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Modulated photoconductivity method for investigation of band gap states distribution in silicon-based thin films
Journal of Non-Crystalline Solids 352 (2006) 1176–1179 www.elsevier.com/locate/jnoncrysol
Modulated photoconductivity method for investigation of band gap states distribution in silicon-based thin films A.G. Kazanskii a
a,*
, K.Yu. Khabarova a, E.I. Terukov
b
Department of Physics, M.V. Lomonosov Moscow State University, Lenisky gory, 119992, Moscow, Russia b A.F. Ioffe Physikotechnical Institute, Russian Academy of Sciences, 194021, St. Petersburg, Russia Available online 31 March 2006
Abstract It has been demonstrated that the well known modulated photocurrent technique can be modified to escape imperfect data in intrinsic parameters of amorphous and microcrystalline silicon films and to simplify measurements of the density of localized states distribution in the band gaps of these semiconductors. The information on the density-of-states distribution can be extracted from temperature dependence measurements of the constant and modulated components of the photoconductivity in the film illuminated by the light modulated with some selected frequencies. The modified method has been applied to microcrystalline hydrogenated silicon films with n- and p-type conduction. The study has demonstrated that the tail of the density-of-states distribution near the valence band of microcrystalline hydrogenated silicon is less steep than that near the conduction band. 2006 Elsevier B.V. All rights reserved. PACS: 61.82.Fk; 73.50.Pz; 73.50.Gr; 73.61.r Keywords: Silicon; Microcrystallinity; Photoconductivity
1. Introduction It is quite important to obtain detailed information on the localized electronic states in disordered semiconductors to understand not only optical and electronic properties but possibility their further device application. In particular, information on the energy distribution of the localized states in the band gap is essentially important. The measurement of spectral dependence of absorption coefficient in the sub-band gap region [1] and modulated photocurrent (MPC) method [2–5] are the most widely used among different methods of obtaining the information on energy distribution of the localized states in the band gap of amorphous (a-Si:H) and microcrystalline (lc-Si:H) hydrogenated silicon. The MPC technique allows one to obtain information on localized states, which participate in nonequilibrium charge carrier trapping. Such states are located *
Corresponding author. Tel.: +7 095 9394118; fax: +7 095 9393731. E-mail address: [email protected] (A.G. Kazanskii).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.11.111
near the conduction band in n-type materials and near the valence band in p-type materials, respectively. This technique is based on the measurements and analysis of the ac photocurrent flowing through a biased sample exposed to a monochromatic modulated excitation light. It has been shown that the density of localized states N(E) could be deduced from the measurement of the amplitude of the ac photocurrent and its phase shift referred to the modulated light excitation, using a recursive procedure [2]. The conventional MPC technique requires an accurate value of charge carrier mobility and capture cross section in order to obtain the magnitude of the density of states distribution. The exact values of these parameters are not yet known in a-Si:H and lc-Si:H. In this work we have developed further the Oheda’s ideas [2] and proposed a simple method to estimate the N(E) distribution using modulating frequencies out of low frequency region of MPC spectrum. The N(E) distribution can be obtained from the measurements of the temperature dependences of the constant and modulated
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
components of the photoconductivity in this frequency region. We applied a modified MPC method to lc-Si:H films with varied level of boron doping to obtain the density of states distribution in the band gap of this material. 2. Principle of the method In the MPC experiment two frequency regions can be clearly distinguished: the high-frequency region and the low-frequency region [2,5]. According to Oheda [2] for ntype semiconductors these frequency regions differ by relative positions of the electrons quasi-Fermi level EFn and the energy Ex at which the thermal emission rate of a trapped electron coincides with the modulation frequency x. The position of Ex level relative to the conduction band edge Ec is determined by the relation N c vS Ec Ex ¼ k B T ln ; ð1Þ x where Nc is an effective density of states for the conduction band, v the thermal velocity and S is a capture cross section for an electron. For high-frequency region the electron quasi-Fermi level EFn is below Ex level and for low frequency region the quasi-Fermi level EFn is above Ex level. Up to now, most of the conventional MPC measurements deal with high-frequency region. So to obtain the density of states distribution N(E) the measurement of modulation frequency dependence of the phase shift between modulated photocurrent and the light excitation is required. The upper boundary of the low frequency region is x < NcvS Æ exp[(Ec EFn)/kBT]. According to Oheda [2] in the low frequency region the amplitude of oscillatory component of electrons concentration in the conduction band n can be approximated to n ¼
