of the substrate. Therefore, only heat radiation was used to maintain a certain temperature at the Si substrate. With this heating system, any substrate temperature up to 700 C could be reached. During the experiments, three different substrate temperatures were used: 500 C, 550 C, or 600 C. Moreover, an arbitrary biasing signal was fed to the substrate electrode via a function generator and a broadband amplifier. In this experiment, rectangular and triangular waveforms at frequencies between 0.80 MHz and 1.60 MHz were used. Further details about the substrate biasing can be found in chapter 4.1.3, page 50. In order to generate thin films with similar thickness, ellipsometry was carried out to measure the film thickness during the deposition process. A film thickness of approximately 1 µm was achieved for all samples. A more plastic scheme of the experimental set-up is given within Figure 4.2. A vacuum chamber plus loadlock can be identified within the picture. The samples Figure 4.2: Schematic set-up of the CCP reactor, were inserted to the loadlock, which established by Inventor Professional was connected to the main chamber by Student 2010 [52]. a valve. This method of introducing the samples to the deposition chamber guarantees a minimal amount of water vapour and other disturbing gases within the deposition chamber. 47

48 4 Experimental set-up Feedback loop The previously described hysteresis effect in sputter rate requires a regulation of the oxygen flow to the chamber. The control of the oxygen partial pressure is necessary to work at a certain point within the hysteresis curve. The emission line of aluminium is the key parameter to control the deposition process when using a reactive gas component. The formation of the desired stoichiometry at the substrate can be realised by the control of the oxygen partial pressure within the reaction chamber. Further, constant deposition conditions are guaranteed by the control of the oxygen partial pressure. The optimal formation of the desired stoichiometry for Al 2 O 3 is located at the falling edge of the hysteresis. Photomultiplier A Plasma: Al Emission Line Intensity (Al) Oxygen Valve vs. Desired Intensity (Al) New Oxygen Flow (Voltage) Figure 4.3: The functional principle of the oxygen feedback loop is based on the measurement of the Al emission line and the adaptation of the oxygen partial pressure within the deposition chamber. Here, a feedback loop was installed, which worked with an optical filter observing the Al I emission line at 396 nm. At the level of the plasma discharge an optical filter and a photomultiplier were aligned. The intensity of this emission line was measured by a photomultiplier. The photomultiplier signal was read out by a PCI multifunction card of the computer. A LabVIEW program [53] calculated the oxygen flow to the chamber on the basis of the photomultiplier signal using the above described feedback loop. In detail, a PID (proportional integral differential) feedback loop compared the measured value of the emission line with the target value and adjusted the partial pressure of oxygen. The response time of the feed- 48

49 4.1 Configuration of the deposition chamber back loop reached a value of approximately 35 ms. This value correlates with the transition time from the intermediate mode to the poisoned mode of the discharge. The working principle of the feedback loop is illustrated within Figure Temperature measurement The temperature measurement was realised by ellipsometry. Any alternative temperature measurement methods were not applicable to this deposition system. For example, thermocouple measurements would be inappropriate in this systems because it would be difficult to realise it with the moveable sample holder system. A good thermal contact between thermocouple and substrate would be difficult to realise with the moveable substrate holder. Second, the substrate electrode and also the substrate itself was biased by an rf signal with an amplitude of 100 V and more. This signal is coupled capacitively onto the thermocouple signal, which is in the range of few mev, inducing a large systematic error. Therefore, an optical method to monitor substrate temperatures is preferred as it is standard in semiconductor plasma systems. The refraction index n of Si at a wavelength of nm is proportional to the temperature of Si, according to Kroesen et al. [54]. Determination of temperature was realised by the linear equation of the refractive index for silicon, which is given by T (n) n K. First, the refractive index of a silicon wafer at room temperature and at final heating temperature was determined. The difference in refractive index defines the absolute temperature of the heated substrate through T = n hot n cold C + 21 C. (4.1) Using equation 4.1, the substrate temperature was determined with respect to the given room temperature within the lab of 21 C, for more details see [24]. 49

50 4 Experimental set-up Substrate biasing parameter Rectangular and triangular biasing signals were used for the biasing of the substrate electrode. For both waveforms, the applied parameter are presented in the next subsections. Biasing parameters for rectangular biasing The substrate electrode was biased with rectangular waveforms with different amplitudes U max and frequencies f between 0.80 MHz and 1.60 MHz. The applied frequencies are limited to the mentioned range due to the broadband amplifier performance and coupling conditions to the substrate electrode. Table 4.1 shows the applied frequencies and the used duty-cycles. Frequency f Period T Duty-cycle τ on τ off [MHz] [µs] [%] [µs] [µs] Table 4.1: Overview of different rectangular biasing signals applied within the experiments. Besides the frequency f, the duty-cycle and the resulting off-time τ off are indicated. Table 4.1 includes the different rectangular biasing signals applied to the substrate electrode during the experimental series. Biasing signals were applied under a constant on-time τ on of the biasing signal, which was maintained at 500 ns. Therefore, under increasing frequency f a raising of the duty-cycle and a drop in the off-time τ off of the signals is observed. 50

