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Slow photoconductive kinetics in Cl- and Ga-doped CdTe
Solid State Communications,
Vol. 13, PP. 8 19—822, 1973.
Pergamon Press.
Printed in Great Britain
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe D.L. Losee, R.P. Khosla, D.K. Ranadive and F.T.J. Smith Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. (Received 31 May 1973 by R.H. Silsbee)
The slow photoconductive kinetics associated with CI and Ga donors in CdTe are examined by Schottky-barrier capacitance methods. The results indicate that a nonelectronic mechanism is the rate-limiting step in the photodecay process.
RECENTLY Iseler and co-workers1 have reported extremely long recombination times observed in donordoped CdTe. Their equilibrium transport measurements under hydrostatic pressure have suggested that most donors in CdTe are associated primarily with one of the higher-lying conduction-band minima with ground-state energies at zero pressure above the energy of the F minimum. These authors have further suggested that the slow photoconductive decay observed in Cl- and Ga-doped CdTe is a feature of these ‘non-F’ donor states. An alternative, ‘double-acceptor,’ model has been given by Lorenz, Woodbury, and Segall2 to explain the slow decay rates seen in nominally pure CdTe. In this communication we present emission-rate data which are at variance with both these models and are, at least for the Ga centers, inconsistent with any purely electronic excitation mechanism.
cm3 for Cl and 4.2)< 1017 cm’3 for Ga. Photoconductive decay time measurements on adjacent bars agreed well with the results of MacMillan4 being characterized as = I X 10-13 exp [0.51 eV/kT} and 1 X iO’~exp [0.31 eV/kT] sec, respectively. Bars of these materials were etched in 5% Br-methanol solution and ohmic In contacts soldered to them. The bars were cleaved in air and immediately placed in an oil-free vacuum system where an array of Au dots was deposited by evaporation. The samples were placed in a thermostated dewar, where capacitance of the devices was measured. Plots of C~vs V, in the dark, first at high temperatures (~200°K) and then at low temperatures (~100°K),determine the relative densities of conduction-band electrons, N, (fast responding), and those trapped in slow states, N~, First we measured the rate of emptying of the slow levels by monitoring the time dependence of the capacitance after application of a reverse bias voltage step. The junction capacitance essentially measures the position of the edge of the free-carrier distribution if no deep levels are responding to the a.c. test signal. Assuming relatively shallow levels, it is straightforward to show that to a good approximation the rate of level emptying is given by
Sah and his co workers3 have described numerous experimental variations afforded by the junction diode configuration for examination of the kinetics of slow trapping states. Here we present results of two such measurements on Schottky-barrier diodes: (1) transient capacitance after application of a reverse bias voltage step; and (2) field enhancement of the thermal emissiori rate, Schottky-barrier diodes were formed on Bridgmangrown CdTe, which had been doped from the melt with Cl or Ga and annealed at 800°C under saturated
Te
1 ~ C~ C~ dt
.
.
±
where C
=
—
+ ~
\
(1)
Ni’,!
4 is the capacitance just after applying a voltage step (at t = 0). C,.. is the new steady-state capacitance and (dCldt)~~0~ is the rate of charge of the
Cd pressure. Hall coefficient measurements showed room-temperature carrier concentrations of 6.5 X 1017 819
820
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
capacitance just after t = 0. The factor (1 +N~/N,)’ reflects the nonlinear dependence of capacitance on charge density. Consider first the low-temperature behavior. At 77°Kapplying a voltage step 0.6 V to junctions on either Cl- or Ga-doped material, we find an upper bound on the rate of emission at this temperature, 1/re < l0~sec1.(Thiscorresponds to less than 0.0! pF change in C over a 16 hr interval.) This upper bound allows an estimate of the mixing of a supposed non-F donor wave function with conduction-band wave functions. We apply Fermi’s ‘Golden Rule’ in a Wannier representation and require I < 1.5 X 10-11 eV, where V is a perturbing potential due to the substitutional impurity, s > is the donorstate wave function, and I k > is a conduction-band wave function. Such small mixing of wave functions supposedly due to substitutional impurities degenerate with the conduction band seems unlikely and no selection rules are applicable. Therefore, this result is inconsistent with the non-F donor picture. It differs from theoretical estimates5 of Te by a factor of nearly —
1016.
