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Effect of ageing on the open-circuit voltage of MIS-solar cell
Applied Surface Science 126 Ž1998. 65–68
Effect of ageing on the open-circuit voltage of MIS-solar cell P. Chattopadhyay a
a,b
Department of Electronic Science, UniÕersity College of Science, 92 Acharyya Praf. Chandra Road, Calcutta 700 009, India b Jawaharlal Nehru Centre for AdÕanced Scientific Research, Jakkur P.O., Bangalore 560 064, India Received 10 June 1997; accepted 17 October 1997
Abstract The effect of ageing on the open-circuit voltage of the MIS-solar cell is addressed. It is shown that the open circuit voltage may increase substantially with ageing time for Al–SiO 2 –nSi solar cells. The change in the open-circuit voltage has been found to depend upon various parameters related to interface reaction. q 1998 Elsevier Science B.V.
1. Introduction Metal–insulator–semiconductor ŽMIS. solar cells have received considerable attention in the past for their simple fabrication procedure and low cost of production compared to standard p–n junction solar cells. In many publications, the role of insulating layer has been investigated w1–7x. The observed change in the open-circuit voltage of these devices has been explained considering tunneling current through the oxide w2x, fixed charge density in the oxide layer w3,4x and pinholes in the oxide w5,6x. In this paper, an interesting effect of interface reaction on the open-circuit voltage of the device has been reported. It is shown that, depending on the reactivity of the metal with the oxide layer, the device may undergo ageing effects and in such cases the opencircuit voltage may increase with time for devices on n-type silicon. 2. Evaluation of the open-circuit voltage In a recent work, it has been pointed out that the barrier height of an Al–SiO 2 –Si tunnel diode becomes dependent on time because of the chemical
reaction of Al with the SiO 2 layer w8x. Aluminium being used quite extensively for silicon MIS-type solar cells, one cannot ignore the above chemical reaction while evaluating the photovoltaic properties of the device. It has been shown in Ref. w8x that the chemical reaction between Al and the adjacent SiO 2 layer gives rise to an Al 2 O 3 layer and free silicon atoms. The latter act as electron traps in the SiO 2 layer and therefore yield a negative charge density. For the first order calculation, the chemical reaction taking place at the interface may be considered independent of the illumination. Fig. 1 shows the energy band diagram of a MISsolar cell, where fm is the work function of the metal, D the drop across the interfacial layer, d the thickness of the I-layer, x the electron affinity of the semiconductor, f 0 the neutral level w9x, qVn the energy difference between the Fermi level and the bottom of the conduction band in the bulk, Eg the band gap, Cs the surface potential and VOC is the open-circuit voltage developed under the illumination. The charge neutrality condition in the presence of such silicon traps can be written as w8x Q m q Qsc q Q it q Q f q QSi s 0
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 7 . 0 0 5 1 3 - 8
Ž 1.
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
66
where
f bn Ž t . s f bn Ž 0 . q C P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
f bn Ž 0 . s C2 Ž fm y x . q Ž 1 y C2 . Ž Eg y f 0 . y qC2 d Nfr´ i
Ž 4.
C s 4 qfC2 d NSiO 2Ž 0 . r´ i C1 s 2 q´s Nd d 2r´ i2 , C2 s ´ ir Ž ´ i q q 2d D it . , where Nd is the doping concentration, w bnŽ t . is the barrier height, ´ i is the permittivity of the oxide layer and D it is the interface state density. The surface potential can be calculated from the illuminated current–voltage characteristics given by w7x Fig. 1. Energy band diagram of a MIS-solar cell.
J s Jsc y A) T 2 exp Ž yf 1r2d .
where Q m is the charge density in the metal, Qsc the space charge density, Qit the interface state charge density, Qf the fixed charge density and QSi is the charge density that developed at the released Si atoms. An expression for Q Si has been derived in Ref. w8x given by QSi s qfNSiO 2Ž 0 . P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
.
Ž 2.
where t is the ageing time, b 1 and bp are constants related to the linear and parabolic growth rate of Al 2 O 3 layer, NSiO 2Ž0. is the surface concentration of SiO 2 molecules at time t s 0 and f is a parameter that determines the charge state of the liberated Si atoms. The general procedure to evaluate the electrical characteristics of MIS-devices is to use the Gaussian law, energy band diagram and the charge neutrality equation w9x. In the presence of an interface reaction and illumination, the above procedure leads to the following equation
f bn Ž t . y Cs Ž t . y C2 VOC y Vn s C2 C1Cs Ž t .
1r2
Ž 3.