51 4.2 Film analysis methods Biasing parameters for triangular biasing For the triangular biasing scheme, frequencies between 0.80 MHz and 1.60 MHz were applied to the substrate electrode. According to the shift in the biasing signal, an overview over the different biasing parameters for the given triangular signals are shown in Table 4.2. The table consists of rows presenting the frequency and the resulting on-time τ on and off-time τ off. Frequency f Period T τ on τ off [MHz] [µs] [µs] [µs] Table 4.2: Overview of different triangular biasing signals applied within the experiments. Besides the frequency f, the duty-cycle and the resulting off-time τ off are indicated. 4.2 Film analysis methods Different analysis methods were used to evaluate the deposited films. A similar film thickness was required to compare typical characteristics of these films. Therefore, profilometry was used to determine the height of the aluminium oxide films. As mentioned before, control of film thickness was realised by ellipsometry during the deposition process. Both techniques are described in the first two subsections of this section. The identification of crystallinity was achieved by X-ray diffraction under grazing incidence to monitor the short-range order. A volume analysis of the crystallinity was reached by Fourier-Transform Infrared Spectroscopy (FTIR) through a typical fingerprint spectrum. Subsequently, chemical analysis was performed using XPS. Here, stoichiometry was determined and a detailed analysis of the argon peak within the spectra was realised. Finally, stress measurements characterised the mechanical properties of the aluminium oxide films. 51

52 4 Experimental set-up Profilometry Film thickness measurements were used to maintain equality in film thickness and to determine the deposition rate g, which is also required for calculation of the mean energy < E > per deposited atom, see section 2.4.2, page H e ig h t [n m ] F ilm T h ic k n e s s P o s itio n [µ m ] Figure 4.4: Example for the edge between film and substrate, determining the film thickness. In profilometry, a tip, which is moving over a surface, measures height changes relatively to a zero level. The height changes are detected by a variation in voltage of a piezocrystal and recorded versus the horizontal position of the tip. Here, profilometry was performed using a Veeco «Dektak6M Stylus Profiler». A tip with a radius of 5 µm was installed and a horizontal distance of 3,000 µm was scanned. Height changes of 6,000 µm limited the measurement interval in vertical direction. Film thickness was measured at the edge between film and substrate (see Figure 4.4). The edge was created by the mounting system of the Si substrate within the sample holder. The Si wafer was mounted below a cm 2 large window within the sample holder. Non-coated areas were created through overlapping areas of the silicon wafer. A height profile was generated by running perpendicular to this edge from the sample down to the substrate with the profilometer tip. Using a baseline, the absolute film thickness was measured by determining the vertical distance between film and substrate using a mathematical evaluation program. 52

53 4.2 Film analysis methods The deposited films did not show a homogeneous surface, as also shown in Figure 4.4. Film thickness varied over the film surface. Therefore, a measurement in the middle of each sample side was performed to minimise the error within the measurements. The arithmetic average for the film thickness d as well as the root mean square deviation d were calculated Ellipsometry The working principle of ellipsometry is the measurement of changes in polarisation state of a polarised beam at a sample surface [55]. Within the measurement, phase information of the wavelength depending optical characteristic numbers is given by, while tan(ψ) contains the amplitude. The overall description of the complex reflectance ratio ρ is given by the expression ρ = tan(ψ) exp(i ). A measured spectrum of the optical characteristic numbers implies the film thickness and the refractive index. Therefore, a model was fitted to the measured data in order to resolve the desired characteristic numbers. Within this model, fit parameters such as the film thickness and the optical constants (n, k) are implied. Using the refractive index n of the Si wafer, for example, the temperature of the silicon substrate was determined. The film thickness of the growing aluminium oxide film was measured during the deposition process to achieve a comparable film thickness. Ellipsometry measurements were performed using a Woollam M-2000U ellipsometer, working with a xenon lamp, which creates light with wavelengths between 245 nm and 1,000 nm. Figure 4.5 shows the model of the Si substrate, which was utilised for temperature measurements of the Si wafer. The non-heated and the heated substrate were measured by ellipsometry. First, the thickness of the natural SiO 2 layer on top of the Si wafer was figured out for the non-heated situation. The thickness of the SiO 2 layer was once determined for the cold substrate and not modified for the 53

54 4 Experimental set-up heated situation. An intermediate layer, a so-called interlayer, was added to reach a smoother fitting result. Then, the angle dependent refractive index was fitted for the non-heated and the heated substrate, respectively. Finally, the refractive index of the Si layer at nm was read out from the fitted model. Taking this value into account, the temperature of the silicon substrate was calculated. The refractive index revealed to be in the range of 3.86 to 4.20, indicated within Figure 4.5. Name of layer Thickness Refractive index SiO 2 Fit: d 1.8 nm Fixed interlayer d = nm Fixed Si d = 1 mm Fit: n(632.8 nm) = Figure 4.5: Fit model for the fitting of the refractive index for Si. Determination of the underlying substrate was also required for the model calculating the aluminium oxide film thickness during the deposition process. In the first deposition sequence, film thickness of the growing aluminium oxide was too low that it got transparent for the ellipsometric measurements. The previously determined fit parameters were superposed by an aluminium oxide model, shown in Figure 4.6. With increasing film thickness of aluminium oxide, the silicon substrate got negligible for the fit process. Name of layer Thickness Refractive index Al 2 O 3 Fit (d = 0...1, 000 nm) Fixed SiO 2 Fixed (Fitted before d 1.8 nm) Fixed Si d = 1 mm Fixed (adopted from heated measurement) Figure 4.6: Film thickness model for aluminium oxide including the underlying Si wafer. A model including the underlying substrate plus the growing aluminium oxide film was established. With this model, the film thickness of aluminium oxide was observed during the measurement. This ensured the control of film thickness during the deposition process. 54