/ /
/
10,000
t
// or / EzO.5~eV / / /1 hr
Vol. 13, No. 7
At higher temperatures, thermally activated emission from the slow states is observed. The measurement of the emission rate with reverse bias applied to the junction is complicated slightly by the effect of the strong electric field acting on the centers. We observe, however, that only the Cl-doped samples show a field enhancement of emission rate. The emission rate, defined by equation (I) and measured with a reverse bias step equal to —0.6 V, is shown as a function of 1/Tin Fig. 1. For Ga-doped material, the slow centers empty with an activation energy of 0.31 eV, precisely equal to that determined for the photoconductive decay and the photocapacitance decay. The emission rate activation energy for Cl must be corrected for the effect of the strong electric field acting on the center. When this is done, the zero-field emission-rate activation energy is found to be 0.49 eV, only slightly below the photoconductive (and photocapacitative) activation energy 0.51 eV. The emission rate, normalized to the zero-field limit, is shown as a function of magnitude of the reverse bias voltage step in Fig. 2 for Cl- and Ga-doped samples. The rate for the Ga centers is constant, even in the
-Photoconductiv~ty —Photocapacitonce o - Transient Capacitance
0pholoca~7’
bOo-
/ %
b
E~O.47eV CdTe:C1
ioo-
e~
..._E=O.3IeV CdTe:Ga
Jo
A
J5.0
6,0
70
8.0
9.0
10 0
O~/T(OKH) FIG - 1. Time constants for emission,
Te, and photoconductive and photoca~acitativedecay. Te is determined by application of—0.6V to the Schottky barrier diode at time t = 0. From C’ vs Vwe find for doping with Cl: N~=2.6X1017,N,=’8.2X10’7withGa:N 17,N 82.4X 10 1=4.OX l0’~(seetext).
Vol. 13, No. 7
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
Here z_ and z4 are depletion layer widths just before and just after application of the voltage step, = z, and r’(V) is the measured rate of emission defined by equation (1). The factor ‘y is a correction for the local field acting on a center. ‘y varies between 1 and (2/3 + c/3c~)depending on the size of tile center involved and the ionicity and structure of the material. With equation (1) we obtain a good fit to the data with an effective interaction radius of(4.9 ±0.1) A for Cl using the Lorentz local field approximation (~y= 3.88). The effective radius of the Ga center is found to be (0 ±0.02) A. The fIt is indicated in Fig. 2. If a coulombic potential well is assumed instead of the localized well approximation, 6 predicts a then the strong increase usual Poole—Frenkel in the ionizationexpression rate of the center. This can be included in the calculation of the transient capacitance decay but a noticeably inferior fit to these data is obtained for Cl-doped material andexhibits no fit atnoall is given for the Ga-doped material (which effect of electric field). These results also are inconsistent
/
/
-
-
—
9/ /o
~
~/ / / /
3 .
~
o—~ aI AiG~
/
O
-
/ ,-J —Localized
2~-
Po~enliolWell Model lLorentz Field Approx,)
/‘ /7 /
-~
/
,~‘-
-——-
Poole-Frenkel Model
.
,~
~
A
~
A
~
/ /
c0
0.2
~
~ o~0.6
0.8
.0
V
2. Relative emptying rates for tile slow centers as a function of magnitude of the voltage step. Each set of data is normalized to the zero field limit (at 173 and 110 K for Cl and Ga respectively). We measure barrier heights 0.81 and 0.69 V for Cl and Ga doped material respectively (from C’2 vs V). At —0.6 V the electric field at time = 0+ is 6 X i0~and 4 X iO~V/cm respectively. The data have been fit to the localized potential model of equation (2). The fitted value of potential well radius is 4.9 ±0.1 and 0.0 ±.02 A for Cl and Ga respectively. For comparison an attempt to fit a Poole—Frenkel model to the Cl data is shown, FIG.
presence of high fileds (> i0~V/cm). In the limit of low fields, for either donor, the emptying rate is nearly equal to the photoconducting decay rate. If one assumes a localized potential well for the slow center, the electric field should increase the emptying rate by a factor exp [Ea/kT] where E is the local electric field and a is an effective radius of the potential well. A relatively straightforward calculation including the field distribution in the Schottky barrier then yields -2 -1 -2 ~ l 2[(~j +zi~ ) exp~~z)—(~j ,
~
Te(V)
Te(0)
—
(2) where 2~
ekT
821
with a non-F donor picture in that the potential must asymptotically approach coulombic even for a non-F donor center The complete localization for the Ga center indicated by the absence of a field dependence is actually inconsistent with any electronic mechanism as the rate-limiting step in the excitation process. Thus .
.
2
particularly for this center, a double-acceptor model must also be ruled out. A double-acceptor center also seems unlikely in Cl-doped material because of the lack of sensitivity to holes generated by band-gap irradiation.4 Other models, such as the clustered defect model suggested by Eernisse and Norris7 to explain slow recombination kinetics in epitaxial Si, do not seem likely because of(1) the simplicity of the activation (for the Ga centers the rate is given by a simple exponential over ten decades8), (2) the absence of a field dependence and (3) rough agreement between total center concentrations and mass spectrographic analysis of Cl and Ga concentrations.4 In separate experiments, attempts were made to increase the free-carrier concentration (and hence raise the Fermi level) by doubly doping CdTe with Cl and Ga. Melt-grown samples (Cd-annealed), however, have free carrier concentrations approximately 8 X 1016 cni’~’3,a factor of nearly 10 lower than singly doped samples. Mass spectrographic analysis showed large concentrations of Cl and Ga and mobility data indicate
822
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
that these samples are closely compensated. Although the photoconducting behavior of these samples is rather complex, persistent photoconductivity is observed with components that can be attributed to Cl and Ga separately. Here the magnitude of the persistent photoconductivity is not consistent with the non-F donor picture and the assignments previously made for the donor-level energies.’ ‘~
High-temperature equilibrium transport measurements on CdTe show that there is a strong tendency for formation of donor complexes.9 These facts indicate that the slow kinetics in Cl- and Ga-doped
1.
