Fig. 4.1 Poole-Frenkel conduction mechanism

Transcription

1 Fig. 4.1 Poole-Frenkel conduction mechanism

2 Fig. 4.2 Schottky effect at a metal-semiconductor contact

3 Fig. 4.3 X-ray diffraction pattern of the MgO films deposited at 450 o C on Si (111)

4 Fig. 4.4 Illustration of the fabricated MOS capacitor structure used for electrical measurements

5 Fig. 4.5 Experimental arrangement of measuring electrical parameters

6 Current (A) 1E-5 1E-6 1E-7 1E o C 100 o C 50 o C 30 o C 1E-9 1E-10 Region I Region II Region III Voltage (V) Fig. 4.6 I-V Characteristics at various temperatures of MgO films with film area 3.14 mm 2

7 E g Activation energy (ev) E 1/2 (V/cm) 1/2 Fig. 4.7 Activation energy as a function of square root of applied field ( E )

8 Current (A) 1E-5 1E-6 1E-7 1E o C 100 o C 50 o C 30 o C 1E V 1/2 (Volt) 1/2 Fig. 4.8 Variation of current with applied voltage at the high field region

9 20 15 Z'' (x10 6 ohms) Z' (x10 6 ohms) Fig 4.9 Nyquist plot of impedance at 30 C for Al/MgO/p-Si capacitor

10 10 1 Al/MgO/p-Si MIS capacitor Z' (x 10 6 ohms) o C 50 o C 70 o C 90 o C Frequency (Hz) Fig Frequency and temperature dependence of Z of the Al/MgO/Si capacitor

11 16 12 Al/MgO/p-Si MIS capacitor 30 o C 50 o C 70 o C 90 o C Frequency (Hz) Fig Frequency and temperature dependence of Z

12 R gb (Mohm) C gb (pf) Temperature ( o C) 0 Fig Variation of grain boundary resistance and capacitance with temperature

13 Log /Z/ Tan (δ) Log (f) Fig Variation of log (z) and tan (δ) with frequency at room temperature

14 6 Al/MgO/p-Si MIS capacitor 30 o C 50 o C 70 o C 90 o C 4 ε' Frequency (Hz) Fig Frequency dependence of real part of permittivity of MgO at different temperature.

15 Al/MgO/p-Si MIS capacitor 30 o C 50 o C 70 o C 90 o C ε Frequency (Hz) Fig Frequency dependence of imaginary part of permittivity of MgO at different temperatures.

16 35 Al/MgO/p-Si MIS capacitor M' o C 50 o C 70 o C 90 o C Frequency (Hz) Fig Variation of M with frequency at different temperature

17 20 15 Al/MgO/p-Si MIS capacitor 30 o C 50 o C 70 o C 90 o C Frequency (Hz) Fig Variation of M with frequency

18 o C 50 o C 70 o C 90 o C ln(σ) (S/m) ln(ω) Fig Frequency dependence of σ AC (ω) for the MgO thin film at different temperatures

19 high frequency region low frequency region s-parameter Temperature ( o C) Fig Temperature dependence of S-parameter

20 KHz 1 KHz 10 KHz 100 KHz ln(σ) (S/m) /T (K -1 ) Fig Temperature dependent conductivity of MgO films at different frequencies

21 CHAPTER IV DIELECTRIC IMPENDANCE AND AC CONDUCTIVITY PROPERTIES OF CRYSTALLINE MgO THIN FILMS 4.1 INTRODUCTION The effect of crystalline structure of dielectric films on their electrical characteristics are discussed in this chapter with reference to experimental results obtained with MgO thin films. The Poole-Frenkel and Schottky mechanisms and the evidence for electronic hopping are discussed in detail. The main objective is to discuss the various mechanisms of electronic, ionic currents through dielectric magnesium oxide thin films. Conductivity is concerned primarily with sandwich structures in which the dielectric medium is bounded between a metal and semiconductor electrodes. In dielectric films, electronic conduction is due to the motion of electrons in the conduction band and holes in the valence band or hopping of bound carrier between localized sites in the dielectric material. Electronic conduction requires high energy to excite a carrier, and this energy can be supplied thermally by the applied electric field that leads avalanche process. Where as in hopping process, less energy is required and this process is favored in the case of highly disordered thin films. In addition, dielectric films differ in their electric properties according to the preparation conditions. 4.2 CONDUCTION MECHANISMS Normally electrical conduction in the MIS structure is a complicated process and involves many conduction mechanisms such as Poole-Frenkel emission, Schottky- Richardson emission, hopping conduction, space charge limited conduction, quantum mechanical tunneling etc. Any one of this mechanism or combinations of two or many mechanisms contributes electronic conduction in the constructed MIS structure. The details of each mechanism are summarized in the coming subsections. 81