55 4.2 Film analysis methods X-ray diffraction Using X-ray diffraction (XRD) for structural analysis of aluminium oxide, crystallinity and orientations of different grains within the sample can be identified. This measurement method is non-destructive and allows to follow the transition between amorphous and crystalline aluminium oxide. The measurement method is explained in the following subsection. X-ray diffraction patterns of aluminium oxide samples of amorphous and γ-crystalline Al 2 O 3 samples are presented. Bragg diffraction In general, diffraction pattern result from scattered X-rays at a crystal structure. The Bragg diffraction is based on the interaction of an X-ray beam at a sample without energy transfer between X-rays and sample atoms. However, the momentum of the incoming wave is affected through the interaction with the sample atoms. In contrast, the sample atoms are also affected by the X-rays, but the resulting oscillation is compensated by the overall lattice. a1 d Q dsinq a2 a3 Figure 4.7: Principle of bragg diffraction. A schematic description of a Bragg scattering situation can be found in Figure 4.7. The interaction between an X-ray beam and material atoms is given by a change in momentum of the beam, which is characterised by the angle Θ. This angle shift can be measured by a detector, placed at the right side of the sample in Figure 4.7. Using the geometrical relation between diffraction angle and lattice parameter, the measurement of the diffraction angle includes the lattice parameter. By measuring different angles between the X-ray source and the detector, one can determine the lattice parameter of the material. The crystal structure can be associated with a certain crystal orientation of the incident grains if the chemical characteristic of the material is known. 55

56 4 Experimental set-up A geometrical relation of the angle between beam and sample Θ and the lattice parameter d can be extracted from Figure 4.7. It derives as n λ = 2 d sin(θ). (4.2) By fixing the wavelength λ to a certain value, the Bragg condition results in a relation between the angle of incidence Θ and the given lattice parameter d. Only one solution for the appearance of a Bragg diffraction exists for a certain lattice parameter d. The observation depth of the measurement method has to be considered because the observation depth may exceed the sample thickness. Using a silicon substrate, the Si diffraction patterns superpose the diffraction patterns of the aluminium oxide when exploring a too thick observation depth. Therefore, a lower observation depth than the film thickness has to be ensured. The observation depth of this analysis method depends on the examined material and is given by the expression [56]: I/I 0 = exp( µ d ρ 1 ). (4.3) The intensity ratio I/I 0 given by equation 4.3 is lowered exponentially with the linear absorption coefficient µ, the film thickness d, and the density of the film ρ. So, higher film densities lead to lower observation depths compared to less dense films. As already mentioned, due to the large observation depth for Al 2 O 3, the silicon substrate dominated the XRD diffractogram when using a regular Bragg-Brentano set-up. Therefore, an alternative measurement method to the «normal» Bragg- Brentano measurement method had to be considered. To avoid superposition of Si and Al 2 O 3 peaks, a special set-up was chosen, which is called «grazing incidence». The grazing incidence set-up was used because of a lower information depth of the X-ray beam which is approximately some hundreds of nm in the case of the deposited aluminium oxide samples. Within the Bragg- Brentano set-up, the detector and the beam are aligned symmetrically to the surface normal of the sample, which is also indicated in Figure 4.7. Hence, the angles of the incoming beam and the outgoing beam relative to the surface normal are similar. However, in a grazing incidence configuration, this symmetry is broken, see Figure 56

57 4.2 Film analysis methods Detector Incoming X-Rays ω Lattice Plane Θ Figure 4.8: Schematic set-up of a grazing incidence, copied and modified from [57] Using the grazing incidence set-up, the X-ray beam hits the surface under an angle ω. The scattered beam is measured by an area detector. When moving the detector on a circular path with respect to the sample surface, diffraction patterns are detected in the respective angle interval. The measured intensity of a Bragg pattern depends on the angle between the X-ray beam and the orientation of the grains within the sample, which is also indicated in Figure 4.8. Therefore, the detector needs to be adjusted under a specific angle Θ compared to the normal of a certain grain in order to detect a Bragg diffraction pattern. Diffraction patterns of different grains are only measured, if the normal of the grain and the detector angle is equal to the Bragg condition, for example grain number 2 and 4 within Figure 4.8. Only grains which are oriented under the Bragg condition to the detector are measured. Thus, a deformation of peak intensity has to be considered when analysing the samples. Moreover, the grazing incidence measurement set-up is useful for a monocrystalline substrates like the used silicon substrate as it will not produce any peak within the diffractogram. Determination of crystallinity within XRD pattern of aluminium oxide XRD measurements were realised by a Bruker D8 General Area Diffraction System (GADDS) on the deposited Al 2 O 3 thin films. The incident angle of the beam was 57

