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Determination of surface state parameters from surface photo-voltage transients for p-type CdTe
Surface Science 105 (1981) 565-569 North-Holland Publishing Company
DETERMINATION PWOTO-VOLTAGE
S. KUZ~INSKI
OF SURFACE STATE PA~METERS TRANSIENTS FOR p-TYPE CdTe
FROM SURFACE
and A.T. SZAYNOK
Institute of Physics, Trrchnicul University of Wroclaw, Wybrzeze Wyspianskiego 27, X1-370 Wroclaw, Poland Received 8 April 1980; accepted for publication 22 December 1980
The surface photovoltage transients for p-type CdTe sample, illuminated with light of 16 Mm wave-length have been measured. The exper~ent was performed at 2 X 10q6 Torr and 77 K. An analysis of electron transitions was carried out and surface state parameters calculated.
1. Introduction
The results of the surface ~hotovoltage spectroscopy of the p-type CdTe sample have been reported in the paper [ 11. The distinct change in contact potential difference at 16 pm suggests an existence of surface states of the energy 0.08 eV above the top of the valence band. Basing on the phenomenological theory proposed by Bale&a et al. [2] and results of surface photovoltage transients, measured for the wave-length of 16 pm, surface parameters were calculated, such as: capture cross section for holes, capture cross section for photons of the surface states and density of the surface states,
2. Experimental The investigated CdTe sample was p-type with a doping concentration of 3 X lOi cmv3. The measurements were performed for the (110) surface. The sample was mechanically polished and etched in bromine in alcohol solution. Before the measurements the sample was kept in dark for 24 h. As a light source, a silit glow-bar was used. The measurements were carried out at the pressure of 2 X 10e6 Torr at the liquid nitrogen temperature. The results are presented in fig. 1. From the transient of the Vs(t) curve we can calculate the following quantities: tg a?0 = r’,” )
tg (Yr= ;ci,’ ,
The band bending ~39-6028~8
tg QI= vs .
of the non-illuminated
l~OOOO-0000~$02.50
surface amounted
0 Noah-Holland
~blis~ng
to Vg = 0.11 eV. The Company
S. Kuzrn~~~ki~A. T. Szaynok / ~e~~rrnina~io~
iighf
~1
of surfuee state parameters
aqht Off
Fig. 1. Surface photovoltage
transient.
energetic model of the surface layer was presented in ref. [I]. As in the calculation of the Fermi level position a mistake was made, we have presented in fig. 2 the correct band scheme. The value of EF amounts 0.03 eV instead of 0.39 eV, as given in ref. [ 11. This mistake does not change the correctness of the proposed model. The proper value of EF (0.03 eV) makes even more probable the possibility of electron transitions from the valence band to the surface states. The surface states can be empty and accept electrons as they are situated close to the Fermi level. 3. Discussion In order to calculate the surface state parameters, we must consider the surface layer of the investigated sample. It is the depletion p-type layer. The surface is posi-
Fig. 2. Energetic scheme of the surface layer.
S. Kuzminski. A.T. Szaynok / Determination
561
of surface state parameters
tively charged (Q,, > 0) and the space charge Q,, is negative. The light-induced electron transitions from the valence band to the surface states cause a change in SUrfaCC charge AQ,, which is negative. The change in the surface potential barrier which is associated with it. AL’,, is also negative (fig. I). The phenomenological model of such a surface layer, according to the ref. [2], is based on the following assumptions: (1) There are no minority carriers (free electrons). in dark as well as when illuminated with light within the sub-bandgap energy range (hv = 0.08 eV). (2) There is no measurable change in the bulk-free hole concentration as a result 01 electron transitions from the valence band to the surface states. (3) There is the Schottky-type depletion layer at the surface because: qVz/kT
= 16.7
77 K .
at
(4) The surface photovoltage results from transitions of electrons from the valence band to the surface states. induced by illumination with light of energy hv z E, -I; >V’ If the assumptions (I), (2) and (3) are satisfied, a relation between the potential barrier height us and the surface charge density Q,, can be expressed as follows: Q,, = q(uv:”
,
(1)
where CY= (2w,,kTp,,/q2)“’
,
v, =qV,/kT.