22 4.2.1 Poole-Frenkel Emission The Poole-Frenkel Emission is lowering of a coulomb potential barrier surrounding a localized charge, when it interacts with an electric field [1, 2]. The illustration of the Poole-Frankel effect (field assisted thermal ionization) is shown in Fig. 4.1 The Poole-Frenkel effect is usually considered to explain the strong field dependence of current on electric field in insulating material under high field conditions. The Poole-Frenkel effect lowers the effective ionization energy of a donor by the applied field. For ionization energy E 1, the field is lowered by an amount E 1 - βf 1/2 where, F is the applied field and β is the Poole-Frenkel constant given by, [ ] 2 o β = e π ε ε (4.1) ε is the relative dielectric constant for low or high frequencies depending on the polarization of donor medium within the emission time. Thus, the conductivity is obtained by substituting E g =E 1 -βf 1/2 in the intrinsic current density equation, The equation reduces to, I = eμn c E g F exp 2kT (4.2) 1 2 β F σ = σ o exp (4.3) 2kT where, σ o =eμn c exp (-E g /2kT) is the low field conductivity. In terms of current density equation (4.3) becomes, 1 2 β F J = J o exp (4.4) 2kT where, the pre-exponent factor J o = σ o F is the low field current density Several investigations have been confirmed for a field dependent conductivity, which shows the bulk-limited conductivity in many of dielectric films [3-5]. 82

23 4.2.2 Richardson-Schottky Emission Richardson-Schottky emission is the high-field conduction process that occurs in a field that lowers a metal-semiconductor interfacial barrier [6]. The change in potential in this process is due to the result of image forces. This force arises because of the positive charge on the metal surface due to polarization by an escaping electron. This in turn results an attractive force on electron and hence the potential energy of the electron is given by, 2 e φ im = (4.5) 16π εε x where, x is the distance of the electron form the electrode surface. The potential step at the neutral barrier with the image potential as a function of distance x from the interface is given by, o 2 e φ (x) = φo + φim = φo - (4.6) 16 πε ε x The potential barrier variation with x is shown in Fig It is clear that for x < x o, a constant image force is assumed and the potential energy is a linear function of x. The image force is illustrated by the line AB in Fig When a field is applied, the barrier height is reduced and is shown as the dotted line, which is less than Δφ s from the bottom of the conduction band. The potential barrier under the influence of the electric field can be written as, The change Δϕ s in the barrier height is given by, 2 e φ (x) = φ o - - e Fx (4.7) 16π εε x e Δ φs = F = β F 4πε0ε o (4.8) Because of this lowering potential barrier, the electrode-limited current does not saturate according to the Richardson s equation, Δφ J = AT exp - kt 2 φ - 0 (4.9) 83

24 1 2 2 φ0 β F J= AT exp - exp s kt (4.10) kt where, A = 4 π e m (kt) 2 /h 2 Now, it is possible to differentiate both Schottky and Poole-Frenkel effects in thin-film insulators from their different rate of change of conductivity with field strength [1]. From the slope of the plot lnj vs. F 1/2 /kt results in a straight line of slope β s or β PF depending on whether the conduction process is Richardson-Schottky or Poole-Frenkel Space Charge Limited Conduction An insulator does not contain donors and therefore normally not conduct significant current. However, if an ohmic contact is made to the insulator, the conduction band is capable of carrying current, because of the space charge injection. In this experiment, voltage applied across a thin diode causes an electrode to inject a nonequilibrium density of electronic charge, which populates the empty states above the Fermi level E F in the vicinity of the electrode. When the applied voltage is large enough, the rate of carrier injection from the contact exceeds the rate at which the carriers can be transported across the film; a space charge will be built up in the gap state of the material. Almost all the charges are trapped, but an extremely small fraction is thermally promoted to the conduction band edge. This increases the current, but the space charge opposition against the applied voltage impedes the flow of charge carriers. At low applied basis, if the injected carrier density is lower than the thermally generated free carrier density, Ohm s law is obeyed. When the injected carrier density is greater than the thermally generated free carrier density, the current becomes space charge limited. The electronic density of states distributed in the gap of insulating and polycrystalline thin films materials can be determined by measuring the space charge limited current. Experimentally, the space charge limited conduction can be identified from the slope of the current voltage characteristic curve. If the slope exceeds a value greater than two then the current is known as space charge limited current. This current provides information regarding the density of states above the equilibrium Fermi level. Valuable information can be obtained from the current-voltage dependence of materials. For the 84

25 case of trap free space charge limited conduction, the Mott and Gurney [7] equation is sufficient to establish the relation between the current and voltage. 9 εεμ 8d o 2 I= V 3 (4.11) where, μ is the drift mobility of the charge carriers, V is the applied voltage and d is the thickness of the insulator. This equation predicts that space charge limited current is proportional to V 2 and inversely proportional to d 3. Further, it predicts much higher currents than that observed in practice and the space charge currents are temperature independent. These results are contrary to the real experimental observations. The theory of space charge limited current in defect insulator has been proposed initially by Ross [8]. If the insulator contains traps, more number of the injection space charge will condense therein, which means that the free charge carrier density is much lower than in a perfect insulator. Moreover, since the occupancy of the traps is a function of temperature, the space charge limited current is also temperature dependent. If the insulator contains N t shallow traps positioned at energy E t below the conduction band, the ratio of free to trapped charges is given by, E t Nc θ = exp - Nt kt (4.12) where, N c is the density of states at room temperature. Thus the space charge limited conduction currents for an insulator with shallow traps is given by, I 9εεμθ 8d 0 2 = V 3 (4.13) From these equations, one can understand the dependence of current I with the applied voltage V. In the ohmic region, I is proportional to V and in the space charge trap limited current region I is proportional to V n with V>2. In the ohmic region, the I-V dependence should be of the form, V I μ (4.14) = Aq p P 0 d 85