58 Intensity [a.u.] Intensity [a.u.] 4 Experimental set-up 15. Within the measurements, the nomenclature for the analysis angle is given as 2Θ. Because the incident angle of the beam to the surface is 1Θ and the angle between surface and outgoing beam is 1Θ as well, a measured angle regime of 2Θ is given. The analysed angle range 2Θ was between 20 and 75. The applied voltage and current settings were 40 kv and 40 ma, respectively. Focussing on the sample was realised by a laser pointing to the surface of the Al 2 O 3 film. With the help of a camera, the optimal measurement height was adjusted by observing the reflection of a laser on the surface. A typical XRD spectrum for an X-ray amorphous sample is shown in Figure 4.9 (a). No characteristic peak can be found in this graph. Figure 4.9 (b) shows a XRD measurement of an X-ray crystalline aluminium oxide sample. Three different peaks which can be associated to the γ phase of Al 2 O 3 are present within this figure, where the peaks and their associated direction are marked. The (311) direction can be found within the XRD pattern at an angle of Two peaks at and can be identified as (400) and (440) orientations, respectively. According to Saniger et al. [58], the already described orientations can be identified to γ-aluminium oxide (a) Scattering Angle 2Q [ ] (b) (311) (400) (440) Scattering Angle 2Q [ ] Figure 4.9: Typical XRD measurement of an amorphous (a) and a γ-crystalline aluminium oxide sample (b). However, to identify more subtle effects like preferred orientations of crystal directions or ratio of amorphous and crystalline regions, the GADDS measurements are not feasible. Due to the fact that the measurements were realised under grazing incidence, even a peak shift within the diffraction patterns may occur, which 58

59 4.2 Film analysis methods does not inevitably suffer from a change in crystallinity of the film. Because the X-ray beam is focused to the surface of the sample, a peak shift may be generated to a small disalignment of the beam. Therefore, interpretation of XRD data has to be realised under the consideration of shifts caused by the measurement process. Measurements with an area detector like it was done for this thesis, were not showing characteristics of a preferred orientation of the peaks. Specially, the height relation between the different peaks did not represent a physical effect. Further interpretation requires additional investigation of the sample with other analysis methods, which are described in the following sections Fourier-Transform Infrared Spectroscopy Since the 1970 s, Fourier-Transform Infrared Spectroscopy (FTIR) is a well-known analysis method. The principle behind this method is the measurement of light absorption in the infrared (IR) regime by a sample. FTIR is sensitive for periodic changes in dipole moment [59]. In contrast, with Raman spectroscopy one can observe rotational and vibrational properties of molecules excited by changes in polarisation also induced by infrared light. However, these changes are not measurable by FTIR. Specifically, both methods are independent from each other. Here, the main focus is on the observation of infrared-active spectra, which reveals FTIR measurements on aluminium oxide. Therefore, an introduction to the FTIR measurement method will be given and characteristic spectra of the measured aluminium oxide films will be presented. Measurement method Vibrational and/or rotational oscillations in molecules are excited by a periodic change in dipole moment through light absorption, which are characteristic for the observed material. However, for symmetric molecules, for example N 2, the change in dipole moment is not detectable. In this case, the change in dipole moment of one atom is compensated by the change in dipole moment of the other atom. One distinguishes linear and non-linear valence oscillations of molecules. In case of a linear molecule, three possible kinds of oscillation can be named: symmetric oscillation (along the axes of the molecule), antisymmetric oscillation (oscillation 59

60 4 Experimental set-up along bonding direction of a three-atom molecule for example, but with a stronger oscillation amplitude of one of the atoms), and deformation oscillation (vertically to the bonding direction) [60]. The FTIR measurement technique consists of one laser beam, which is split into two beams using a beam splitter. The so-called reference beam is directly guided to a detector. The second beam is reflected at a moving mirror, which generates a path offset to the reference beam. This path offset creates interference pictures, which are measured at the detector. Using the Fourier-Transformation, a wavenumber depending spectrum is calculated. In case of a solid material as Al 2 O 3, separated oscillations between Al and O atoms do not arise. Aluminium and oxygen atoms are placed within the crystal structure and bondings to their next neighbours may differ. Therefore, distinction between specific atoms is not possible, but the crystal structure is reflected within the spectrum. m f 2 f 1 f 2 f 1 f 2 M m M m M x n-1 x n x n+1 X n-1 X n X n+1 r a Figure 4.10: Linear chain of two different atoms with mass m and M, having binding forces f 1 and f 2, from Weidlein et al. [59]. Phonon excitation of atoms within the structure of aluminium oxide is stimulated by laser light. Phonons are physical phenomena which basically consist of collective excitations of atoms within a solid. In a simple case, aluminium and oxygen atoms are placed beside each other in a linear chain, which is shown in Figure Within this scheme, different atoms with masses m and M, and the relating bonding forces f 1 and f 2 are marked. Positions of the atoms are highlighted with X n 1...X n+1 for atom type 1 with mass M and with x n 1...x n+1 for atom type 2 with mass m, respectively. The calculation of the oscillation for two atom species is more complex due to mainly two reasons: the distances between the atoms vary because of the bonding between the atoms, and the masses of the atoms differ. This leads to an 60