G s 1
½1 þ ðxsph Þ2 2
;
ð2Þ
where G is the amplitude of generation rate oscillatory component, s the recombination time and sph = s[1 + N(EFn)kBT/n0]. However the value of sph is the photoresponse time [6], where n0 is a constant component of electrons concentration in the conduction band and nt = N(EFn)kBT is the concentration of electrons trapped near EFn. For x > (1/sph) n becomes independent of recombination time s and one can obtain the expression N ðEFn Þ ¼
G n0 n0 G n0 . xk B T n k B T xk B T n
ð3Þ
Using the photoconductivity components, N(EFn) can be expressed as N ðEFn Þ ¼
G Dr ; xk B T Dr
ð4Þ
where Dr and Dr are constant component and the amplitude of the modulated component of the photoconductivity, respectively. Thus in the low frequency region in the case x > (1/sph) one can determine the N(E) distribu-
1177
tion from the Dr and Dr measurements by varying the EFn position by either the temperature or excitation intensity. The condition x > (1/sph) in the low frequency region is satisfied the better the higher N(E) values are. The experimental method proposed can be used to estimate the density-of-states distribution in amorphous and microcrystalline hydrogenated silicon. 3. Experimental details We applied the above mentioned method to the study of N(E) in microcrystalline hydrogenated silicon films. The lc-Si:H films 0.6–0.7 lm thick were deposited onto a quartz substrate at a temperature of 220 C in a standard PECVD reactor by glow-discharge decomposition of silane-hydrogen mixture containing 1.5% monosilane (SiH4). The films were doped by introducing diborane (B2H6) into the reaction chamber. The volume ratio of the gases k = [B2H6]/[SiH4] was in the range 2 · 106– 105. According to thermoelectric data, the films obtained at k 6 3 · 106 had n-type conduction, and those for which k P 4 · 106, p-type conduction. According to electronmicroscopic data, the films were composed of columns 30–100 nm in diameter, which contained 5–30 nm crystallites. The crystalline component in the Raman spectra of these films constituted 85%. Magnesium contacts were deposited on the surface of the films. The measurements were performed in a vacuum at a residual pressure of 103 Pa. Before each cycle of measurements the films were vacuum-annealed at 180 C for 30 min. The modulated light emitted by an IR LED with the wavelength of 0.87 lm has an intensity of I0(1 + sin(xt)), where I0 = 10151.5 · 1016 cm2 s1. 4. Results The Dr frequency dependence measurements have demonstrated that Dr(x) is nearly inversely proportional in the frequency range f = x/2p > 7 kHz for all the samples under study. Therefore the condition x > (1/sph) was satisfied for this frequency range and all the measurements described below were carried out at f = 8 kHz. Fig. 1 shows the temperature dependences of the dark conductivity rd and of Dr and D r, measured at different intensities of modulated light for lc-Si:H film doped with boron at k = 4 · 106. It can be seen that, as the illumination intensity increases, the value of Dr does not change significantly, whereas Dr grows appreciably. The result obtained confirms that the condition xsph > 1 is satisfied for the modulation frequency used. Indeed, the strong dependence of carrier lifetime s on excitation intensity in lc-Si:H in the temperature range investigated results in the small value of the exponent c in the current-light characteristic ðDr / I c0 Þ [7]. It results in the slight increase of Dr on raising the illumination intensity. On the contrary if the condition xsph > 1 is satisfied, the value Dr must be
1178
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
1018
-5
10
1 2 3
-6
N (eV cm )
-3
-7
10
-1
σd , Δσ−, Δσ~ (S/cm)
10
1 2 2' 3 3' 4 4'
-8
10
-9
10
1016 0.25
-10
10
2
3
4
5
6
1017
7
0.30
-1
0.40
0.45
0.50
0.55
(EFp-Ev) (eV)
1000/T (K ) Fig. 1. Temperature dependences of (1) the dark conductivity rd, (2 – 4) the dc component of photoconductivity Dr and (2 0 –4 0 ) the amplitude of the modulated component of photoconductivity Dr at different illumination intensities for a sample fabricated at k = 4 · 106. I0: (2, 2 0 )1015, (3, 3 0 ) 4 · 1015 and (4, 4 0 ) 1.3 · 1016 cm2 s1.