26 where A is the electrode active area, q is the electronic charge μ p is the hole mobility and P o is the hole concentration. The hole mobility can be found from this equation [9]. I AV μ 11 pt -E t/kt = 6.51 x 10 e 3 dnt (4.15) This equation suggests that the plot of log 10 I vs. T -1 is a straight line and μ p can be determined from the slope and intercept. Also Lambert [10, 11] has suggested that the voltage V x at which the transition from ohmic to space charge limited conduction occurs to be, V x = e n θ ε o 0 d 2 ε (4.16) where n o is the injected free carrier density. If sufficient charge is injected into the insulator, the traps become filled (TFL). Further injected charge exists as free charge in the conduction band and contributes into current. Beyond the trap-filled limit, the current rises rapidly by an amount θ -1. The voltage V TFL at which the TFL occurs is given by, e N d t V TFL = (4.17) 2 ε ε 0 Thus from the I-V characteristics of an insulator one can identify the three possible regions, ohmic law region, traps square law region, and trap-free square law region. At lower voltages (V<V x ), the characteristic is ohmic, because the bulk-generated current exceeds the space charge limited current. In the voltage region V x < V < V TFL, the space charge limited current predominates and IαV 2. When V = V TFL, sufficient charge has been injected into the insulator to fill the traps. Therefore, when V exceeds V TFL, current increases rapidly and the I-V characteristics obey the trap-free law. From these observations, the trap concentrations in an insulator can be deduced Tunneling Conduction Transfer of electrons from one electrode to other by tunneling through a thin insulating film required strong electric field in the order of V/cm. If the potential drop between the electrodes is greater than the work function of the second 86

27 electrode, some of the tunnel electrons could pass through a thin layer without being attenuated significantly. According to quantum theory, the wave function of an electron has finite values within the classically forbidden barrier of a thin film insulator surrounded by two electrodes. If the energy of the electron is less than the potential barrier in the system, the electrons cannot penetrate the barrier, according to the classical theory. However, according to quantum theory, some electrons penetrate the barrier and reach the other electrode by tunneling through their Fermi surface levels. This tunneling process occurs only if the thickness of the film is in the order of few tens of angstroms. Also, if the applied field is very low, tunneling current is not possible Hopping Conduction Localized states arise in disordered materials due to defects in composition, impurities, lack of long-range order etc. If the space between these localized states are not very close to form the impurity band and if it is sufficient for phonon assisted tunneling, then this type of electrical conduction is known as hopping conduction. Since the localized states have quantized energies extending over a certain range, activation energy is required for each hop. Hopping occurs either near the Fermi level or near the maximum of the density of states. Hopping near the Fermi level dominates at low temperatures while hopping near the maximum of the density of states dominates at high temperatures. The hopping conduction is dominant only at low electric fields, because at high fields the heights of the potential barrier around a trap is lowered and hence release a charge carrier from localized states that predominates the hopping conduction process. Mott [12, 13] has proposed the mechanism of electrical conduction in amorphous semiconductors and defined the hopping conductivity as, 2 2 R σ = e ν o exp (-2αR- Δ /kt) (4.18) 6 where, R is the hopping distance, ν o is the frequency that depends on the strength of electron phonon coupling, exp (-2αR) is the probability for the charge carrier to transfer 87

28 by tunneling, 1 is the spatial extension of the wave function associated with the localized α states and exp (-Δ/kT) is the probability for the existence of phonon of energy (Δ). Hopping to a nearest neighbor is unfavorable at low temperatures because of the larger energy separation between them. Since most distant sites have smaller energy separation, tunneling is more favorable [13]. This type of long-range hopping is known as variable range hopping (VRH) process. In VRH process at low temperature, the hopping conductivity is defined as, 1 T 2 σ T = σo exp - o T 1 4 (4.19) where, T o is the Mott temperature and the pre-exponential factor σ o is related to the density of localized states N(E) and the wave function decay constant α by the relation, T C3α = k N(E ) where, C 3 is a number [14] and σ o is given by, f (4.20) σ o f A N(E) = α where A is a complex parameter given by [15], 2 3e γ ph A = 8π k γ ph is the phonon frequency which is nearly Hz [16]. The expression for the range of hopping in three dimensions is given by, Rhop ( T) = T 0 T a 8 where a is the localization radius and the activation energy for hopping is (4.21) (4.22) W hop o = k (T T ) (4.23) Experimentally, a plot is drawn between ln σ(t) versus T -1/4 and if it is a linear fit then the conductivity in that temperature range is said to be of the variable range hopping type. 88