=exp yq Cs Ž t . q Vn 4 rkT
Ž 5.
where Jsc is the short circuit current, A) is the Richardson constant, T is the temperature, expŽyf 1r2d . is the tunneling exponent and f is the mean barrier of the oxide layer. Under open-circuit condition Ži.e. at J s 0., Eq. Ž5. yields
Cs Ž t . s kTrq ln A) T 2 exp Ž yf 1r2d . rJsc y Vn
Ž 6. Substituting Eq. Ž6. in Eq. Ž3., we obtain VOC Ž t . s f bn Ž t . ykTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 rC2 y C1 kTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 y Vn
1r2
Ž 7. The change in the open-circuit voltage Ž DVOC s VOC Ž t . y VOC Ž0.. has been calculated as a function of ageing time and plotted in Fig. 2. An expression for VOC can also be derived for p-type devices by
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
67
Fig. 2. Dependence of open-circuit voltage change Ž DVOC . of an MIS-solar cell on ageing time. The calculation is made for a typical ˚ and Dit s 10 12 cmy2 eVy1. Al–SiO 2 –nSi solar cell with parametric values: d s 20 A
using equations similar to Eqs. Ž3. and Ž6. with Nd replaced by acceptor concentration Ž Na . given by VOC Ž t . s f bp Ž t . ykTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 rC2 y C1 kTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 y Vp
1r2
Ž 8. where
f bp Ž t . s f bp Ž 0 . q C P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
Ž 9.
and
f bp Ž 0 . s C2 Ž Eg q x y fm . q Ž 1 y C2 . f 0 q qC2 d Nfr´ i .
Ž 10 .
3. Discussion It is apparent from Fig. 2 that the open circuit voltage of the device increases with ageing time for an n-type device until it attains a saturation. The saturation value depends predominantly on the val-
ues of C and b 1. For example, an increase in the value of C increases the saturation value of the open-circuit voltage. The saturation would be faster for relatively higher values of b 1. A similar calculation on p-type devices would show an opposite behaviour, namely a reduction in the open-circuit voltage followed by a saturation after prolong ageing. The above features can be realised in terms of the negative charge build-up at the released silicon atoms which, for n-type silicon increases the surface potential while decreasing it for a p-type silicon. It is interesting to note that the change in the open-circuit voltage may be quite significant depending on the value of C. The value of C would be larger for a relatively thicker oxide layer and higher values of C2 . In the case of Al–SiO 2 –Si devices, the observed change in the barrier height with time can be explained considering a value of C s 0.25 eV w8x. One can readily correlate the change in the open-circuit voltage DVOC with the change in the value of barrier height using Eqs. Ž4. and Ž7. given by DVOC s D f brC2 s CrC2 Žsince D f b s C .. Therefore, the expected change in the open-circuit voltage may be estimated indirectly using the experimentally observed value of D f b Žor C .. Card w10x has reported
68
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
a change in the barrier height of about 0.25 eV. For a value of C2 s 0.734, the expected change in DVOC is about 0.348 V, which agrees with the predicted change in the open-circuit voltage for C s 0.25 eV and b s 10y3 sy1 in Fig. 2. The analysis presented here is based on the assumption that the chemical reaction taking place at the interfacial insulating layer is independent of the illumination. In the case when the reaction is dependent on the illumination, one can still proceed with Eq. Ž2. by suitably defining the rate constants b 1 or bp . The optical sensitivity of these constants may be determined by fitting the experimental data of opencircuit voltage measured at different times and illuminations. In conclusion, the ageing effect on the open-circuit voltage has been found remarkable for Al– SiO 2 –Si solar cells. This happens because of the reaction of Al with the SiO 2 layer resulting in an Al 2 O 3 layer and free silicon atoms in the oxide. The trapped charge density at these silicon sites determines the open-circuit voltage of the ageing devices.
Acknowledgements The author would like to thank the Jawaharlal Nehru Centre for Advance Scientific Research, Bangalore for inviting him to the visiting fellowship programme 1996–1997.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
R.J. Stirn, Y.C.M. Yeh, Appl. Phys. Lett. 27 Ž1975. 95. J.P. Ponpon, P. Shiffert, J. Appl. Phys. 47 Ž1976. 3248. D.L. Pulfrey, IEEE Trans. Electron Devices 23 Ž1976. 587. J.T. Lue, Solid State Electron. 23 Ž1980. 236. A. Rothwarf, I. Pereyra, Solid State Electron. 24 Ž1981. 1067. K. Rajkhanan, R. Singh, J. Shewchun, IEEE Trans. Electron Devices 27 Ž1980. 250. P. Chattopadhyay, Phys. Status Solidi Ža. 740 Ž1993. 587. P. Chattopadhyay, K. Das, J. Appl. Phys. 80 Ž1996. 4229. A.M. Cowley, S.M. Sze, J. Appl. Phys. 36 Ž1965. 3212. H.C. Card, IEEE Trans. Electron Devices 23 Ž1976. 538.