0.35
Fig. 2. Distribution of the density of states near the valance band for a sample fabricated at k = 4 · 106, determined from the results of measurements of different illumination intensities. I0: (1) 1015, (2) 4 · 1015 and (3) 1.3 · 1016 cm2 s1.
1019
1018
1017
-1
-3
N (eV cm )
independent of lifetime s and vary in proportion to G Æ (n0(EFn)/N(EFn)). If N(E) dependence is close to exponential one with parameter kBT0, which is the same order of magnitude as kBT, then the ratio n0(EFn)/N(EFn) should weakly depend on EFn. In this case Dr must vary in proportion to G I0, which is actually observed in the experiment. The position of the quasi-Fermi level in lc-Si:H relative to the edge of the conduction band for p-type samples, (Ec EFn), or to the edge of the valence band for p-type samples, (EFp Ev), can be determined by the relation jEc(v) EFn(p)j = kBTln(r0/Dr), where r0 = 200 S/cm [8]. The evaluations of Ex and EFn(p) locations have shown that the actual modulation frequency x was in the low frequency range for the films under study inside specified temperature range. Fig. 2 shows the distribution of density of states near the edge of the valence band Ev, calculated for a sample obtained at k = 4 · 106 from the temperature dependences of Dr and Dr, presented above. It can be seen in the figure, that the density-of-states, determined by the method considered above, is virtually independent of light intensity, as it should be if the necessary conditions for the applicability of the technique described are satisfied. Fig. 3 shows the density-of-states distribution as a function of energy E in the energy gap of lc-Si:H, obtained for n- and p-type samples studied by processing the temperature dependences of Dr and Dr. The probe energies for samples with p-type conduction were calculated for the energy gap of lc-Si:H, which was obtained from optical measurements as 1.12 eV [9].
1 2 3 4 5 6
1016
1015
1014 0.0
0.2
0.4
0.6
0.8
1.0
(Ec- E) (eV) Fig. 3. Distribution of the density of states in the energy gap of lc-Si:H for (1–5) the samples studied and (6) data of [10]. k: (1) 2 · 106, (2) 3 · 106, (3) 4 · 106, (4) 5 · 106 and (5) 105.
5. Discussion For comparison, Fig. 3 shows the distribution of the density of states near the conduction band edge in lcSi:H, obtained in [10] by photomodulation spectroscopy from phase-shift measurements. It can be seen in Fig. 3 that for our n-type lc-Si:H samples the distribution of the density of states near Ec is in an agreement with the results obtained in [10]. The density of states distribution near
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
the conduction band edge is nearly exponential with the characteristic energy kBT0C = 0.04–0.06 eV. For p-type samples under study, an exponential tail of the distribution of density of states is also observed near the valence band, and the characteristic energy of this tail kBT0V = 0.06– 0.07 eV is somewhat greater than the energy kBT0C obtained for the conduction band tail. This result confirms the assumption made in the literature according to which the tail of localized states near the valence band in lcSi:H is less steep than that near the conduction band [11]. At present there are no data on the effect of the doping level and, accordingly, the position of Fermi level EF on the distribution of the density of states in the energy gap of lcSi:H. If we assume that the density of localized states distribution is independent of EF, then the data presented in Fig. 3 reflect the distribution of the density of localized states in the energy gap of lc-Si:H. However, if the distribution of the density of localized states depends on EF and accordingly on the doping level and the type of the conduction in the material, then the curves in Fig. 3 characterize the N(E) dependence in the upper half of the lc-Si:H band gap for n-type samples and in the lower half for p-type samples. 6. Conclusion In conclusion, we have proposed an experimental method based on modulated photocurrent measurements to estimate the density-of-states distribution in disordered silicon-based thin films. The method is based on the measurements of the temperature dependences of the dc component and the amplitude of the modulated component