61 4.2 Film analysis methods unsymmetrical oscillation behaviour of the atoms within the chain. According to Weidlein et al. [59], the oscillation can be described as M d2 X n dt 2 = f 1 (X n x n ) f 2 (X n x n 1 ). (4.4) The sum of forces affecting the second atom can be written as m d2 x n dt 2 = f 1 (x n X n ) f 2 (x n x n+1 ). (4.5) Forces between the different atoms within the chain are solved by the approach of standing waves with X n = A cos(πkn/n) cos(2πν k t) and x n = B cos(πk/n(n r/a)) cos(2πν k t), respectively. This solutions contain different amplitudes for the two atom species. Inserting the solutions of the standing wave into equation 4.4 and 4.5, the dispersion relation reveals to be ( 1 (4π 2 νk) 2 2 (4π 2 νk) 2 (f 1 + f 2 ) M m) f1f ( 2 πk ) Mm sin2 = 0. (4.6) 2N This dispersion relation includes two solutions due to the square relation within 4π 2 νk 2, resulting in two dispersion graphs. The first one is called acoustic wave because the atoms of the different elements are moving in the same phase, like acoustic waves do. However, within an optical wave, the electric component and the magnetic component of the wave are propagating under a relative phase shift to each other. Therefore, the second solution of the oscillation equation is called optical wave. Optical waves can be divided into longitudinal optical (LO) and transversal optical (TO) components, which are both excited by infrared radiation. In general, an LO absorption is always associated to a TO absorption, which is detected by FTIR [61]. An optical model established by Chu et al. [62] describes the different oscillation modes for aluminium oxide. According to the model, the optical dielectric function of aluminium oxide is composed of a series of classical Lorentz oscillators: 61

62 4 Experimental set-up ɛ 2 (ω) = ɛ + n S n ω 2 t,n ω 2 l,n ω2 ıωγ n. (4.7) S n is the strength of the oscillation, ωt,n 2 the wavenumber of the transversal oscillation, ωl,n 2 the wavenumber for the longitudinal oscillation, and γ the damping factor. ɛ describes the contribution of the optical transitions outside the infrared spectral range. Each oscillator consists of a longitudinal and a transversal component. Especially, crystalline γ-alumina can be identified by a pronounced peak at 950 cm 1 corresponding to the LO phonon [61], whereas amorphous alumina layers exhibit a rather featureless absorption spectrum. Equation (4.7) has been used to devise an optical model of aluminium oxide thin films on silicon wafers and to simulate the infrared transmission spectra. Typical transmission spectra for amorphous and γ-crystalline Al 2 O 3 To analyse the aluminium oxide samples, ex-situ FTIR transmission measurements were performed using a Bruker IFS 66/S spectrometer. A polariser was placed in front of the sample, through which only s polarized light passed to the sample. The angle between the sample surface and the laser beam was 60. Measurements were performed in the wavenumber range between 400 cm 1 and 6,000 cm 1. Background spectra of non-coated silicon wafers were subtracted from the measured spectrum. The transmission measurements of the samples enabled bulk analysis of the Al 2 O 3 films. The oscillation amplitudes within the infrared spectrum are in the order of the bonding width of atoms, which make variations within the bonding situation of the aluminium oxide measurable. However, changes in stoichiometry or crystallinity are not detectable by FTIR without further analysis methods. Figure 4.11 shows typical FTIR spectra for a γ-crystalline (a) and an amorphous (b) sample of aluminium oxide. The shown spectra represent the measured transmission of a sample versus the wavenumber. Only a wavenumber interval between 400 cm 1 and 1,200 cm 1 is shown in the figure because characteristic peaks identifying crystallinity were found within this region. The spectra are normalised to 1 for a wavenumber of 1,200 cm 1. 62

63 4.2 Film analysis methods T ra n s m is s io n (a ) T ra n s m is is o n (b ) W a v e n u m b e r [c m -1 ] W a v e n u m b e r [c m -1 ] Figure 4.11: Typical FTIR spectra for a γ-crystalline (a) and an amorphous (b) Al 2 O 3 sample. Brüesch et al. [61] investigated FTIR spectra of amorphous and γ-aluminium oxide. The evolution of a sharp peak (or dip within transmission spectra) at approximately 950 cm 1 identified γ-al 2 O 3. Further oscillations for γ-al 2 O 3 films at lower wavenumbers were declared by Chu et al. [62]. The intensity and appearance of further peaks at lower wavenumbers were assigned to 357 cm 1, 536 cm 1, and 744 cm 1. The identification of these peaks was confirmed by a software, simulating the superposition of harmonic oscillators at the corresponding wavenumbers, see Figure A good agreement to the announced wavenumbers was found which confirmed the identification of the γ phase. Further investigations of the detected oscillations did not reveal new results on the crystal structure, which is the reason why these fits are not discussed in detail at this point. T ra n s m is s io n M e a s u re m e n t O p tic a l m o d e l W a v e n u m b e r [c m -1 ] Figure 4.12: Comparison of FTIR measurement and fit using the model from Chu et al. [62]. 63

64 4 Experimental set-up X-ray Photoelectron Spectroscopy The working principle of the X-ray Photoelectron Spectroscopy (XPS) is the photoeffect, which was established by Heinrich Hertz in 1887 [63]. The XPS measurement method was used in this work to quantify the chemical composition of the aluminium oxide samples. Also trapped argon from the plasma background was observed. In this thesis, it was discovered that the shape of the argon peak in the XPS spectra has the great possibility to provide information about the local structure within the deposited thin films. The physical background for the analysis of the deposited Al 2 O 3 films will be shown within this section. First, a short overview over the measurement method of XPS will be given. A description of general features of the measured spectra is presented afterwards. Especially the reason for a shift in binding energy within the XPS spectra will be focussed on. Finally, the analysis procedure of the aluminium oxide films by XPS will be given. XPS measurement method The measurement principle of XPS is based on the extraction of electrons from a sample surface irradiated by X-ray photons, see Figure X-rays are produced when an electron beam with enough energy to promote transitions between atomic core levels impacts an anode. The produced X-rays are redirected to a monochromator, where radiation with an energy of ev is selected. These X-ray photons are guided onto a sample. The interaction of the X-ray beam with the sample atoms results in excitation and extraction of electrons. Extracted electrons are collected in a detector, where their kinetic energy is measured. The relationship between the kinetic energy of the electron and the energy of the X-rays is given by Barr et al. [63]: hν = E kin + E bin + qφ. (4.8) By knowing the energy of the incoming X-rays (hν), the required binding energy (BE) of the electron (E bin ) within the atom can be determined. The detector of 64