29 According to Seto [17], the variation in conductivity at the high temperature region is given by, Ea σ T = σo exp (4.24) kt where, E a is the activation energy of conductivity. It is proposed that the trapped charges at grain boundaries produce carrier depletion and this further cause the grain boundary potentials. The grains at these high temperatures are spatially depleted and the transport is mainly due to thermionic emission of carriers over the grain boundaries [18]. 4.3 CURRENT VOLTAGE MEASUREMENTS The miniaturization of microelectronic devices enhances the speed and performance of modern electronics. Recently, dielectrics have attracted great attention in the field thin film capacitors. Magnesium oxide is considered as a potential replacement of SiO 2 due to its large band gap (>7 ev), high breakdown electric field (7-15 MV/cm) and low leakage current level. The conduction mechanism in MgO thin films is an important subject for these applications. Therefore, the electrical properties of MgO films are studied by means of current voltage measurements on the metal-insulatorsemiconductor (MIS) structure Preparation of MIS Structure In the present study, Al/MgO/Si structure was fabricated by the spray pyrolysis technique. Even though there is difficulty in fabrication of hetero-structures with good interface quality, some researches have been reported about the feasibility of making MgO/Si structure with out inter-diffusion [19-23]. Reported results shown that the MgO layers in contact with Si substrate at RT is stable and the probability of formation of silicate interface layer increases as the deposition temperature increases. MgO films were deposited on single crystalline (111) Si at the optimized deposition temperature of 450 o C. Prior to deposition, Si wafers of resistivity 2-5 Ω cm were thoroughly cleaned by agitating in trichloroethylene (TCE) and acetone, with an intermittent cleaning by deionized and doubly distilled water. Later they were etched in hydrofluoric acid in order to remove the residual oxide. After drying, the wafers were 89

30 transferred to the substrate holder for MgO film deposition. The substrate holder was placed over a heater and the distance between the substrate and nozzle was adjusted for uniform coating. Magnesium acetate in ethanol was used as the precursor of MgO with an acid catalyst and tri ethylene glycol (TEG) was also added with the solvent to facilitate high temperature processing. The precursor was sprayed into fine droplets from the atomizer and was carried to the substrate by a compressed carrier gas. The sprayed solution of magnesium acetate was thermally decomposed into oxide layer on the silicon substrate. Deposited MgO films are adherent to the substrate and appeared uniform and shiny with a bright blue color. The thicknesses of the deposited films were measured using the styles profiler and the thickness is found to be μm. The crystallographic structure and orientation of the films were determined with a x-ray diffractometer using the CuKα radiation. The XRD pattern of the as-deposited film at the deposition temperature 450 o C is shown in Fig The XRD pattern revealed the fact that the films are (200) dominant. The (200) peak domination may be due the lower energy requirements during nucleation, that leads the migration of molecules to the growing plane. The (200) plane is energetically stable and hence the migrated Mg and O species are fixed to that plane and forming stable (220) layer. Comparatively the other peak (220) is weak indicates that the heating energy of the substrate provides insufficient migration for the surface atoms to form the layer. The peak at 2θ=28.86 corresponds to the (111) reflection of the Si substrate. After structural confirmation, circular aluminium dot electrode of diameter 2mm were evaporated on to the film top surface to obtain the MOS capacitor structure. Fig. 4.4 shows a sketch of the sandwich structure of the test capacitor. After identifying the crystallinity modifications using XRD, aluminium contact electrode was made over the films surface. Aluminium is chosen as electrode material because of its small grain size in comparison with film thickness [24] Circuit Description The measurement of the electrical properties of high resistivity semiconductors and insulators is complicated by factors, which are considered to be of second order in 90

31 low resistivity materials and often can be ignored. In high resistivity materials, contact resistance affects the accuracy of measurements due to the presence of space charges, which distort their internal electric fields. The stray capacitance of leads and cables and the large specimen resistance produce long time constants for achieving steady-state conditions during the measurements. Further, high specimen resistance requires high impedance current and voltage apparatus for precise measurements. A common method of measurement is to use a single power supply and two sensitive detectors, one for current and the other for voltage measurements. In the present study, the circuit used for measuring current and voltage of MgO specimens that offer high DC resistance is shown in Fig. 4.5 The dc investigation was carried out in a heating chamber capable of heating the samples in the temperature range C. The specimens were placed in intimate thermal contact with a block of copper and care was taken to allow sufficient time for thermal equilibrium to be attained. With this apparatus, the temperature can be maintained with in ± θ.1 C during the time required to measure the current and voltage. The controlled temperature is measured with a digital thermometer (CE-305) to a precision of ±0.1 C. The dc volt-current characteristics at constant temperature are measured by setting a predetermined voltage across the junction (M 1 ). The current through the junction is measured from the voltage (M 2 ) drop across the resistance R (± 0.05%) in series with the sample. The electrometers used are the high input impedance type (Oriel) meters. A DC power source, supply the voltage (V) which can be varied between 0 and 100 V by means of a potentiometer. Voltage is maintained with in the limit to avoid carrier injection and sample heating. The characteristics are reproducible and reversible, tested for many trials I-V Measurements on MgO Thin Films Electrical properties of spray deposited film are measured by applying direct current in the temperature range o C and covering a wide range of electric fields. Fig. 4.6 shows the doubly logarithmic I-V characteristics of MgO film deposited over Si 91