1179
of the photoconductivity performed at modulation frequencies in low frequency region of MPC spectrum. The modified method has been applied to microcrystalline hydrogenated silicon films with n- and p-type conduction. The study demonstrated that the tail of the density-ofstates distribution near the valence band of microcrystalline hydrogenated silicon is less steep than that near the conduction band. Acknowledgment The authors are grateful to Dr H. Mell for providing the boron-doped lc-Si:H films. References [1] J. Kocka, J. Non-Cryst. Solids 90 (1987) 91. [2] H. Oheda, J. Appl. Phys. 52 (1981) 6693. [3] R. Bruggemann, C. Main, J. Berkin, S. Reynolds, Philos. Mag. B 62 (1990) 29. [4] R.R. Koropecki, J.A. Scmidt, R. Arce, J. Appl. Phys. 91 (2002) 8965. [5] J.P. Kleider, C. Longeaud, M.E. Gueunier, Phys. Stat. Sol. C 5 (2004) 1208. [6] M. Hoheisel, W. Fuhs, Philos. Mag. B 57 (1988) 411. [7] P.A. Forsh, A.G. Kazanskii, H. Mell, E.I. Terukov, Thin Solid Films 383 (2001) 251. [8] H. Overhof, M. Otte, Future Directions in Thin Film Science and Technology, World Scientific, Singapore, 1997, p. 23. [9] A.G. Kazanskii, H. Mell, E.I. Terukov, P.A. Forsh, Semiconductors 34 (2000) 267. [10] R. Bruggemann, J.P. Kleider, C. Longeaud, F. Houze, in: J.M. Marshall et al. (Eds.), Materials for Information Technology in the New Millennium, Bookcraft, Bath, UK, 2001, p. 212. [11] F. Finger, J. Muller, C. Malten, R. Carius, H. Wagner, J. Non-Cryst. Solids 266–269 (2000) 511.
Modulated photoconductivity method for investigation of band gap states distribution in silicon-based thin films A.G. Kazanskii a
a,*
, K.Yu. Khabarova a, E.I. Terukov
b
Department of Physics, M.V. Lomonosov Moscow State University, Lenisky gory, 119992, Moscow, Russia b A.F. Ioffe Physikotechnical Institute, Russian Academy of Sciences, 194021, St. Petersburg, Russia Available online 31 March 2006
Abstract It has been demonstrated that the well known modulated photocurrent technique can be modified to escape imperfect data in intrinsic parameters of amorphous and microcrystalline silicon films and to simplify measurements of the density of localized states distribution in the band gaps of these semiconductors. The information on the density-of-states distribution can be extracted from temperature dependence measurements of the constant and modulated components of the photoconductivity in the film illuminated by the light modulated with some selected frequencies. The modified method has been applied to microcrystalline hydrogenated silicon films with n- and p-type conduction. The study has demonstrated that the tail of the density-of-states distribution near the valence band of microcrystalline hydrogenated silicon is less steep than that near the conduction band. 2006 Elsevier B.V. All rights reserved. PACS: 61.82.Fk; 73.50.Pz; 73.50.Gr; 73.61.r Keywords: Silicon; Microcrystallinity; Photoconductivity
1. Introduction It is quite important to obtain detailed information on the localized electronic states in disordered semiconductors to understand not only optical and electronic properties but possibility their further device application. In particular, information on the energy distribution of the localized states in the band gap is essentially important. The measurement of spectral dependence of absorption coefficient in the sub-band gap region [1] and modulated photocurrent (MPC) method [2–5] are the most widely used among different methods of obtaining the information on energy distribution of the localized states in the band gap of amorphous (a-Si:H) and microcrystalline (lc-Si:H) hydrogenated silicon. The MPC technique allows one to obtain information on localized states, which participate in nonequilibrium charge carrier trapping. Such states are located *
Corresponding author. Tel.: +7 095 9394118; fax: +7 095 9393731. E-mail address: [email protected] (A.G. Kazanskii).