Effect of ageing on the open-circuit voltage of MIS-solar cell P. Chattopadhyay a
a,b
Department of Electronic Science, UniÕersity College of Science, 92 Acharyya Praf. Chandra Road, Calcutta 700 009, India b Jawaharlal Nehru Centre for AdÕanced Scientific Research, Jakkur P.O., Bangalore 560 064, India Received 10 June 1997; accepted 17 October 1997
Abstract The effect of ageing on the open-circuit voltage of the MIS-solar cell is addressed. It is shown that the open circuit voltage may increase substantially with ageing time for Al–SiO 2 –nSi solar cells. The change in the open-circuit voltage has been found to depend upon various parameters related to interface reaction. q 1998 Elsevier Science B.V.
1. Introduction Metal–insulator–semiconductor ŽMIS. solar cells have received considerable attention in the past for their simple fabrication procedure and low cost of production compared to standard p–n junction solar cells. In many publications, the role of insulating layer has been investigated w1–7x. The observed change in the open-circuit voltage of these devices has been explained considering tunneling current through the oxide w2x, fixed charge density in the oxide layer w3,4x and pinholes in the oxide w5,6x. In this paper, an interesting effect of interface reaction on the open-circuit voltage of the device has been reported. It is shown that, depending on the reactivity of the metal with the oxide layer, the device may undergo ageing effects and in such cases the opencircuit voltage may increase with time for devices on n-type silicon. 2. Evaluation of the open-circuit voltage In a recent work, it has been pointed out that the barrier height of an Al–SiO 2 –Si tunnel diode becomes dependent on time because of the chemical
reaction of Al with the SiO 2 layer w8x. Aluminium being used quite extensively for silicon MIS-type solar cells, one cannot ignore the above chemical reaction while evaluating the photovoltaic properties of the device. It has been shown in Ref. w8x that the chemical reaction between Al and the adjacent SiO 2 layer gives rise to an Al 2 O 3 layer and free silicon atoms. The latter act as electron traps in the SiO 2 layer and therefore yield a negative charge density. For the first order calculation, the chemical reaction taking place at the interface may be considered independent of the illumination. Fig. 1 shows the energy band diagram of a MISsolar cell, where fm is the work function of the metal, D the drop across the interfacial layer, d the thickness of the I-layer, x the electron affinity of the semiconductor, f 0 the neutral level w9x, qVn the energy difference between the Fermi level and the bottom of the conduction band in the bulk, Eg the band gap, Cs the surface potential and VOC is the open-circuit voltage developed under the illumination. The charge neutrality condition in the presence of such silicon traps can be written as w8x Q m q Qsc q Q it q Q f q QSi s 0
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 7 . 0 0 5 1 3 - 8
Ž 1.
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
66
where
f bn Ž t . s f bn Ž 0 . q C P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
f bn Ž 0 . s C2 Ž fm y x . q Ž 1 y C2 . Ž Eg y f 0 . y qC2 d Nfr´ i
Ž 4.
C s 4 qfC2 d NSiO 2Ž 0 . r´ i C1 s 2 q´s Nd d 2r´ i2 , C2 s ´ ir Ž ´ i q q 2d D it . , where Nd is the doping concentration, w bnŽ t . is the barrier height, ´ i is the permittivity of the oxide layer and D it is the interface state density. The surface potential can be calculated from the illuminated current–voltage characteristics given by w7x Fig. 1. Energy band diagram of a MIS-solar cell.
J s Jsc y A) T 2 exp Ž yf 1r2d .
where Q m is the charge density in the metal, Qsc the space charge density, Qit the interface state charge density, Qf the fixed charge density and QSi is the charge density that developed at the released Si atoms. An expression for Q Si has been derived in Ref. w8x given by QSi s qfNSiO 2Ž 0 . P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
.
Ž 2.
where t is the ageing time, b 1 and bp are constants related to the linear and parabolic growth rate of Al 2 O 3 layer, NSiO 2Ž0. is the surface concentration of SiO 2 molecules at time t s 0 and f is a parameter that determines the charge state of the liberated Si atoms. The general procedure to evaluate the electrical characteristics of MIS-devices is to use the Gaussian law, energy band diagram and the charge neutrality equation w9x. In the presence of an interface reaction and illumination, the above procedure leads to the following equation
f bn Ž t . y Cs Ž t . y C2 VOC y Vn s C2 C1Cs Ž t .
1r2
Ž 3.