32 substrates for a thickness of μm. As seen from the figure, for a wide range of electric fields (20-20x10 4 V/cm), three regions of conduction occurs. Ionic and ohmic region at low fields (Region I), space charge effects at moderate fields (Region II) and thermally activated field assisted hopping process (Poole-Frenkel conduction) at high fields. It is evident from Fig. 4.6, region I and II are distinguishable at lower fields. Region I corresponds to ohmic conduction and is observed at low fields and it has strong temperature dependence. In comparison, region II shows faster increase of current with voltage. This nature suggests that the current conduction is purely electronic. The activation energy in these two regions pertaining to constant electric field is deduced from the Arrhenius plot and is displayed in Fig The activation energy of the ohmic region I is ~0.64 ev and this value is comparatively larger than the values in other regions. Higher value of activation energy is assigned to the ionic conduction and their decrease revealed the beginning of electronic conduction from ionic conduction. Region III is the high field region in which the I-V characteristic exhibits a straight line and is represented as log I against V 1/2 in Fig In this linear region, the current-voltage dependence can be explained with the barrier lowering equation, 1 2 I = Io exp e 3βE Va / kt (4.25) where, E = V d is the applied field, d is the film thickness, V a is the barrier height for thermal excitation and β is given by 1 2 e β = a π εε 0 (4.26) where, e is the electronic charge ε is the high frequency dielectric constant. The coefficient a=4 for Richardson-Schottky emission [25] and a=1 for Poole-Frankel emission [2]. The high frequency dielectric constant ε is given by [20]. ε = n 2 (4.27) 92

33 where n is the refractive index of the material. For MgO thin film, the theoretical value of β is calculated by assuming the refractive index n as and is found to be 2.18 x The value of β found from the slope of the straight lines in Fig. 4.8 is 2.86 x This value agrees very well with the theoretical value if the parameter a is chosen as 4. This would appear to support the Schottky barrier mechanism. The I-V characteristic curves can also be drawn as ln I against 1/kT at constant V. Their slopes should be equal to (βe 1/2 -V a ) according to equation From the slopes, the barrier height E a for excitation should be obtainable (Fig. 4.7). Plotted graph is a straight line with slope (-β) and the projection of the line to E=0 gives a zero-field activation energy ~ ev. This value is in agreement with the activation energy of the MgO thin films calculated in the previous chapter (Chapter III). Hartman et al [27] deduced high frequency dielectric constants of 3 and 12 for Schottky and Poole-Frenkel emission respectively. A value of 3 is reasonable for the high frequency dielectric constant of MgO and 12 is impossible for the prepared MgO films. In view of the above facts, it is almost certain that β is consistent with β s rather than β PF. From this observation, it is apparent that the field dependent conductivity in MgO-MIS structure, which fits the Richardson-Schottky law rather than the Poole-Frenkel law. 4.4 A.C IMPEDANCE AND MODULUS SPECTROSCOPY STUDIES ON MgO THIN FILMS Basically, magnesium oxide is an insulating material having the special property of strong and dissipating electrical energy when subjected to electromagnetic field. This material in thin film form, find a wide range of application as capacitors and secondary electron emitters in ac plasma display panels. A study of this material, particularly in a.c fields provides an insight into the electrical conduction behavior. Usually a dielectric film is sandwiched between two electrodes to form a metal-insulator-semiconductor (MIS) structure and is subjected to ac impedance studies. Capacitors, which have high working voltages and ability to withstand very low and high temperatures and a wide spectrum of frequencies, are always desirable. Hence, it is desirable to study their dielectric properties namely, the dielectric constant, loss 93

34 tangent, dielectric strength, current transport mechanism etc. and their dependence with temperature and frequency. The impedance spectroscopy is a powerful technique to characterize may electrical properties of materials. It is useful to evaluate and separate the contribution of the over all electrical properties in the frequency domain due to electrode reactions at the electrode / film interface and migrations of ions through the grains and across the grain boundaries in a polycrystalline material. Detailed literature survey reveals that no work has been done on ion implanted MgO ceramics. However, impedance studies and frequency response at different temperatures of other oxide and related materials have been reported [28-32]. In the present study, electrical properties (material impedance, electrical relaxation process, dielectric behavior, electrical relaxation process, electrical modulus, etc) of MgO and MgO implanted with H +, Li + ions are analyzed using the complex impedance spectroscopy technique Principle of Impedance Spectroscopy The simplest method of measuring the dielectric properties of a material is to subject it to an electric field and to record the polarization developed in the sample with time. Experimentally, a step-voltage is applied to the sample and the current is recorded as a function of time. A decreasing curve is obtained in a way until a stationary level corresponding to the ohmic conductivity is reached. When the voltage is switched off, a similar current response of opposite sign is recorded. A step-function represents a wide Fourier-spectrum containing component of very low frequencies (depending on the duration of the recording) up to very high frequencies (depending on the rise time of the step function). Thus, the recorded current response contains all the information needed for constructing the recorded spectrum. In order to extract the information from the recorded spectrum in the wide frequency range from about 10-4 Hz up to Hz, the recorded current response is subjected to Fourier transformation to get the dielectric spectrum. The complex impedance spectroscopy is a non-destructive experimental technique for the characterization of micro structural and electrical (impedance/dielectric) 94