65 4.2 Film analysis methods Energy Analyzer (SCA) Electron Source Quartz Crystal Monochromato kv electrons Al K X-rays Multi-channel Rowland Circle Photoelectrons Al Anode Sample Figure 4.13: Principle of the X-ray Photoelectron Spectroscopy, taken from [64]: An X-ray beam is guided onto a sample, where a photoelectron is ejected. By measuring the energy of the extracted photoelectron, the chemical structure of the measured sample can be determined. the photoelectron spectrometer measures the kinetic energy E kin of the extracted electron. The spectrometer work function is given by the expression qφ. Photoelectron E fermi level 2p X-ray (photon) Binding Energy 2s 1s Binding Energy = X-ray Energy Photoelectron Kinetic Energy Figure 4.14: Extraction of a photoelectron after irradiation with X-rays, taken from [64]. Each element is characterised by the binding energies of electrons in the different atomic core levels. The only elements which are not detectable within the XPS are hydrogen and helium. Chemical bonding between atoms leads to a shift in binding energy position, which allows a chemical analysis of the measured samples. This technique is called ESCA (Electron Spectroscopy for Chemical Analysis). In order to determine binding energy of the measured elements correctly, the BE scale needs to be aligned. 65

66 4 Experimental set-up Using a conductive sample, alignment of the Fermi level from the sample and the spectrometer is reached. Determining the work function and the kinetic energy simultaneously is not possible within the same measurement step, but the work function is needed for calculation of the binding energy in equation 4.8. Therefore, a constant work function, the one of the spectrometer, is taken, when the sample is conductively connected to the spectrometer. The work function of the spectrometer is determined using a gold sample. The core level of Au4f is measured at a BE of ev and the work function of the spectrometer is aligned to it. When measuring conductive samples, the Fermi level of the spectrometer and the sample are aligned to each other, which leads to a correct determination of binding energy position (see Figure 4.15). However, when analysing insulating samples, another reference for the correct binding energy is taken, which is explained in the next paragraph. Vac level fsample E tot E bin E kin E kin f spect Fermi level Figure 4.15: Alignment of Fermi levels of the sample and XPS device, based on [65]. A further effect that has to be taken into account is the possible charging of the surface during irradiation with X-rays. After the extraction of an electron, the left atom is charged positively. If the charge of the atom cannot be balanced, a net positive surface charge builds up, creating a retarding electric field. Considering an insulating sample, a positive charge of the surface will attract the photoelectrons which leave the atomic shell and modify their kinetic energy. This variation in kinetic energy is observed as a shift towards higher BE values. Therefore, it is very important to neutralise the sample surface by using an electron shower of low energetic electrons. An extra neutralisation effect is reached with argon ions of 20 ev which care for a homogeneous neutralisation [66]. 66

67 4.2 Film analysis methods General features about analysis of the aluminium oxide samples with XPS X-ray Photoelectron Spectroscopy was performed using a Versaprobe spectrometer from Physical Electronics (PHI 5000 VersaProbe). At an aluminium anode, Al K α radiation with an energy of hν = ev was produced. A resolution of 2.82 ev was achieved for survey spectra using a pass energy of ev. A spectral resolution of 0.35 ev for a pass energy of 23.5 ev was applied for measurements of single peaks. The measurement spot had a diameter of 200 μm unless otherwise indicated. Standard measurements were performed at a tilt angle of 45 between the sample and the detector. For angle resolved measurements, angles between 15 and 85 were used. The measurement depth was at around 2-8 nm for a tilt of 45. XPS is a precise measurement method to determine binding energies. Within this thesis, aluminium oxide was measured, which is an insulating material. For metallic samples, the Fermi level of the sample and of the spectrometer are aligned due to the conductive connection. However, for aluminium oxide, the alignment of the Fermi levels from the spectrometer and sample is not possible, which results in a floating binding energy scale. The BE scale is aligned to the carbon peak (C1s), which is a common reference peak. Because of adventitious carbon from the exposure of the sample to air, a thin carbon layer can be found on the sample. The C-C bond is fixed to a position of ev [63]. However, within the XPS measurements, the top layer of the sample was removed using an ion beam of several kv, which leads to a removal of the carbon and of the reference position. On the non-sputtered samples, the BE scale is fixed by setting the C1s at ev. This puts the core level of aluminium to 74.0 ± 0.3 ev. When removing the carbon during the sputter process, the Al2p at 74.0 ev position is used as the reference position. Binding energy shift effects After shifting the whole spectrum towards the reference position, still a shift in BE position of the different elements may be observed. Three mechanisms can be named which can cause a shift in BE position. First, a shift in BE position may be due to chemical bonding of the measured element. Second, a shift because of final state effects because of the measurement method itself (spin-orbit splitting etc.) is 67

