P type transparent conducting CU AL o thin films prepared by PE MOCVD 3

Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue It is noted that the films were of different thicknesses After being normalized to the same thickness of 100nm, the difference in the transmittance (shown in Figure 5-9(b)) of films was smaller except for the film grown at the lowest temperature The main reason of the large transmittance of the film grown at 650°C might be the different compositions compared with other films because only this film showed a different XRD spectrum (Figure 5-8) SEM was used to observe the morphology of the films (shown in Figure 5-10) except the sample grown at 650°C, because it was non-conductive and charged under electron bombardment When the substrate temperature was low, the film was composed of nano-particles of 25-50nm When the substrate temperature increased, the nano-particles gradually linked to each other When the temperature reached 800°C, no obvious particles and intersected chains appeared AFM was also employed to view the morphology of the films In Figure 5-11, it is clear that the surface of the film grown at 650°C was quite flat and there were some islands of about 100nm diameter In the film grown at 700°C, more and smaller (2050nm) islands appeared In the film grown at 750°C, rougher and more connected stalagmitic islands were observed However, when temperature increased further, the islands turned into flatter clusters with ridges Here film grown at 750°C appeared to show different information from what was gathered from SEM This is due to the over-enhanced z-scale effect of the AFM image P-type transparent conducting Cu-Al-O thin films 110 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue (a) (b) (c) (d) Figure 5-11 AFM images of the films grown at different temperatures, (a) 650°C, (b) 700°C, (c) 750°C and (d) 800°C The data scale of z axis is 50nm Optical Bandgap (eV) 3.64 3.60 3.56 3.52 3.48 3.44 650 700 750 800 O Growth Temperature ( C) Figure 5-12 Optical bandgaps of the films prepared from dpm precursors versus growth temperature P-type transparent conducting Cu-Al-O thin films 111 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue Figure 5-12 shows growth temperature dependence of the direct optical bandgap of the as-deposited films The bandgap was estimated from a plot of (αhν)2 versus hν which yielded a straight line with an intercept on the hν axis (see appendix B) The film grown at 650°C showed the largest optical bandgap of 3.62eV The bandgap was the smallest at 700°C with the value of 3.45eV and then increased with the growth temperature The bandgap of the films correlated with the result of optical transmittance A film with larger bandgap appeared to have a higher transmittance The electrical properties of the films including sheet resistance, conductivity, mobility and Hall coefficient are listed in Table 5-2 The film grown at 650°C was an insulator showing no conductivity From the table, both the conductivity and carrier concentration increased with the growth temperature The bandgap widening with the growth temperature mentioned above could be due to the increase of the carrier concentration, i.e., the Burstein shift (refer to section 5.4.2) took effect Croitoru and Bannett 11 suggested that the contribution of grain boundary scattering potential decreased as the substrate temperature increased With an increase in substrate temperature, the grain size increased12 causing a decrease in grain boundary potential and hence an increase in mobility The decrease in grain boundary potential could also be responsible for an increase in carrier concentration with substrate temperature, thus an improvement in conductivity The mobility was of the order of 1.0cm2·V-1·s-1 The Hall coefficient was positive at first, and then decreased with the growth temperature and the sign became negative for the film grown at 800°C The positive sign undoubtedly indicated p-type conductivity of the films P-type transparent conducting Cu-Al-O thin films 112 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue Table 5-2 Electrical properties of the as-deposited films prepared from dpm precursors (“∞” means out of range, “⎯” means not measurable) Film A Film B Film C Film D Growth temperature (°C) 650 700 750 800 Sheet resistance (Ω/sq) ∞ 108500 12600 3081 Bulk conductivity (S·cm-1) ∞ 0.91 5.88 17.2 Mobility (cm2·V-1·s-1) ⎯ 1.07 2.33 ⎯ Sheet Hall coefficient (m2·c-1) ⎯ +11.6 +2.95 -0.32 Sheet carrier concentration (×1013cm-2) ⎯ 5.38 21.2 ⎯ Bulk carrier concentration (×1018cm-3) ⎯ 5.33 15.7 ⎯ Referring to the expression of Hall coefficient in Appendix C (Eq.C-14), the sign change of Hall coefficient might be due to the existence of two types of charge carriers In the present films, as the crystal size was nanoscale, grain boundary scattering was a very important factor to affect the mobility of the carriers Because the mass of a hole was much larger than that of an electron, the mobility of a hole was reduced more than that of an electron.13 This resulted in a larger value of b ( b = − µn , µp where b>0, µn, µp are drift mobilities of electrons and holes, respectively) Although the hole concentration p was larger than the electron concentration n, the Hall coefficient R might be negative, which led to inaccurate results and even the wrong sign for the conductivity type In the growth process, a small amount of Cu+ ions were oxidized to Cu2+ ions, which acted as electron donors With the increase of growth temperature more Cu2+ ions existed, causing the inversion of the Hall coefficient From Appendix C, it is known that all the data for conductivity are reliable For the P-type transparent conducting Cu-Al-O thin films 113 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue films grown at 700°C and 750°C, the actual Hall coefficient and mobility for hole conduction should be larger than the experimental data but the actual hole concentration should be smaller However, this does not affect the qualitative analysis given in last chapter and this chapter For the film grown at 800°C, probably because nb2>p, the Hall coefficient, mobility and carrier concentration changed sign and the experimental values for these parameters were meaningless To confirm the type of conduction, the Seebeck coefficient was measured A plot of ∆V versus ∆T of the film grown at 800°C is shown in Figure 5-13 Here ∆V is the voltage difference and ∆T is the temperature difference between two ends of the film From the linear fit of the figure, the Seebeck coefficient was found to be +5.45µV/K, indicating p-type conductivity The Seebeck coefficients of the as-deposited films are listed in Table 5-3 0.06 ∆V (mv) 0.05 0.04 0.03 0.02 0.01 0.00 10 O ∆T ( C) Figure 5-13 Seebeck measurement (∆V versus ∆T) of the film grown at 800°C The solid line is the linear fit curve P-type transparent conducting Cu-Al-O thin films 114 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue Table 5-3 Seebeck coefficients of the as-deposited films prepared at different growth temperatures Film A Film B Film C Film D Growth temperature 650°C 700°C 750°C 800°C Seebeck coefficient ── 30.0µV/K 22.5µV/K 5.45µV/K As reported by Kawazoe et al.5, the Seebeck coefficient of CuAlO2 prepared by laser ablation was +183µV/K with conductivity of 0.095S·cm-1 Nagarajan et al.14 reported that the Seebeck coefficient of CuYO2 prepared by thermal co-evaporation was +284µV/K with conductivity of 0.025S·cm-1 All these values were much larger than those found in the present study The Seebeck coefficient decreased with the increase of conductivity can be explained by referring to the Seebeck coefficient of degenerate semiconductors given by15 α ≅ π k B T / 3eE F … ……………………………… (5-3) where kB is Boltzmann’s constant For p-type semiconductors, EF is the Fermi energy measured from the top of the valence band For p-type degenerate semiconductor, the Fermi level is below the top of the valence band High carrier concentration causes high conductivity and pushes the Fermi level down, leading to a small value of the Seebeck coefficient Compared with other works, the present films had better conductivities and smaller Seebeck coefficients and the Seebeck coefficient decreased when the conductivity increased This conclusion is also applicable to a nondegenerate system as the expression of the