=exp yq Cs Ž t . q Vn 4 rkT
Ž 5.
where Jsc is the short circuit current, A) is the Richardson constant, T is the temperature, expŽyf 1r2d . is the tunneling exponent and f is the mean barrier of the oxide layer. Under open-circuit condition Ži.e. at J s 0., Eq. Ž5. yields
Cs Ž t . s kTrq ln A) T 2 exp Ž yf 1r2d . rJsc y Vn
Ž 6. Substituting Eq. Ž6. in Eq. Ž3., we obtain VOC Ž t . s f bn Ž t . ykTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 rC2 y C1 kTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 y Vn
1r2
Ž 7. The change in the open-circuit voltage Ž DVOC s VOC Ž t . y VOC Ž0.. has been calculated as a function of ageing time and plotted in Fig. 2. An expression for VOC can also be derived for p-type devices by
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
67
Fig. 2. Dependence of open-circuit voltage change Ž DVOC . of an MIS-solar cell on ageing time. The calculation is made for a typical ˚ and Dit s 10 12 cmy2 eVy1. Al–SiO 2 –nSi solar cell with parametric values: d s 20 A
using equations similar to Eqs. Ž3. and Ž6. with Nd replaced by acceptor concentration Ž Na . given by VOC Ž t . s f bp Ž t . ykTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 rC2 y C1 kTrq ln A) T 2 exp Ž yf 1r2d . rJsc 4 y Vp
1r2
Ž 8. where
f bp Ž t . s f bp Ž 0 . q C P
½
1 y exp Ž yb 1 t . 1 y exp ybp't
ž
/
Ž 9.
and
f bp Ž 0 . s C2 Ž Eg q x y fm . q Ž 1 y C2 . f 0 q qC2 d Nfr´ i .
Ž 10 .
3. Discussion It is apparent from Fig. 2 that the open circuit voltage of the device increases with ageing time for an n-type device until it attains a saturation. The saturation value depends predominantly on the val-
ues of C and b 1. For example, an increase in the value of C increases the saturation value of the open-circuit voltage. The saturation would be faster for relatively higher values of b 1. A similar calculation on p-type devices would show an opposite behaviour, namely a reduction in the open-circuit voltage followed by a saturation after prolong ageing. The above features can be realised in terms of the negative charge build-up at the released silicon atoms which, for n-type silicon increases the surface potential while decreasing it for a p-type silicon. It is interesting to note that the change in the open-circuit voltage may be quite significant depending on the value of C. The value of C would be larger for a relatively thicker oxide layer and higher values of C2 . In the case of Al–SiO 2 –Si devices, the observed change in the barrier height with time can be explained considering a value of C s 0.25 eV w8x. One can readily correlate the change in the open-circuit voltage DVOC with the change in the value of barrier height using Eqs. Ž4. and Ž7. given by DVOC s D f brC2 s CrC2 Žsince D f b s C .. Therefore, the expected change in the open-circuit voltage may be estimated indirectly using the experimentally observed value of D f b Žor C .. Card w10x has reported
68
P. Chattopadhyayr Applied Surface Science 126 (1998) 65–68
a change in the barrier height of about 0.25 eV. For a value of C2 s 0.734, the expected change in DVOC is about 0.348 V, which agrees with the predicted change in the open-circuit voltage for C s 0.25 eV and b s 10y3 sy1 in Fig. 2. The analysis presented here is based on the assumption that the chemical reaction taking place at the interfacial insulating layer is independent of the illumination. In the case when the reaction is dependent on the illumination, one can still proceed with Eq. Ž2. by suitably defining the rate constants b 1 or bp . The optical sensitivity of these constants may be determined by fitting the experimental data of opencircuit voltage measured at different times and illuminations. In conclusion, the ageing effect on the open-circuit voltage has been found remarkable for Al– SiO 2 –Si solar cells. This happens because of the reaction of Al with the SiO 2 layer resulting in an Al 2 O 3 layer and free silicon atoms in the oxide. The trapped charge density at these silicon sites determines the open-circuit voltage of the ageing devices.
Acknowledgements The author would like to thank the Jawaharlal Nehru Centre for Advance Scientific Research, Bangalore for inviting him to the visiting fellowship programme 1996–1997.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
R.J. Stirn, Y.C.M. Yeh, Appl. Phys. Lett. 27 Ž1975. 95. J.P. Ponpon, P. Shiffert, J. Appl. Phys. 47 Ž1976. 3248. D.L. Pulfrey, IEEE Trans. Electron Devices 23 Ž1976. 587. J.T. Lue, Solid State Electron. 23 Ž1980. 236. A. Rothwarf, I. Pereyra, Solid State Electron. 24 Ž1981. 1067. K. Rajkhanan, R. Singh, J. Shewchun, IEEE Trans. Electron Devices 27 Ž1980. 250. P. Chattopadhyay, Phys. Status Solidi Ža. 740 Ž1993. 587. P. Chattopadhyay, K. Das, J. Appl. Phys. 80 Ž1996. 4229. A.M. Cowley, S.M. Sze, J. Appl. Phys. 36 Ž1965. 3212. H.C. Card, IEEE Trans. Electron Devices 23 Ž1976. 538.