35 properties of electro ceramic system. These systems have potential applications in a diverse range of fields, including chemical sensors, fuel cells, and electronic and electrooptical systems. For thin film systems, parallel plate electrode geometry is used to apply a small sinusoidal voltage to the sample. The impedance of the sample (both resistive and reactive contributions) is measured over wide range of frequencies. The advantage of impedance spectroscopy over static frequency techniques is that for a complicated system, individual components (grain and grain boundary phases) in poly crystalline electro ceramics can be separated and characterized according to their different relaxation times/frequencies Dielectric Measuring Technique Initially, the Al/MgO/p-Si MIS capacitor structure was fabricated on p-type single crystal silicon wafer. Ohmic contact of the electrodes was formed by evaporating Al in high vacuum and subsequently annealing them for a few minutes at 450 o C. The area of the top electrode is 3.14 mm 2. The thickness of the MgO thin film was determined with a profilometer. For fabricating ion implanted MIS structure, prepared MgO thin films were irradiated with 1.5 MeV H + and Li + beam for a fluence of ions/cm 2. After confirming the structural modifications, Ohmic contacts were formed over the surface of the MgO film. In the present study, three different MIS capacitor was fabricated (Al/MgO/p-Si, Al/MgO-H + /p-si, Al/MgO-Li + /PSi) for impedance and modulus measurements. The impedance measurements were carried out in the frequency range 40 Hz to 100 khz using HP 4192 A LF impedance analyzer at the test signal of 40 mv rms. All measurements were carried out in the temperature range o C. For the accurate measurement of dielectric constant, it is necessary to apply thin metallic electrode to the specimen before it is placed in the measuring cell. When electrodes are applied to the two sides of the sample, the capacitance between them is greater than that defined by the electrodes. This is due to the edge capacitance beyond the electrodes and the capacitance to ground of the high electrode. Also, the magnitude of the edge capacitance depends on the size of the specimen and is proportional to the electrode perimeter. Edge capacitance effect arises due to the size of the electrodes and is smaller if the electrodes are unequal. In addition to edge capacitance, ground capacitance also adds 95

36 to the effective capacitance of the structure and it depends on the distance of the high electrode from the grounded surface of the equipment. The effect of both capacitances can be eliminated by the use of micrometer electrodes. The connecting leads have both inductance and resistance, which at high frequencies, increases the measured capacitance (C) and dissipation factor (D). The changes in C and D are given by, ΔC = ω 2 LC 2 (4.28) ΔD = RωC (4.29) where, L is the series inductance, R is the series resistance of the lead and C is the capacitance of the capacitor. Therefore, it is desirable to have leads as short as possible. In the present study, all these requirements are taken into consideration for the accurate measurements of impedance parameters. The complex impedance and complex electric modulus formalism have been discussed for the characterization of electrical properties of some electro ceramic materials [33-37]. The technique is based on analyzing the ac response of a system to a sinusoidal perturbation and subsequent calculation of impedance as a function of the frequency of the perturbation. The analysis of the electrical properties carried out using relaxation frequency values gives unambiguous results when compared with those obtained at an arbitrarily selected fixed frequency. The frequency dependent properties of a material can be described as complex permittivity (ε*), complex impedance (Z*) complex admittance (y*), complex electric modulus (M*) and dielectric loss or dissipation factor (tan δ). The real and imaginary parts of these complex parameters are interrelated as, ε * = ε - jε (4.30) where, ' ε = ε " = 0 z " '2 "2 ( Z Z ) ω C + 0 Z' '2 "2 ( + ) ωc Z Z (4.31) (4.32) " 1 * M * = M' + j M = jωε * 0Z ε = (4.33) 96

37 1 Z * = Z' - j Z" = j ω Co ε * (4.34) * ' * Y = Y + j Y" = jωcoε (4.35) " ε M" Z' Y' tan δ = = = = (4.36) " " ε ' M' Z Y where, ω = 2πf is the angular frequency and C o is the geometrical capacitance of the films i.e., C o = ε o (A/d), where ε o is the permittivity of free space (8.85 x F/m) and A, d are the area of the top electrode and thickness of the dielectric layer respectively Complex Impedance Spectroscopy Studies Impedance analysis has been widely used to study the dielectric behavior of polycrystalline ceramic material. In general, the dielectric properties of materials arise due to intra-grain, inter-grain and other electrode effects. In dielectrics, the motion of charge could take place by charge displacement, dipole reorientation, space charge formation etc [38, 39]. In order to understand the electric properties of a sample, grain, grain boundary and electrode combinations must be separated out. To achieve this, appropriate equivalent circuit representation has been formulated interms of impedance. In the present study, the impedance, dielectric and modulus analysis are carried out by forming metal-insulator-semiconductor (MIS) structure. Magnesium oxide thin films acts as the insulating layer between the silicon and aluminium electrodes. The effect of implantation on MgO film surface with H + and Li + ions and their dependence in impedance and dielectric properties have been analyzed. Obtained results are summarized in the coming sections Impedance Analysis Nyquist plot analysis is used to characterize bulk grain, grain boundary and electrode interface contribution from the successive semicircles of impedance exhibiting in the complex plane. This enables one to study the grain or bulk resistance (R g ) and grain boundary resistance (R gb ), which are useful in understanding the charge transfer phenomena. 97