Seebeck coefficient is of the form15 α= E kB ( + A − F ) … ……………………… (5-4) k BT e P-type transparent conducting Cu-Al-O thin films 115 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue where A is a constant related to the scattering mechanism and here EF is negative With the increase of carrier concentration, the Fermi level becomes closer to the valence band for a p-type sample, and thus a smaller Seebeck coefficient To investigate the conduction mechanism of the films, the temperature dependence of resistance was measured in vacuum (2×10-5Torr) from RT to 200°C The resistance was determined by the two-probe method and the temperature was controlled by a temperature controller and measured by a thermalcouple that was in contact with the film surface The natural logarithm of the inverse of resistance as a function of temperature is plotted in Figure 5-14 When the growth substrate temperature was 800°C, ln(1/R) decreased with the inverse of temperature linearly (see Figure 5-14(a)) However, for the films grown at lower temperatures, the curves were obviously not linear (Figure 5-14(b) and (c)) This suggested different conduction mechanisms for the films grown at different temperatures The details of the conduction mechanisms will be described in section 5.4.1 5.3.3 The effect of oxygen flow rate on the properties of Cu-Al-O films In this part, the properties of copper aluminum oxide prepared from dpm precursors with the varying oxygen flow rates will be discussed In the work described in section 4.3.3, it was observed that oxygen flow rate had no obvious effect on the transmittance of the films and there was an optimum value for conductivity In this section, the oxygen flow rate was varied from 20 to 35sccm, and other growth parameters were kept constant: the substrate temperature at 750°C, the Ar flow at 30sccm, the pressure at 75mTorr and the plasma power at 200W P-type transparent conducting Cu-Al-O thin films 116 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue 1000/T (1000/K) 2.2 -7.71 2.4 2.6 3.0 3.2 O -7.73 ln(1/R) 2.8 Grown at 800 C -7.75 -7.77 -7.79 -7.81 (a) -7.83 440 420 400 380 360 340 320 T (K) 1000/T (1000/K) 2.2 2.4 2.6 2.8 3.0 -8.79 3.2 O Grown at 750 C ln(1/R) -8.82 -8.85 -8.88 -8.91 (b) -8.94 440 420 400 380 360 340 320 T (K) 1000/T (1000/K) 2.2 -11.8 2.4 2.6 2.8 3.0 ln(1/R) -11.9 3.2 O Grown at 700 C -12.0 -12.1 -12.2 -12.3 -12.4 (c) (c) -12.5 440 420 400 380 360 340 320 T (K) Figure 5-14 Natural logarithm of the inverse of resistance as a function of temperature for the films prepared from dpm precursors at substrate temperatures of (a) 800°C, (b) 750°C and (c) 700°C The unit of resistance R is ohm P-type transparent conducting Cu-Al-O thin films 117 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue Growth Rate (nm/min) 3.0 2.7 2.4 2.1 1.8 20 25 30 35 Oxygen Flow Rate (sccm) Figure 5-15 Growth rate of films prepared from dpm precursors versus oxygen flow rate The growth rate (Figure 5-15) first decreased with the increase of oxygen flow rate, and then rose slightly when the oxygen flow rate exceeded 30sccm Films grown at 30sccm showed the lowest growth rate Intensity (a.u.) • β-CuAlO2 • 35sccm • • 30sccm 25sccm 20sccm 10 20 30 40 50 60 70 80 Scattering Angle 2θ (deg.) Figure 5-16 XRD spectra of the films prepared from dpm precursors at different oxygen flow rates P-type transparent conducting Cu-Al-O thin films 118 Chapter Properties of Cu-Al-O films grown from dpm precursors Wang Yue XRD spectra of the films are shown in Figure 5-16 The peaks were located at 43.36° (2.088Å), 50.42° (1.810Å), 74.18° (1.279Å) and a big hump existed around 21.30° (4.173Å) All the peaks matched the PDF of β-CuAlO2 and the hump was from the quartz substrate but might also contain the peak from β-CuAlO2 Figure 5-17 shows a high-resolution TEM image of the film grown at 35sccm oxygen flow There were clearly grains of crystals in Figure 5-17 and the sizes of the grains were all less than 10nm The lattice spacings were measured to be around 2.84±0.02Å and 2.46±0.02Å These values could all be attributed to rhombohedral CuAlO2 and the 2.460Å could also be attributed to Cu2O Figure 5-17 A high-resolution TEM image