The change in charge concentration ,
dp, = -dn,
dQ,, = q dp, >
in the surface states with energy Et equals:
where nt is the concentration of electrons in the surface states and pt is the concentration of holes in the surface states. Differentiating eq. (1). we get: de,,
= -q dlzt % ;qau;“2
Therefore,
du, .
(2)
the rate of electron concentration
change in the surface states equals:
dn,/dr = ri, = $Y,,‘~~ tis .
(3)
This rate is related with the optical and other, mainly thermal, processes of generation and recombination. dn,/dt=G;+
+G,,t
Rt+.
The rate of the light-induced face states: G’;+ =KpPdp1 where K$
(4) electron
transitions
from the valence band to the sur-
9
is the capture
(5) cross section and I is the illumination
intensity
in pho-
568
S. Kuzminski, A.T. Szaynok /Determination
tons/cm2 s. The rate of the thermally valence band to the surface states: G v-+t =KpPtPt
PI =N, exp[-(4
electron
transitions
from the
(61 cross section for holes, multiplied
by their
,
-- &J/W
where p1 is the thermal recombination is: = Kpntps
generated
3
where K, is the surface state capture thermal velocity.
H t+
of surface state parameters
emission
rate constant
3
for holes. The rate of electron
(7)
where ps is the hole concentration at the surface. Basing on the analysis presented in ref. [2], and accepting the approximation of the low illumination intensity lAu,/u~ I< 1, we can express the phenomenological parameters of the surface states in terms of the reduced surface photovoltage potentials:
where u; = q V,o/kT ,
v: = q V;/kT
.
The density of the surface states is: N,=n;
+p;
where $ and pj are the electron and hole concentrations, respectively, in the surface states after illumination. From the analysis of the surface photovoltage transients (fig. 1) p,“,‘p: and E: can be also obtained [2], and the suitable equations have the forms:
(10)
us -
l=” nt
2(~,‘)“~
u;
1 - (D,/rj’) exp(u, - ub)
.
Calculations of phenomenological parameters describing the surface states were performed by applying eqs. (8)-(12). The experimental data accepted for the cal-
S. Kuzminski, A. T. Szaynok / Determination
Table 1 Parameters characterizing valence band (Y (cm-*) 4.89
x 1O’O
the surface
states
569
of surface state parameters
of the energy
Et = 0.08 eV above
KP
Kh
Nt
(cm3 s-l)
(cm*)
(cm-*)
1.5 x 10-r*
4 x 10-14
3.5 x 10’0
the top of the
culations were as follows: V,O=llOmV,
V,’ E91.5 mV ,
AV: = 18.5 mV ,
V,= lOOmV,
V,= lOmV,
I = lo’* photons/cm*
ti; = -1.50
ti; = 7.71 x 10-J v/s )
vs = 1.02 x lo+
x 10-a v/s,
*s ,
v/s .
The results of the calculations are presented in table 1. The results obtained can be compared with that for CdS presented in ref. [3] and for GaAs in ref. [4]. The density of states Nt is of the same order, 10” cm -* for the all three semiconductor compounds. The K, value obtained for CdTe is similar to that for GaAs (Kp > lo-‘* cm3/s). The value of KFh for CdTe (4 X IO-l4 cm*) is the largest one (5 x lo-‘6 to 4 x lo-‘9 cm* for the different groups of states of CdS, and lo-” cm* for GaAs).
References [l] [2] [3] [4]
S. Kuiminski, K. Pater and A.T. Szaynok, Surface Sci. 91 (1980) 707. C.L. Balestra, J. Eagowski and H.G. Gatos, Surface Sci. 64 (1977) 457. J. tagowski, C.L. Balestra and H.G. Gatos, Surface Sci. 29 (1972) 203. A. Morawski, M.G. Slusarczuk, J. Lagowski and H.G. Gatos, Surface Sci. 69 (1977)
53.