68 4 Experimental set-up possible. Third, shifts in BE position may due to matrix effects, where the electron shell is deformed because of the surrounding of the atom. In general, one can merge all shifts in binding energy to one expression: E bin V chem, V matrix, R (4.9) Equation 4.9 includes all named effects (chemical bonding, V chem, matrix effects, V matrix, and final state effects, R) which are responsible for a shift in binding energy. Analysis of aluminium, oxygen or carbon peaks reveal shifts due to the chemical bonding. Information about the local structure can be resolved by the investigation of BE position of noble gases embedded to the aluminium oxide film. The electronic structure of noble gases prevents it from sharing electrons in chemical bonds with atoms from the surrounding matrix. A shift due to chemical bonding can be neglected. Final state effects are eliminated because of the neutralisation system and the use of the reference position of Al2p. Therefore, observing the Argon Ar2p peak present shifts in the peak position are only related to matrix effects. Peak shape The peak shape depends on the measured core level of the element. When measuring carbon or oxygen, the 1s core level is observed. An electron located within an 1s core level has its origin in the n= 1 shell. Here, the electron is not affected by the spin-orbit splitting due to the azimuthal quantum number of l = 0. This results in a singlet structure for O1s and C1s. In the case of aluminium and argon, the 2p core level is measured, relating to electrons from the n = 2 shell. The principal quantum number n = 2 correlates to the azimuthal quantum numbers of l = 0,1, which reveals an overall total angular momentum of j= 1/2 and j = 3/2. Therefore, a spin-orbit splitting is present, which results in two peaks at different BE positions with a height ratio of 2:1 between the 2p 3/2 and 2p 1/2 components. The distance in BE of the two components is defined by the electronic structure of the measured element and varies between 0.1 ev and several ev. 68

69 4.2 Film analysis methods A r2 p 3 /2 In te n s ity [a.u.] A r2 p 1 / B in d in g E n e rg y [e V ] Figure 4.16: The spin-orbit splitting for Ar2p peak can be seen by the 2p 3/2 and 2p 1/2 components. Figure 4.16 shows the Ar2p core level of argon embedded in an Al 2 O 3 film. The height ratio between the two components is 1:2. The spin-orbit splitting (distance between both peaks) for Ar2p is 2.12 ev, while it is determined to 0.4 ev for the Al2p peak. Peak fit procedure By determining precisely the BE position, XPS allows to resolve chemical composition and stoichiometry of a given sample. It is necessary to perform a mathematical analysis of the measured peaks in order to determine the BE position and the peak area. XPS on aluminium oxide samples revealed the presence of four elements: aluminium and oxygen were analysed by the core levels Al2p and O1s. Further, adventitious carbon from the exposure to air, C1s, and trapped argon from the deposition process, Ar2p, were measured. Mathematical analysis of the XPS spectra was realised by fit programs such as Multipak [67] or Unifit [68]. A distinction of the binding energy positions was realised by references such as papers or the «Handbook for X-ray Photoelectron Spectroscopy» [69]. In the following, a discussion of the mathematical analysis and interpretation approach is done for each element of the aluminium oxide samples: 69

70 4 Experimental set-up O1s: Figure 4.17 shows the normalised O1s peak from an Al 2 O 3 sample, where the continuous line in Figure 4.17 shows the measured peak. The background is fitted using a Shirley function [70], shown as dotted grey line. The fit contains of two singlet peaks (dashed lines) which consist each of a product of a Lorentzian and Gaussian component. The Lorentzian width is associated to the lifetime of the photohole, while the Gaussian width represents the broadening due to the X-rays, the spectral resolution of the detector and chemical bonding. The sum of both components, shown as continuous grey line in Figure 4.17, fits very well to the measured spectrum. In case of the shown O1s peak, the two fitted peaks are associated to O-Al and Al-OH (from water within the deposition chamber) bondings [71]. All fit parameters (relative height ratio, Gaussian and Lorentzian width, and BE position) were left open for the mathematical fit. M e a s u re d S p e c tru m In d iv id u a l C o m p o n e n ts S u m C u rv e B a c k g ro u n d In te n s ity [a.u.] O H -A l O -A l B in d in g E n e rg y [e V ] O 1 s Figure 4.17: Exemplary O1s peak from an aluminium oxide sample, showing two components: O-Al and OH-Al bonding. The measured spectrum (continuous line) is fitted by two peaks (dashed lines). The sum curve (continuous grey line) fits to the measured spectrum very well. Al2p: Aluminium was also fitted using a product of a Lorentzian and Gaussian line profile. One doublet structure was assumed, representing the Al-O bonding. The height ratio of the 2p 3/2 and 2p 1/2 component was fixed to 1:2, while the spin-orbit splitting was 0.4 ev. The Gaussian widths of the 2p 1/2 and 70