of the film grown at 35sccm oxygen flow rate Referring to the discussion in Chapter 4, rhombohedral CuAlO2 existed in the film as nanograins with preferred orientation and could not be observed by XRD β-CuAlO2 detected by XRD decomposed to Cu2O under electron bombardment or upon heating P-type transparent conducting Cu-Al-O thin films 119 Chapter Properties of Cu-Al-O films grown from dpm precursors 31 32 33 34 35 36 37 Wang Yue N F Mott, Conduction in non-crystalline materials, Clarendon Press, Oxford (1987) W N Shafarman and T G Castner, Phys Rev B33, 3570 (1986) R Mansfield, Hopping transport in solids (eds M Pollak and B I Shklovskii), Elsevier Science, Amsterdam (1991) A L Efror and B I Shklovskii, J Phys C: Solid State Phys 8, L49 (1975) B J Ingram, T O Mason, R Asahi, K T Park and A J Freeman, Phys Rev B 64, 155114 (2001) P A Cox, Transition metal oxides, Clarendon Press, Oxford (1992) J Nell, B J Wood, S E Dorris and T O Mason, J Solid State Chem 82, 247 (1989) 38 H L Tuller and A S Nowick, J Phys Chem Solids 38, 859 (1977) 39 F A Benko and F P Koffyberg, J Phys Chem Solids 45, 57 (1984) 40 J I Pankove and P Aigrain, Phys Rev 126, 956 (1962) 41 M Balkanski, A Aziza and E Amzallag, Phys Status Solid 31, 323 (1969) 42 J W Slotboom and H C deGraaf, Solid State Electron 19, 857 (1976) 43 A P Roth, J B Webb and D F Williams, Phys Rev B 25, 7836 (1982) 44 D G Deppe, N D Gerrard, C J Pinzone, R D Dupuis and E F Schubert, Appl Phys Lett 56, 315 (1990) 45 D Olego and M Cardona, Phys Rev B22, 886 (1980) 46 H C Casey and F Stern, J Appl Phys 47, 631 (1976) P-type transparent conducting Cu-Al-O thin films 154 Chapter Conclusions and suggestions for future work Wang Yue Chapter Conclusions and Suggestions for Future Work 6.1 Conclusions Highly conductive transparent p-type oxides had been considered rare or even nonexisting, until the first success of conductive p-type CuAlO2 (0.1S⋅cm-1) deposited by pulsed laser ablation (PLD) being reported in Nature in 1997 The work described in this thesis was started shortly after that first report Due to the difficulty in achieving p-type transparent semiconductor films, it was a challenge to prepare p-type Cu-Al-O films by other methods or to achieve even higher conductivity The present work reflected the first effort in using a home-made plasma enhanced metal-organic chemical vapor deposition system (PE-MOCVD), a method suitable for industrial mass production, to prepare p-type transparent conducting copper aluminum oxide thin films Up to now, no other reports have been found using the same method to prepare p-type Cu-Al-O films, possibly due to the lack of the facility in handling solid precursors in commercial CVD systems Our group has designed and made a PEMOCVD system, which can handle solid precursors An American patent (No.10/095, 163) on the achievement of highly conductive p-type Cu-Al-O films with this method has been issued Two kinds of β-diketonates were successfully used as precursors: copper/aluminum acetylacetonate (acac) and copper/aluminum dipivaloylmethanate (dpm) A systematic study was made, and a comparison revealed that the films prepared by the latter precursors showed better stability and conductivity The properties of the films were found to vary with growth conditions P-type transparent conducting Cu-Al-O thin films 155 Chapter Conclusions and suggestions for future work Wang Yue The highest conductivity of the films prepared from acac precursors reached 2.0S⋅cm-1 while that of the films prepared from dpm precursors was up to 41.0S⋅cm-1, which was 400 times higher than that of the film reported in Nature This conductivity is also the highest conductivity achieved until now according to the author’s knowledge The conductivity difference between n-type (103S⋅cm-1) and p-type transparent oxide semiconductors is greatly reduced The transmittance of the conductive films was about 30-50% in the visible (400700nm) range, which was comparable to the film reported in Nature The optical bandgaps of the films prepared from both acac and dpm precursors were in the range of 3.45-4.14eV, higher than that PLD prepared films Such a variation indicated that the bandgap could