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Reply to “Comments on theoretical C(V) equation of an amorphous-crystalline heterojunction at low frequency”
0038-l lOlj88 $3.00 + 0.00 Copyright 0 1988 Pergamon Press plc
Solid-StoreHecrronics Vol. 31, No. 8, pp. 1351-1352, 1988 Printed in Great Britain. All rights reserved
REPLY TO “COMMENTS ON THEORETICAL C(V) EQUATION OF AN AMORPHOUS-CRYSTALLINE HETEROJUNCTION AT LOW FREQUENCY”? (Received 16 November 1987)
We also have:
In my paper, eqn (3) of the net charge per unit area in the crystalline depletion zone must be read as:
as Liou says. In eqn (6), EC, and Eu, are the mobility edges in amorphous silicon and EC* and Ev2 are the mobility edges in crystalline silicon. The differences EC, - EFN and EFp- Ev, can be written as EC, - EF, and EF, - Ev, + (-qV) where EF, is the position of the quasi Fermi level at equilibrium in the amorphous silicon bulk and V the applied voltage. The differences EC, - EF, and EF, - Ev, are referred to the amorphous quasi-neutral region. The difference as Ecz - EFN and EFp - Ev2 can be written EC? - EFz + (- qV) and EF2 - Ev2 where EF2 is the position of the quasi Fermi level at equilibrium in the crystalline silicon bulk. The differences EC, - EF2 and EF2 - Ev2 are referred to the crystalline quasi-neutral region. The reference level of the electrostatic potential was taken at the amorphous depletion boundary x,, that is 4(x,) = 0, as Liou says (not x,). Then the free carrier concentrations are given by (amorphous depletion zone):
d(x) 1
nfl (x) = nnoexp [ kT
where: n.,=N,,exp[-*]
,,=h$,exp[--1
i = d($, - 40) -- d+o C dQz dQ,’ near the eqn (13) instead of dQ,,/dQ,. The constancy of the quasi-Fermi levels across the space charge regions of an homojunction has been generally assumed in the literature[l,2]. However, this assumption is valid for low forward voltages (lowlevel injection) and for reverse biases, if they are not too high[3]. At high forward voltages (high-level injection) this assumption fails as Liou says[3,4]. In crystalline heterojunctions, the constancy of the quasi-Fermi levels through both depletion regions has been used in the literature[5,6] and its validity has been questioned also[7,8]. In my paper, the voltage range where this asumption is valid has not been studied. I think that in order to determine this voltage range, a numerical simulation method has to be used taking into account all the dark current mechanisms of an amorphous-crystalline heterojunction. At a given voltage the dominant dark current mechanism in a crystalline homojunction and in an amophours-crystalline heterojunction is not necessarily the same. Furthermore, in the Appendix of my paper it was pointed out that when the applied voltage approximates the built-in voltage the condition ]dQ, ) << 1Q, 1 is not fulfilled (the incremental charge density 1dQ, I is much lower than the space charge density IQ, 1). Then the expression of the capacitance is not valid for these voltages. INTEC Universidad National de1 Litoral Guemes 3450, Santa Fe 3000 Argentina
F. RUBINELLI
REFERENCES
are the equilibrium carrrier concentrations. (The dominant contribution to the amorphous side capacitance C, in the amorphous-crystalline heterojunction comes from the hole trapped carriers if Nd <>g, ED.)
J. L. Mall, Physics
of Semiconductors. MC Graw-Hill,
New York, (1964). S. M. Sze, Physics of Semiconductors Devices.
Wiley, New York (1981). C. T. Sah, IEEE Trans. Electron. Dev. ED-13, 839 (1966). R. K. Willardson and A. C. Beer, Semiconductors and
Semimetals, Vol. 15, Contacts, Junciions and Emitters.
tJ. J. Liou, Solid-Slate Hecrronics 31, 1349 (1988).
Academic Press, New York (1981).
1351
1352
Letters
to the Editor
5. A. G. Milnes and D. L. Feucht, Heterojunctions and Metal-Semiconductor Junctions. Academic Press, New York (1972). 6. B. L. Sharma and R. K. Purohit, Semiconductor Heterojunctions. International Series qf Monographs in the
Science ofthe Solid Stale, Vol. 5. Pergamon, New York (1974). 7. S. J. Fonash, Solar Cell Device Physics. Academic Press, New York (1981). 8. S. J. Fonash. J. appl. Phys. 51, 2115 (1980).