0022-3093/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2005.11.111
near the conduction band in n-type materials and near the valence band in p-type materials, respectively. This technique is based on the measurements and analysis of the ac photocurrent flowing through a biased sample exposed to a monochromatic modulated excitation light. It has been shown that the density of localized states N(E) could be deduced from the measurement of the amplitude of the ac photocurrent and its phase shift referred to the modulated light excitation, using a recursive procedure [2]. The conventional MPC technique requires an accurate value of charge carrier mobility and capture cross section in order to obtain the magnitude of the density of states distribution. The exact values of these parameters are not yet known in a-Si:H and lc-Si:H. In this work we have developed further the Oheda’s ideas [2] and proposed a simple method to estimate the N(E) distribution using modulating frequencies out of low frequency region of MPC spectrum. The N(E) distribution can be obtained from the measurements of the temperature dependences of the constant and modulated
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
components of the photoconductivity in this frequency region. We applied a modified MPC method to lc-Si:H films with varied level of boron doping to obtain the density of states distribution in the band gap of this material. 2. Principle of the method In the MPC experiment two frequency regions can be clearly distinguished: the high-frequency region and the low-frequency region [2,5]. According to Oheda [2] for ntype semiconductors these frequency regions differ by relative positions of the electrons quasi-Fermi level EFn and the energy Ex at which the thermal emission rate of a trapped electron coincides with the modulation frequency x. The position of Ex level relative to the conduction band edge Ec is determined by the relation N c vS Ec Ex ¼ k B T ln ; ð1Þ x where Nc is an effective density of states for the conduction band, v the thermal velocity and S is a capture cross section for an electron. For high-frequency region the electron quasi-Fermi level EFn is below Ex level and for low frequency region the quasi-Fermi level EFn is above Ex level. Up to now, most of the conventional MPC measurements deal with high-frequency region. So to obtain the density of states distribution N(E) the measurement of modulation frequency dependence of the phase shift between modulated photocurrent and the light excitation is required. The upper boundary of the low frequency region is x < NcvS Æ exp[(Ec EFn)/kBT]. According to Oheda [2] in the low frequency region the amplitude of oscillatory component of electrons concentration in the conduction band n can be approximated to n ¼
G s 1
½1 þ ðxsph Þ2 2
;
ð2Þ
where G is the amplitude of generation rate oscillatory component, s the recombination time and sph = s[1 + N(EFn)kBT/n0]. However the value of sph is the photoresponse time [6], where n0 is a constant component of electrons concentration in the conduction band and nt = N(EFn)kBT is the concentration of electrons trapped near EFn. For x > (1/sph) n becomes independent of recombination time s and one can obtain the expression N ðEFn Þ ¼
G n0 n0 G n0 . xk B T n k B T xk B T n
ð3Þ
Using the photoconductivity components, N(EFn) can be expressed as N ðEFn Þ ¼
G Dr ; xk B T Dr
ð4Þ
where Dr and Dr are constant component and the amplitude of the modulated component of the photoconductivity, respectively. Thus in the low frequency region in the case x > (1/sph) one can determine the N(E) distribu-
1177
tion from the Dr and Dr measurements by varying the EFn position by either the temperature or excitation intensity. The condition x > (1/sph) in the low frequency region is satisfied the better the higher N(E) values are. The experimental method proposed can be used to estimate the density-of-states distribution in amorphous and microcrystalline hydrogenated silicon. 