be controlled by the growth conditions The mixed states of nanostructure and amorphous regions revealed by XRD and TEM suggested the variation and wideness of the bandgap could be due to a combined effect of the quantum confinement, the Burstein-Moss Shift and the bandgap narrowing effects The films prepared from different precursors showed different trends of bandgap variation with growth temperature, illustrating the competition of the Burstein-Moss shift and the gap narrowing effect In the low conductive films, the bandgap narrowing effect dominated but in highly conductive films the Burstein-Moss shift dominated The high carrier concentration and the relationship between bandgap and growth temperature suggested that these films were degenerate In the Seebeck measurements, all the conductive films showed stable p-type conduction In the Hall measurements, most films showed positive Hall coefficients, also indicating p-type conduction, but a few highly conductive films showed negative P-type transparent conducting Cu-Al-O thin films 156 Chapter Conclusions and suggestions for future work Wang Yue Hall coefficients This Hall coefficient inversion of highly conductive films might provide an evidence of the coexistence of another kind of charge carrier (electron) as well as the main carrier (hole) This phenomenon has not been reported before, probably due to the lack of a systematic study of CuAlO2 system In this thesis, the origins of p-type conduction were thought to be oxygen interstitials or copper vacancies The origin of minor n-type charge carriers was proposed to be Cu2+ which was oxidized from Cu+ The effect of annealing on the conductivity was explained by the competition of the co-doping theory and the concentration decrease of interstitial oxygen The co-doping theory might also explain the increase of conductivity with growth temperature and the very high conductivity obtained The temperature dependence of resistance was measured for the study of the carrier transport mechanism Careful comparisons of various mechanisms and analysis showed that the films grown at a high temperature (800°C) obeyed a typical thermal activation rule and the films grown at lower temperatures were dominated by grain boundary scattering In both conditions, the activation energies were a few tens of meV, much smaller than those reported Such a small activation energy was consistent with the high conductivity This work also included a pioneering study of the depth profile of copper aluminum oxide thin film observed by XPS, which showed that the aluminum had more uniform depth distribution than copper Dedicated peak fitting revealed the dominance of Cu+ and the content of Cu2+ varying with the depth and the growth temperature The proportion of Cu2+ increased with growth temperature might account for the Hall coefficient inversion and the high conductivity of some samples P-type transparent conducting Cu-Al-O thin films 157 Chapter Conclusions and suggestions for future work Wang Yue 6.2 Future Work More work needs to be done to improve the conductivity and transparency of the CuAlO2 films, thus to promote the applications of p-type TCOs Beyond the current work, more detailed structural analysis is necessary because the origins of p-type conduction were thought to be related to the defects in the films and a detailed structural study especially the high-resolution images from TEM may provide helpful information It would be ideal if an optimum annealing condition could be found to improve the conductivity and transparency Several kinds of annealing temperatures were tried in this project: high temperature up to 1100°C, intermediate temperature (750°C) and low temperature (350°C) and several ambients: Ar, air and growth condition Not only was a normal furnace used but RTP (rapid thermal post-annealing) was also employed Most anneals reduced the conductivity seriously That is why those results were not presented in this thesis In this thesis, co-doping theory was used to explain several phenomena To test if it is correct, Ag can be used as a substitute for Cu because Ag has similar properties to Cu but it is difficult to produce valence +2 