Solid-StoreHecrronics Vol. 31, No. 8, pp. 1351-1352, 1988 Printed in Great Britain. All rights reserved
REPLY TO “COMMENTS ON THEORETICAL C(V) EQUATION OF AN AMORPHOUS-CRYSTALLINE HETEROJUNCTION AT LOW FREQUENCY”? (Received 16 November 1987)
We also have:
In my paper, eqn (3) of the net charge per unit area in the crystalline depletion zone must be read as:
as Liou says. In eqn (6), EC, and Eu, are the mobility edges in amorphous silicon and EC* and Ev2 are the mobility edges in crystalline silicon. The differences EC, - EFN and EFp- Ev, can be written as EC, - EF, and EF, - Ev, + (-qV) where EF, is the position of the quasi Fermi level at equilibrium in the amorphous silicon bulk and V the applied voltage. The differences EC, - EF, and EF, - Ev, are referred to the amorphous quasi-neutral region. The difference as Ecz - EFN and EFp - Ev2 can be written EC? - EFz + (- qV) and EF2 - Ev2 where EF2 is the position of the quasi Fermi level at equilibrium in the crystalline silicon bulk. The differences EC, - EF2 and EF2 - Ev2 are referred to the crystalline quasi-neutral region. The reference level of the electrostatic potential was taken at the amorphous depletion boundary x,, that is 4(x,) = 0, as Liou says (not x,). Then the free carrier concentrations are given by (amorphous depletion zone):
d(x) 1
nfl (x) = nnoexp [ kT
where: n.,=N,,exp[-*]
,,=h$,exp[--1
i = d($, - 40) -- d+o C dQz dQ,’ near the eqn (13) instead of dQ,,/dQ,. The constancy of the quasi-Fermi levels across the space charge regions of an homojunction has been generally assumed in the literature[l,2]. However, this assumption is valid for low forward voltages (lowlevel injection) and for reverse biases, if they are not too high[3]. At high forward voltages (high-level injection) this assumption fails as Liou says[3,4]. In crystalline heterojunctions, the constancy of the quasi-Fermi levels through both depletion regions has been used in the literature[5,6] and its validity has been questioned also[7,8]. In my paper, the voltage range where this asumption is valid has not been studied. I think that in order to determine this voltage range, a numerical simulation method has to be used taking into account all the dark current mechanisms of an amorphous-crystalline heterojunction. At a given voltage the dominant dark current mechanism in a crystalline homojunction and in an amophours-crystalline heterojunction is not necessarily the same. Furthermore, in the Appendix of my paper it was pointed out that when the applied voltage approximates the built-in voltage the condition ]dQ, ) << 1Q, 1 is not fulfilled (the incremental charge density 1dQ, I is much lower than the space charge density IQ, 1). Then the expression of the capacitance is not valid for these voltages. INTEC Universidad National de1 Litoral Guemes 3450, Santa Fe 3000 Argentina
F. RUBINELLI
REFERENCES
are the equilibrium carrrier concentrations. (The dominant contribution to the amorphous side capacitance C, in the amorphous-crystalline heterojunction comes from the hole trapped carriers if Nd <
J. L. Mall, Physics
of Semiconductors. MC Graw-Hill,
New York, (1964). S. M. Sze, Physics of Semiconductors Devices.
Wiley, New York (1981). C. T. Sah, IEEE Trans. Electron. Dev. ED-13, 839 (1966). R. K. Willardson and A. C. Beer, Semiconductors and
Semimetals, Vol. 15, Contacts, Junciions and Emitters.
tJ. J. Liou, Solid-Slate Hecrronics 31, 1349 (1988).
Academic Press, New York (1981).
1351
1352
Letters
to the Editor
5. A. G. Milnes and D. L. Feucht, Heterojunctions and Metal-Semiconductor Junctions. Academic Press, New York (1972). 6. B. L. Sharma and R. K. Purohit, Semiconductor Heterojunctions. International Series qf Monographs in the
Science ofthe Solid Stale, Vol. 5. Pergamon, New York (1974). 7. S. J. Fonash, Solar Cell Device Physics. Academic Press, New York (1981). 8. S. J. Fonash. J. appl. Phys. 51, 2115 (1980).