71 4.2 Film analysis methods 2p 3/2 components were forced to the same value. The BE position of the 2p 3/2 component, the absolute height as well as the Gaussian and Lorentzian line profile were left open for the fit procedure. The binding energy position of the Al2p at 74.0 ev peak was used as the reference position. An exemplary Al2p peak is shown in Figure 4.18 (a). The mentioned Al2p spin-orbit splitting is due to the small separation not visible here. Ar2p: The Ar2p peak was fitted by a convolution of a Lorentzian and Gaussian line profile. The Lorentzian width was set to 0.12 ev for all components, according to Jurvansuu et al. [72]. The height ratio of 1:2 for the 2p 3/2 and 2p 1/2 components was enforced as well as the same Gaussian width of the two components. A spin-orbit splitting of 2.12 ev was used. For the fit procedure, the absolute height of the 2p 3/2 component, binding energy position, and the Gaussian width were left open. Figure 4.18 (b) shows a typical fit of an Ar2p peak with one doublet structure. A decomposition with two components was realised, when the mathematical fit did not reveal a satisfying fit with one doublet structure (a ) M e a s u re d S p e c tru m F itte d C u rv e B a c k g ro u n d A l2 p (b ) M e a s u re d S p e c tru m F itte d C u rv e B a c k g ro u n d A r2 p A r2 p 3 /2 In te n s ity [a.u.] In te n s ity [a.u.] A r2 p 1 / B in d in g E n e rg y [e V ] B in d in g E n e rg y [e V ] Figure 4.18: Exemplary Al2p peak (a) with the measured spectrum (continuous black curve) and the fitted curve (grey curve). The Ar2p peak is shown in (b). 71

72 4 Experimental set-up Stoichiometry The determination of stoichiometry of the samples is realised by comparison of the peak areas of different elements. The area between the measured peak and the fitted background profile is determined as I 0, which has to be multiplied by to the atomic sensitivity factor S in order to guarantee comparability between areas of different elements. This results in a corrected area I corr of I corr = I 0 S. The sensitivity factor S involves among other things the cross sections between X-rays and the measured elements. The stoichiometry of a measured sample is calculated by the area ratio of the incident element I corr,i to the total area for all considered elements of the sample I corr,i Stress determination Stress is a material parameter which depends on the fitting between substrate and deposited film. According to Smith et al. [23], one has to distinguish between intrinsic and extrinsic stress within thin films. An intrinsic stress is induced by the growing film itself, for example through mismatching of different grains. An extrinsic stress is defined by external forces to the film. For example, this may be induced by different thermal expansion between substrate and growing film. Stress due to thermal expansion has to be considered because of the fact that Al 2 O 3 deposition is realised under temperatures between 500 C and 600 C. In a simplified case, the thermal expansion ɛ is linearly connected to the difference in temperature and thermal expansion coefficient ( α T T ). According to Wieder [73], the extrinsic stress is written as σ ext = (α substrate α film ) (T dep T room ). (4.10) This equation includes the thermal expansion factor of the substrate material α substrate and the factor of the film α film. Further, stress correlates with the difference between room temperature T room and deposition temperature T dep. The over- 72

73 4.2 Film analysis methods all stress is given as σ tot = σ ext + σ int, which is measured using stress sensors, for example. Within the conducted experiments, stress cantilever arrays established and produced by Ludwig et al. [74] were applied. A scheme of the cantilever array is given within Figure A profile of ten thin cantilevers is cut free-standing from the base material. Curvature of these cantilevers indicates the overall stress of the deposited film. Deposition and interpretation was realised by A. Stein [75] in the context of his Bachelor thesis. The measurement of deformation of the cantilevers and, therefore, the determination of the stress was executed by D. Grochla from the Materials Research Department at the Ruhr-Universität Bochum. Figure 4.19: Scheme of a stress cantilever array. The principle of the measurement method is the determination of the curvature of a single cantilever (width and thickness of the cantilever are small compared to the length: b,h s << L). The width of the cantilevers was 600 µm and the lengths increased from 1,500 µm to 4,500 µm in 450 µm steps. Stress of the film induces a moment of force, which is applied to the cantilever and a curvature with a certain radius r is detected. Neglecting the curvature of the cantilever perpendicular to the clamping direction and assuming only longitudinal curvature of the array, the Stoney equation describes the connection between the film stress and the curvature by [76]: σ f = Y (1 νs 2 ) h 2 s. (4.11) 6rh f Here, the stress of the film σ f only depends on the radius of curvature r. The known substrate thickness h s as well as the biaxial elastic modulus Y and the Poisson number ν are known for the (monocrystalline) cantilever material. After the deposition process, the film thickness h f has to be determined. 73

74 4 Experimental set-up Figure 4.20: A deposited stress cantilever array after deposition of an Al 2 O 3 thin film onto it. A deformation of the single cantilevers upwards can be seen. The radius of the deformation from the cantilevers is used to solve the Stoney equation. Analysis of the curvature of the cantilever array is realised by Digital Hologram Microscopy (DHM). This method is based on the measurement of the path offset of two laser beams, which are produced by leading one laser beam through a beam splitter. One beam is directly guided to a detector, whereas the second beam is reflected at the stress cantilever array surface. The measured path offset is related to the path offset of the undeposited cantilever array. Therefore, the change in the path offset describes the deformation of the cantilever through the film stress. To illustrate, the curvature of a deposited cantilever array is represented by an image of the curvature taken from the DHM measurement in Figure A cantilever array is shown, at which only nine cantilevers are left due to the destruction of one cantilever during transportation. The curvature of the cantilever arrays can be clearly seen. The scale within the figure represents the absolute length scale, which also includes curvature of the cantilevers upwards. 74