In specimens using Ag, no Ag2+ exists, and ntype co-doping would then not occur, therefore the p-type conductivity would be much worse and could not be improved very much by a change of growth temperature P-type transparent conducting Cu-Al-O thin films 158 Appendixes Wang Yue Appendix A Degenerate Semiconductors The semiconductor is non-degenerate (obeys the laws of classical statistics) when the Fermi level lies below the bottom of the conduction band or above the top of the valence band at a distance greater than kBT If the Fermi level is more than 5kBT above EC or below EV the semiconductor will be completely degenerate All the results for holes should be analogous to the results for electrons provided the characteristics of electrons are replaced by those of holes For non-degenerate semiconductors, the free carrier concentration can be expressed by * 2πmnd k B T − n = 2( ) e h2 EC − E F k BT , p = 2( 2πm * k B T pd h2 ) e − E F − EV k BT ……………… (A-1) * where mnd , m * are termed electron effective mass and hole effective mass for the pd density of states For degenerate semiconductors, the free carrier concentration can be expressed by n= * * 3 8π 2mnd 8π 2m pd ( ) ( E F − EC ) , p = ( ) ( EV − E F ) …………… (A-2) h h Here it can be seen that the free carrier concentration is independent of temperature Degeneracy may be attained only through heavy doping The critical concentration is very sensitive to the impurity ionization energy and to the effective mass In degenerate semiconductors, the carrier concentration is so high that the impurity level turns into a band that merges with the conduction band for an n-type semiconductor, and valence band for a p-type semiconductor The impurity band is only partially P S Kireev, Semiconductor physics, second edition, Mir Publishers, Moscow (1978) P-type transparent conducting Cu-Al-O thin films 159 Appendixes Wang Yue occupied The result is that degeneracy does not vanish even at very low temperatures since the impurity band conduction mechanism remains active In this case, the heavily doped semiconductor exhibits more metal-like properties and carrier statistics should be described by Fermi-Dirac statistics N(E) N(E) (b) (b) (a) (a) impurities forming a band impurities forming a band CB VB EV EC EF F VB E CB EF EV F EC E Figure A-1 The density of states and the position of the Fermi level in a degenerate (a) electron and (b) hole-type semiconductors The position of the Fermi level of a completely degenerate semiconductor can be calculated from a known charge carrier concentration, which is obtainable from experiment, E F − EC = ( h2 )(3π n ) * m nd h2 EV − E F = ( * )(3π p ) 2m pd …………………… (A-3) …………………… (A-4) Heavily doped semiconductors present principal difficulties for theoretical analysis because high charge carrier concentration leads to a strong interaction between the charge carrier and the donor/acceptor ion, as a result of which the latter is screened P-type transparent conducting Cu-Al-O thin films 160 Appendixes Wang Yue Appendix B Determine Optical Bandgap from Absorption The transparent semiconducting materials are, in general, electrically conductive and optically transparent in the visible and near-infrared range and reflective to thermal infrared radiation Figure B-1 shows the typical spectral dependence of these materials At large wavelengths, high reflection is due to free electrons At very low wavelengths, absorption is due to the fundamental excitation of electrons from valence band to conduction band Figure B-1 Spectral dependence of a semiconducting transparent material: λgap and λp1 are the wavelengths at which the band-gap absorption and free electron plasma absorption take place (Adapted from H L Hartnagel, A L Dawer, A K Jain and C Jagadish, Semiconducting transparent thin films, Institute of Physics Publishing, Philadelphia (1995)) There are a few methods to determine the bandgaps of transparent semiconductors According to Hartnagel et al.2, the variation of the imaginary part of the dielectric H L Hartnagel, A L Dawer, A K Jain and C Jagadish, Semiconducting transparent thin films, Institute of Physics Publishing, Philadelphia (1995) P-type transparent