DETERMINATION PWOTO-VOLTAGE
S. KUZ~INSKI
OF SURFACE STATE PA~METERS TRANSIENTS FOR p-TYPE CdTe
FROM SURFACE
and A.T. SZAYNOK
Institute of Physics, Trrchnicul University of Wroclaw, Wybrzeze Wyspianskiego 27, X1-370 Wroclaw, Poland Received 8 April 1980; accepted for publication 22 December 1980
The surface photovoltage transients for p-type CdTe sample, illuminated with light of 16 Mm wave-length have been measured. The exper~ent was performed at 2 X 10q6 Torr and 77 K. An analysis of electron transitions was carried out and surface state parameters calculated.
1. Introduction
The results of the surface ~hotovoltage spectroscopy of the p-type CdTe sample have been reported in the paper [ 11. The distinct change in contact potential difference at 16 pm suggests an existence of surface states of the energy 0.08 eV above the top of the valence band. Basing on the phenomenological theory proposed by Bale&a et al. [2] and results of surface photovoltage transients, measured for the wave-length of 16 pm, surface parameters were calculated, such as: capture cross section for holes, capture cross section for photons of the surface states and density of the surface states,
2. Experimental The investigated CdTe sample was p-type with a doping concentration of 3 X lOi cmv3. The measurements were performed for the (110) surface. The sample was mechanically polished and etched in bromine in alcohol solution. Before the measurements the sample was kept in dark for 24 h. As a light source, a silit glow-bar was used. The measurements were carried out at the pressure of 2 X 10e6 Torr at the liquid nitrogen temperature. The results are presented in fig. 1. From the transient of the Vs(t) curve we can calculate the following quantities: tg a?0 = r’,” )
tg (Yr= ;ci,’ ,
The band bending ~39-6028~8
tg QI= vs .
of the non-illuminated
l~OOOO-0000~$02.50
surface amounted
0 Noah-Holland
~blis~ng
to Vg = 0.11 eV. The Company
S. Kuzrn~~~ki~A. T. Szaynok / ~e~~rrnina~io~
iighf
~1
of surfuee state parameters
aqht Off
Fig. 1. Surface photovoltage
transient.
energetic model of the surface layer was presented in ref. [I]. As in the calculation of the Fermi level position a mistake was made, we have presented in fig. 2 the correct band scheme. The value of EF amounts 0.03 eV instead of 0.39 eV, as given in ref. [ 11. This mistake does not change the correctness of the proposed model. The proper value of EF (0.03 eV) makes even more probable the possibility of electron transitions from the valence band to the surface states. The surface states can be empty and accept electrons as they are situated close to the Fermi level. 3. Discussion In order to calculate the surface state parameters, we must consider the surface layer of the investigated sample. It is the depletion p-type layer. The surface is posi-
Fig. 2. Energetic scheme of the surface layer.
S. Kuzminski. A.T. Szaynok / Determination
561
of surface state parameters
tively charged (Q,, > 0) and the space charge Q,, is negative. The light-induced electron transitions from the valence band to the surface states cause a change in SUrfaCC charge AQ,, which is negative. The change in the surface potential barrier which is associated with it. AL’,, is also negative (fig. I). The phenomenological model of such a surface layer, according to the ref. [2], is based on the following assumptions: (1) There are no minority carriers (free electrons). in dark as well as when illuminated with light within the sub-bandgap energy range (hv = 0.08 eV). (2) There is no measurable change in the bulk-free hole concentration as a result 01 electron transitions from the valence band to the surface states. (3) There is the Schottky-type depletion layer at the surface because: qVz/kT
= 16.7
77 K .
at
(4) The surface photovoltage results from transitions of electrons from the valence band to the surface states. induced by illumination with light of energy hv z E, -I; >V’ If the assumptions (I), (2) and (3) are satisfied, a relation between the potential barrier height us and the surface charge density Q,, can be expressed as follows: Q,, = q(uv:”
,
(1)
where CY= (2w,,kTp,,/q2)“’
,
v, =qV,/kT.