3. Experimental details We applied the above mentioned method to the study of N(E) in microcrystalline hydrogenated silicon films. The lc-Si:H films 0.6–0.7 lm thick were deposited onto a quartz substrate at a temperature of 220 C in a standard PECVD reactor by glow-discharge decomposition of silane-hydrogen mixture containing 1.5% monosilane (SiH4). The films were doped by introducing diborane (B2H6) into the reaction chamber. The volume ratio of the gases k = [B2H6]/[SiH4] was in the range 2 · 106– 105. According to thermoelectric data, the films obtained at k 6 3 · 106 had n-type conduction, and those for which k P 4 · 106, p-type conduction. According to electronmicroscopic data, the films were composed of columns 30–100 nm in diameter, which contained 5–30 nm crystallites. The crystalline component in the Raman spectra of these films constituted 85%. Magnesium contacts were deposited on the surface of the films. The measurements were performed in a vacuum at a residual pressure of 103 Pa. Before each cycle of measurements the films were vacuum-annealed at 180 C for 30 min. The modulated light emitted by an IR LED with the wavelength of 0.87 lm has an intensity of I0(1 + sin(xt)), where I0 = 10151.5 · 1016 cm2 s1. 4. Results The Dr frequency dependence measurements have demonstrated that Dr(x) is nearly inversely proportional in the frequency range f = x/2p > 7 kHz for all the samples under study. Therefore the condition x > (1/sph) was satisfied for this frequency range and all the measurements described below were carried out at f = 8 kHz. Fig. 1 shows the temperature dependences of the dark conductivity rd and of Dr and D r, measured at different intensities of modulated light for lc-Si:H film doped with boron at k = 4 · 106. It can be seen that, as the illumination intensity increases, the value of Dr does not change significantly, whereas Dr grows appreciably. The result obtained confirms that the condition xsph > 1 is satisfied for the modulation frequency used. Indeed, the strong dependence of carrier lifetime s on excitation intensity in lc-Si:H in the temperature range investigated results in the small value of the exponent c in the current-light characteristic ðDr / I c0 Þ [7]. It results in the slight increase of Dr on raising the illumination intensity. On the contrary if the condition xsph > 1 is satisfied, the value Dr must be
1178
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
1018
-5
10
1 2 3
-6
N (eV cm )
-3
-7
10
-1
σd , Δσ−, Δσ~ (S/cm)
10
1 2 2' 3 3' 4 4'
-8
10
-9
10
1016 0.25
-10
10
2
3
4
5
6
1017
7
0.30
-1
0.40
0.45
0.50
0.55
(EFp-Ev) (eV)
1000/T (K ) Fig. 1. Temperature dependences of (1) the dark conductivity rd, (2 – 4) the dc component of photoconductivity Dr and (2 0 –4 0 ) the amplitude of the modulated component of photoconductivity Dr at different illumination intensities for a sample fabricated at k = 4 · 106. I0: (2, 2 0 )1015, (3, 3 0 ) 4 · 1015 and (4, 4 0 ) 1.3 · 1016 cm2 s1.
0.35
Fig. 2. Distribution of the density of states near the valance band for a sample fabricated at k = 4 · 106, determined from the results of measurements of different illumination intensities. I0: (1) 1015, (2) 4 · 1015 and (3) 1.3 · 1016 cm2 s1.
1019
1018
1017
-1
-3
N (eV cm )
independent of lifetime s and vary in proportion to G Æ (n0(EFn)/N(EFn)). If N(E) dependence is close to exponential one with parameter kBT0, which is the same order of magnitude as kBT, then the ratio n0(EFn)/N(EFn) should weakly depend on EFn. In this case Dr must vary in proportion to G I0, which is actually observed in the experiment. The position of the quasi-Fermi level in lc-Si:H relative to the edge of the conduction band for p-type samples, (Ec EFn), or to the edge of the valence band for p-type samples, (EFp Ev), can be determined by the relation jEc(v) EFn(p)j = kBTln(r0/Dr), where r0 = 200 S/cm [8]. The evaluations of Ex and EFn(p) locations have shown that the actual modulation frequency x was in the low frequency range for the films under study inside specified temperature range. Fig. 2 shows the distribution of density of states near the edge of the valence band Ev, calculated for a sample obtained at k = 4 · 106 from the temperature dependences of Dr and Dr, presented above. It can be seen in the figure, that the density-of-states, determined by the method considered above, is virtually independent of light intensity, as it should be if the necessary conditions for the applicability of the technique described are satisfied. Fig. 3 shows the density-of-states distribution as a function of energy E in the energy gap of lc-Si:H, obtained for n- and p-type samples studied by processing the temperature dependences of Dr and Dr. The probe energies for samples with p-type conduction were calculated for the energy gap of lc-Si:H, which was obtained from optical measurements as 1.12 eV [9].