38 Fig. 4.9 shows the Nyquist plot of the fabricated capacitor with MgO thin films as a dielectric layer between electrodes recorded at room temperature. The impedance plot exhibits semicircle of impedance in the real and imaginary planes. Semicircles can be used to characterize bulk grain, grain boundary and electrode interface configurations. Usually high frequency semicircle originates from the bulk conduction and dielectric processes. Low frequency semicircle is due to ion and electron transfer at the surface containing the electrode. Intermediate frequency semicircle provides information on the grain boundary and/or impurity phase impedance. For the present MIS structure, only one semicircle in the intermediate frequency region is seen which is ascribed to the grain boundary contribution. This type of impedance variation can be represented as an equivalent circuit, which consists of a resistive element in parallel with a capacitor. This is the most common interpretation for polycrystalline materials like MgO, having a contribution of grain boundary. The frequency at the semicircle maxima ω max for each RC element is given by, ω max = 2πf max = (RC) -1 = τ -1 (4.37) where, τ = RC is the relaxation time for the respective regions. Usually, the capacitance of the grain boundaries is larger than that of the bulk grain. Therefore, the relaxation time τ = RC =ρε r ε o (4.38) is larger for the grain boundaries. The grain boundary resistance of the sample is extracted from the Nyquist plot, which is of the order of megohm (28.19 MΩ). The capacitance value for the grain boundaries is calculated by noting the frequencies at the Debye peak maxima and is found to be in the order of picofarad (14 pf). This result is in agreement with the reported values for the TiO 2 thin film capacitors [40]. The relaxation time of the process is about 3.95 x 10-4 sec, which is due to the rotational fluctuations of molecular dipoles. If the frequency of the applied electric field corresponds to reorientation time (τ) of molecular dipoles, the imaginary part of impedance shows a characteristic pattern. In addition, the semicircular arc starts at the origin; hence, no series electrode resistance is included in the equivalent circuit representation. The frequency and temperature dependence of Z (real part of the complex impedance) and Z (imaginary part of complex impedance) are shown in Fig and Fig respectively. It is observed that the magnitude of Z decreases with the increase 98

39 in frequency and temperature. At high frequencies, Z values reach almost zero and this may be due to the release of space charges. The curve also display single relaxation process and indicate decrease in ac conductivity with frequency. The relaxation time (τ) is calculated from the frequency (f max ) at which Z max is observed. The peak height is proportional to the grain boundary resistances according to the following equation in Z vs. frequency plot. ωτ Z " = R 1 ( + ωτ 2 2 ) (4.39) Moreover, in the Z plot, the peak shifts towards higher frequencies as the temperature increases. The magnitude of the imaginary component of the impedance at the peak frequency is also a strong decreasing function of temperature. An Arrhenius plot is drawn between 1000/T and ln (f max ) and the plot slows the thermally activated behavior and the corresponding activation energy is 0.28 ev which is in agreement with many of the dielectric ceramic capacitors [41]. The values of grain boundary resistance (R gb ) and grain boundary capacitance (C gb ) are evaluated from the Nyquist and Z plots and given in Table 4.1. The variations of these parameters with temperature are shown in Fig It is evident from figure that grain boundary resistance decreases and grain boundary capacitance increases with temperature. At lower temperature, the slope of the Nyquist plot is higher, yielding higher grain boundary resistance due to the insulating behavior of the material. With the rise in temperature, the slope of the plot decreases and makes the curves towards less resistive regions. The changes in R gb and the shift in Z with temperature change the grain boundary capacitance accordingly. 99

40 Table 4.1 Impedance parameter of the fabricated MIS structure Impedance parameter Al/MgO/Si at temperature ( C) Grain boundary resistance (R gb ) (MΩ) Grain boundary capacitance (C gb ) pf Grain boundary relaxation time (τ)x10-5 sec Bode plot slope (capacitive behavior) (30 C) Barrier layer capacitance at 1kHz (30 C) (pf) The Bode plot (Fig. 4.13) at room temperature suggests the capacitive behavior of electrode as log Z varies linearly with log (f). Slope of the curve is , which is very close to the theoretical value of -1 for a pure capacitor. Under this condition, Z is related with frequency as, log (Z) = -log (f) log C bl (4.40) where, C bl is the barrier layer capacitance. The value of C bl obtained from Fig is 0.93 nf at room temperature. Also, it is obtained from Fig. 4.13, the value of tan (δ) at 40 Hz and 10 khz are respectively and Dielectric loss factor (tan (δ)) at low frequencies are relatively large, which confirms the contribution of the d.c conductivity to the dielectric magnesium oxide. 100

41 Modulus Analysis The complex dielectric function ε* and its dependence on external electric field frequency and temperature originates from different processes like microscopic fluctuations of molecular dipoles, propagation of mobile charge carriers, polarization due to separation of charges at the interface etc. Contribution of polarization of charges at the interface to the dielectric loss can be orders of magnitude larger than the dielectric response due to molecular fluctuations. The microscopic and macroscopic processes have frequency and temperature dependence of the real and imaginary part of the complex dielectric function. The methods, to quantify the contributions to the dielectric spectra are discussed in this section. Relaxation process are characterized by a peak in the imaginary part ε and a step like decrease of the real part ε of the complex dielectric function ε* = ε j ε with increasing frequency. In contrast, conduction phenomena show an increase of the imaginary part of the dielectric function with decreasing frequency. For pure ohmic conduction, the real part of ε* is independent of frequency and for non-ohmic conduction, the real part of ε* increases with decreasing frequency. Further, the investigation of relaxation process that is related to the rotational fluctuation of molecular dipoles can be analyzed with the complex dielectric function ε*. If the frequency of the applied electric field equals the reorientation time τ of the molecular dipoles, ε decreases with frequency and ε exhibits a maximum. The frequency corresponds to ε maximum is the relaxation frequency of the fluctuating dipoles. The dipole strength Δε of a relaxation process can be determined from the loss peak ε or from the step in ε. In order to allow accurate assessment of the impedance data, complex electric modulus formalism have been discussed for various dielectric materials [42, 43]. In modulus formalism, the electric modulus M* is defined interms of the reciprocal of the complex relative permittivity ε*. M * 1 = = M' + jm" (4.41) * ε 101