The change in charge concentration ,
dp, = -dn,
dQ,, = q dp, >
in the surface states with energy Et equals:
where nt is the concentration of electrons in the surface states and pt is the concentration of holes in the surface states. Differentiating eq. (1). we get: de,,
= -q dlzt % ;qau;“2
Therefore,
du, .
(2)
the rate of electron concentration
change in the surface states equals:
dn,/dr = ri, = $Y,,‘~~ tis .
(3)
This rate is related with the optical and other, mainly thermal, processes of generation and recombination. dn,/dt=G;+
+G,,t
Rt+.
The rate of the light-induced face states: G’;+ =KpPdp1 where K$
(4) electron
transitions
from the valence band to the sur-
9
is the capture
(5) cross section and I is the illumination
intensity
in pho-
568
S. Kuzminski, A.T. Szaynok /Determination
tons/cm2 s. The rate of the thermally valence band to the surface states: G v-+t =KpPtPt
PI =N, exp[-(4
electron
transitions
from the
(61 cross section for holes, multiplied
by their
,
-- &J/W
where p1 is the thermal recombination is: = Kpntps
generated
3
where K, is the surface state capture thermal velocity.
H t+
of surface state parameters
emission
rate constant
3
for holes. The rate of electron
(7)
where ps is the hole concentration at the surface. Basing on the analysis presented in ref. [2], and accepting the approximation of the low illumination intensity lAu,/u~ I< 1, we can express the phenomenological parameters of the surface states in terms of the reduced surface photovoltage potentials:
where u; = q V,o/kT ,
v: = q V;/kT
.
The density of the surface states is: N,=n;
+p;
where $ and pj are the electron and hole concentrations, respectively, in the surface states after illumination. From the analysis of the surface photovoltage transients (fig. 1) p,“,‘p: and E: can be also obtained [2], and the suitable equations have the forms:
(10)
us -
l=” nt
2(~,‘)“~
u;
1 - (D,/rj’) exp(u, - ub)
.
Calculations of phenomenological parameters describing the surface states were performed by applying eqs. (8)-(12). The experimental data accepted for the cal-
S. Kuzminski, A. T. Szaynok / Determination
Table 1 Parameters characterizing valence band (Y (cm-*) 4.89
x 1O’O
the surface
states
569
of surface state parameters
of the energy
Et = 0.08 eV above
KP
Kh
Nt
(cm3 s-l)
(cm*)
(cm-*)
1.5 x 10-r*
4 x 10-14
3.5 x 10’0
the top of the
culations were as follows: V,O=llOmV,
V,’ E91.5 mV ,
AV: = 18.5 mV ,
V,= lOOmV,
V,= lOmV,
I = lo’* photons/cm*
ti; = -1.50
ti; = 7.71 x 10-J v/s )
vs = 1.02 x lo+
x 10-a v/s,
*s ,
v/s .
The results of the calculations are presented in table 1. The results obtained can be compared with that for CdS presented in ref. [3] and for GaAs in ref. [4]. The density of states Nt is of the same order, 10” cm -* for the all three semiconductor compounds. The K, value obtained for CdTe is similar to that for GaAs (Kp > lo-‘* cm3/s). The value of KFh for CdTe (4 X IO-l4 cm*) is the largest one (5 x lo-‘6 to 4 x lo-‘9 cm* for the different groups of states of CdS, and lo-” cm* for GaAs).
References [l] [2] [3] [4]
S. Kuiminski, K. Pater and A.T. Szaynok, Surface Sci. 91 (1980) 707. C.L. Balestra, J. Eagowski and H.G. Gatos, Surface Sci. 64 (1977) 457. J. tagowski, C.L. Balestra and H.G. Gatos, Surface Sci. 29 (1972) 203. A. Morawski, M.G. Slusarczuk, J. Lagowski and H.G. Gatos, Surface Sci. 69 (1977)
53.