conducting Cu-Al-O thin films 161 Appendixes Wang Yue constant ε2 with photon energy for direct allowed band-to-band transition is of the form (hν )2 ε = ε (hν − ∆E ) ………………………………(B-1) when hν > ∆E When hν < ∆E , ε2=0 Here hν is the photon energy, ε0 is approximately constant independent of photon energy and ∆E is the bandgap The curve (h 2ν ε ) versus hν extrapolated to zero gives the value of ∆E For allowed indirect transitions, i.e non-vertical transitions, for a single phonon process, the imaginary part of ε2 is given by (hν )2 ε 2a = A' 1− e E p / k BT (hν − E g + E p ) ……………… (B-2) when hν > ( E g − E p ) a When hν < ( E g − E p ) , ε = Here A′ is a constant independent of photon energy, Ep is the phonon energy and Eg is the indirect bandgap The corresponding form of phonon emission is given by (hν )2 ε 2e A' = e E p / k BT −1 (hν − E g − E p ) ……………… (B-3) when hν > ( E g + E p ) e When hν < ( E g + E p ) , ε = a e a If hν > ( E g + E p ) the total value of ε2 is given by ε = ε + ε The curve hν (ε ) versus hν when extrapolated to hνε 2 =0 gives the value of (Eg-Ep) A similar plot of P-type transparent conducting Cu-Al-O thin films 162 Appendixes e hν (ε ) Wang Yue gives a photon energy intercepting at (Eg+Ep) From these two intercept values, one can obtain values of Eg and Ep (h 2ν ε ) and (h 2ν ε ) versus photon energy curves were commonly used to estimated direct bandgap and indirect bandgap by early workers.3, 4, Now another method is popularly accepted Fahrenbruch et al established for direct/indirect optical transition between parabolic bands that αhν = A(hν − E g ) x ………………….……….(B-4) where A is a constant and α is the absorption coefficient For a direct optical transition, x = 1/2 for the allowed transition and x = 3/2 for the forbidden transition; for an indirect optical transition, x = for an allowed and x = for a forbidden transition The optical bandgaps of the films such as the direct bandgap with the allowed transition and the indirect bandgap with the forbidden transition are determined from a plot of (αhν ) versus hν and (αhν ) versus hν , respectively These curves extrapolate to zero give the values of corresponding bandgaps The theory of Fahrenbruch is the most widely used method to estimate the optical bandgap of the films 7, In this thesis, the bandgap of direct allowed transition is estimated by this method F Demichelis, E M Mezzetti, V Smurro, A Tagliaferro and E Tresso, J Phys D: Appl Phys 18, 1825 (1985) E Shanthi, V Dutta, A Banerjee and K L Chopra, J Appl Phys 51, 6243 (1980) K.B Sundram and G.K Bhagavat, J.Phys D: Appl Phys 14, 921 (1981) A L Fahrenbruch and R H Bube (ed), Fundamentals of solar cells, Academic, New York (1993) H Yanagi, S Inoue, K Ueda, H Kawazoe and H Hosono, J of Appl Phys 88, 4159 (2000) H Yanagi, T Hase, S Ibuki, K Ueda and H Hosono, Appl Phys Lett 78, 1583 (2001) P-type transparent conducting Cu-Al-O thin films 163 Appendixes Wang Yue Appendix C Hall Effect When a magnetic field is applied on electric current flowing in a semiconductor, charge carriers will be deflected, resulting in the side faces of the sample being charged This is the Hall effect and there is r r E H = R( B × J ) ………………………………(C-1) where EH is the Hall field, R is the Hall coefficient, vector B is the applied magnetic field, vector J is the current When an electric field and a magnetic field are applied to a homogeneous semiconductor, the following equations are satisfied,9 r e3 ' r r j = e K E + * K 13 ( E × B) …………………………(C-2) m ' 11 µH = ' eK12 …………………………(C-3) ' m * K 11 '2 e K 12 B σ B = e K + *2 ' …………………………(C-4) m K 11 R= µH = σ B en ' 11 µ2 1+ µ 2B2 µ 1+ µ 2B2 µ2 + 1+ µ 2B2 …………………………(C-5) B2 ' K rs is the kinetic coefficient tensor and its physical meaning depends on the subscripts r and s It has different expressions for non-degenerate and degenerate P S Kireev, Semicondcutor physics, second edition, Mir Publishers, Moscow (1978) P-type transparent conducting Cu-Al-O thin films 164 Appendixes Wang Yue semiconductors µΗ is the Hall mobility, σΒ is the conductivity in the direction of current in the presence of magnetic field, n is the carrier concentration In a weak magnetic field µ2B2