42 where, * ε = 1 jωc 0 Z * (4.42) M M ' " ' ε = '2 "2 ε + ε " ε = ε + ε '2 "2 (4.43) (4.44) C 0 is the vacuum capacitance of the sample holder. The modulus data expressed in the complex modulus formalism enables to understand the phenomenon of conductivity relaxation in terms of variation of M and M as a function of frequency and temperature. The complex modulus plane analysis is based on the plot of imaginary part of M against real part of M over a wide range of frequencies (40 Hz to 100 khz in the present study). The plot is a single or a series of semicircular arcs. Each semicircular arc represents the parallel combination of resistance and capacitance of grain/grain boundary/electrode interface contribution in the conduction process. The semicircular arc in the low frequency region represents grain boundary/electrode interface contribution and an arc in the high frequency region represents the dominance of bulk grains. Magnesium oxide, the material considered in the present study exhibits a single semicircular arc in the low frequency region representing the dominance of grain boundary impedance. The impedance element representing the film/electrode interface is negligible because of the lower value of contact resistance. Extracting the values of R gb, the grain boundary resistance; C gb, grain boundary capacitance and τ, the relaxation time are discussed in detail in the previous section. In this section, importance is given to the electric modulus response with frequency at different temperatures. The real and imaginary component of dielectric constant of the material is determined initially to find out the electric modulus M*. Frequency dependence of real (ε ) and imaginary (ε ) parts of dielectric constant for the MgO thin film at different temperatures are shown respectively in Fig and Fig Both the pattern present dispersion in the lower frequency region, while they merge above 1 khz. It can be seen that at low frequency region, ε increases up to 50 o C 102

43 and then decreases, where as ε gradually decreases with temperature. This may possibly be due to the electrical conductivity of the material that modifies the value of the capacitance as the temperature increases. Because of the polarization effect the real part of ε* increases with decreasing frequency [44]. Fig and Fig shows the real and imaginary parts of the electric modulus M* as a function of frequency over a range of temperature. The value of M is very low nearly zero at the low frequency region, a continuous rise with dispersion in high frequency region and have a tendency to saturate at a maximum asymptotic value designated M for all temperatures. This observation may possibly be related to a lack of restoring force governing the mobility of charge carriers under the action of an induced electric field. This supports the long-range mobility of charge carriers. The step increase in the value of M may be attributed to the short-range mobility of carriers. The variation of M with frequency exhibits well-resolved peaks at characteristic frequency that depends on temperature. In addition, the peak positions have the tendency to move towards higher frequency side with the rise in temperature. The low frequency side of the M peak represents the range of frequencies in which the charge carriers can move over a long distance. Due to long-range mobility, the carriers can perform hopping from one site to the neighboring site. High frequency side indicates the range of frequencies in which the charge carriers are spatially confine to their potential well and therefore only localized motion within the well alone be possible. At the peak frequency region, the transition from long-range to short-range mobility is possible. 4.5 AC CONDUCTIVITY Measurement of AC conductivity in insulating materials has been extensively used to understand the conduction process in these materials. The generally accepted view is that the AC conductivity is dominated by localized states within the energy gap. Measurement of AC conductivity is therefore a powerful experimental method to obtain information about the localized states. Many workers [45-47] have carried out such measurements on a variety of materials. In the present study, complex impedance spectroscopy (CIS) has been carried out for describing the electrical processes occurring in a system on applying an AC signal 103

44 across the sample sandwiched between the electrodes. The output response of such an experimental measurement, when depicted in a complex plane plot, appears in the form of a succession of semicircles representing the contribution to the electrical properties due to the bulk material, grain boundary effect and interfacial polarization. CIS technique is therefore useful to separate the effects arising from each component in a polycrystalline sample very easily. Impedance measurements on a material provide data having both resistive (real part) and reactive (imaginary part) components. It can be displayed in a complex plane plot interms of any of the formalism like complex impedance, complex admittance, complex permittivity, and complex modules. Moreover, the peak of the semicircular arc in the complex impedance spectrum provides the relaxation frequency of the material and their respective resistance and capacitances. The bulk conductivity (σ dc ) of a material is a thermally activated process obeying Arrhenius behavior, which can be estimated interms of the bulk resistance (R b ) evaluated from complex impedance spectrum. The bulk conductivity can be calculated in accordance with the relation, σ dc = 1 R b d (4.45) A where, d is the thickness and A is the area of the sample. The AC conductivity of the material describing the frequency dependent behavior of the conduction process can be evaluated in accordance with the relation. σ AC = ω ε ε o tan δ (4.46) where, tan δ is the dielectric loss, ε the permittivity and ε o the permittivity in vacuum Experimental Details Thin films of magnesium oxide were obtained by conventional spray pyrolysis technique. The film thickness ranged in μm and was measured using stylus profiler. For AC measurements, films were sandwiched between two electrodes. Top aluminium electrode is thermally evaporated on to the MgO film surface to a pre-defined area and the silicon substrate served as the bottom electrode. A programmable LCZ bridge was used to measure the impedance Z, the capacitance C and the phase φ directly. The total conductivity was calculated from the equation. 104