1 2 3 4 5 6
1016
1015
1014 0.0
0.2
0.4
0.6
0.8
1.0
(Ec- E) (eV) Fig. 3. Distribution of the density of states in the energy gap of lc-Si:H for (1–5) the samples studied and (6) data of [10]. k: (1) 2 · 106, (2) 3 · 106, (3) 4 · 106, (4) 5 · 106 and (5) 105.
5. Discussion For comparison, Fig. 3 shows the distribution of the density of states near the conduction band edge in lcSi:H, obtained in [10] by photomodulation spectroscopy from phase-shift measurements. It can be seen in Fig. 3 that for our n-type lc-Si:H samples the distribution of the density of states near Ec is in an agreement with the results obtained in [10]. The density of states distribution near
A.G. Kazanskii et al. / Journal of Non-Crystalline Solids 352 (2006) 1176–1179
the conduction band edge is nearly exponential with the characteristic energy kBT0C = 0.04–0.06 eV. For p-type samples under study, an exponential tail of the distribution of density of states is also observed near the valence band, and the characteristic energy of this tail kBT0V = 0.06– 0.07 eV is somewhat greater than the energy kBT0C obtained for the conduction band tail. This result confirms the assumption made in the literature according to which the tail of localized states near the valence band in lcSi:H is less steep than that near the conduction band [11]. At present there are no data on the effect of the doping level and, accordingly, the position of Fermi level EF on the distribution of the density of states in the energy gap of lcSi:H. If we assume that the density of localized states distribution is independent of EF, then the data presented in Fig. 3 reflect the distribution of the density of localized states in the energy gap of lc-Si:H. However, if the distribution of the density of localized states depends on EF and accordingly on the doping level and the type of the conduction in the material, then the curves in Fig. 3 characterize the N(E) dependence in the upper half of the lc-Si:H band gap for n-type samples and in the lower half for p-type samples. 6. Conclusion In conclusion, we have proposed an experimental method based on modulated photocurrent measurements to estimate the density-of-states distribution in disordered silicon-based thin films. The method is based on the measurements of the temperature dependences of the dc component and the amplitude of the modulated component
1179
of the photoconductivity performed at modulation frequencies in low frequency region of MPC spectrum. The modified method has been applied to microcrystalline hydrogenated silicon films with n- and p-type conduction. The study demonstrated that the tail of the density-ofstates distribution near the valence band of microcrystalline hydrogenated silicon is less steep than that near the conduction band. Acknowledgment The authors are grateful to Dr H. Mell for providing the boron-doped lc-Si:H films. References [1] J. Kocka, J. Non-Cryst. Solids 90 (1987) 91. [2] H. Oheda, J. Appl. Phys. 52 (1981) 6693. [3] R. Bruggemann, C. Main, J. Berkin, S. Reynolds, Philos. Mag. B 62 (1990) 29. [4] R.R. Koropecki, J.A. Scmidt, R. Arce, J. Appl. Phys. 91 (2002) 8965. [5] J.P. Kleider, C. Longeaud, M.E. Gueunier, Phys. Stat. Sol. C 5 (2004) 1208. [6] M. Hoheisel, W. Fuhs, Philos. Mag. B 57 (1988) 411. [7] P.A. Forsh, A.G. Kazanskii, H. Mell, E.I. Terukov, Thin Solid Films 383 (2001) 251. [8] H. Overhof, M. Otte, Future Directions in Thin Film Science and Technology, World Scientific, Singapore, 1997, p. 23. [9] A.G. Kazanskii, H. Mell, E.I. Terukov, P.A. Forsh, Semiconductors 34 (2000) 267. [10] R. Bruggemann, J.P. Kleider, C. Longeaud, F. Houze, in: J.M. Marshall et al. (Eds.), Materials for Information Technology in the New Millennium, Bookcraft, Bath, UK, 2001, p. 212. [11] F. Finger, J. Muller, C. Malten, R. Carius, H. Wagner, J. Non-Cryst. Solids 266–269 (2000) 511.