Vol. 13, No. 7
CdTe may in fact be due to a donor complex. Simple pairing is ruled out on the basis of the asymetry in the field dependence of Te for the two donors. Complexing with a native defect could explain the difference between cation- and anion-substituted donors. To summarize, we have measured emission rates from the slow Ga and CI centers in CdTe. The results are inconsistent with both models proposed previously. Similar slow kinetics have been observed for other donors in compound semiconductors.1°This suggests that previous interpretations of transport data in these materials may require reexamination.
REFERENCES ISELER G.W., KAFALAS J.A., STRAUSS A.J., MACMILLAN H.F. and BUBE R.H., Solid State Commun. 10, 619 (1972).
2.
LORENZ M.R., SEGALL B. and WOODBURY H.H.,Phys. Rev. 134, A75l (1964).
3. 4.
SAH C.T., FORBES L., ROSIER L.L. and TASCH A.F., Jr., Solid State Electron. 13, 759 (1970). MACMILLAN H.F. PhD Thesis, Stanford University, unpublished (1972).
5.
KAPLAN H.,J. Phys. Chem. Solids 24,1593(1963).
6. 7.
FRENKEL J., Phys. Rev. 54, 647 (1938). EERNISSE E.P. and NORRIS C.B., Solid State Electron. 16, 315 (1973).
8.
LOSEE D.L., to be published.
9.
SMITH F.T.J, Bull. Am. Phys. Soc. 18, 325 (1973).
10.
For example, CRAFORD M.G., STILLMAN G.E., ROSS! J.A. and HOLYONYAK N.,Phys. Rev. 168, 867 (1968).
Die langsame Kinetik der Photoleitung in CdTe, dotiert mit Ga oder Cl Donatoren, wird mit der Methode der Schottky-Barrieren Kapazitdt untersucht. Die Ergebnisse weisen darauf hin, dass der geschwindigkeitsbestimmende Schritt beim Abklingen der Photoleitung em nicht-elektronischer Prozess ist.
Vol. 13, PP. 8 19—822, 1973.
Pergamon Press.
Printed in Great Britain
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe D.L. Losee, R.P. Khosla, D.K. Ranadive and F.T.J. Smith Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, U.S.A. (Received 31 May 1973 by R.H. Silsbee)
The slow photoconductive kinetics associated with CI and Ga donors in CdTe are examined by Schottky-barrier capacitance methods. The results indicate that a nonelectronic mechanism is the rate-limiting step in the photodecay process.
RECENTLY Iseler and co-workers1 have reported extremely long recombination times observed in donordoped CdTe. Their equilibrium transport measurements under hydrostatic pressure have suggested that most donors in CdTe are associated primarily with one of the higher-lying conduction-band minima with ground-state energies at zero pressure above the energy of the F minimum. These authors have further suggested that the slow photoconductive decay observed in Cl- and Ga-doped CdTe is a feature of these ‘non-F’ donor states. An alternative, ‘double-acceptor,’ model has been given by Lorenz, Woodbury, and Segall2 to explain the slow decay rates seen in nominally pure CdTe. In this communication we present emission-rate data which are at variance with both these models and are, at least for the Ga centers, inconsistent with any purely electronic excitation mechanism.
cm3 for Cl and 4.2)< 1017 cm’3 for Ga. Photoconductive decay time measurements on adjacent bars agreed well with the results of MacMillan4 being characterized as = I X 10-13 exp [0.51 eV/kT} and 1 X iO’~exp [0.31 eV/kT] sec, respectively. Bars of these materials were etched in 5% Br-methanol solution and ohmic In contacts soldered to them. The bars were cleaved in air and immediately placed in an oil-free vacuum system where an array of Au dots was deposited by evaporation. The samples were placed in a thermostated dewar, where capacitance of the devices was measured. Plots of C~vs V, in the dark, first at high temperatures (~200°K) and then at low temperatures (~100°K),determine the relative densities of conduction-band electrons, N, (fast responding), and those trapped in slow states, N~, First we measured the rate of emptying of the slow levels by monitoring the time dependence of the capacitance after application of a reverse bias voltage step. The junction capacitance essentially measures the position of the edge of the free-carrier distribution if no deep levels are responding to the a.c. test signal. Assuming relatively shallow levels, it is straightforward to show that to a good approximation the rate of level emptying is given by
Sah and his co workers3 have described numerous experimental variations afforded by the junction diode configuration for examination of the kinetics of slow trapping states. Here we present results of two such measurements on Schottky-barrier diodes: (1) transient capacitance after application of a reverse bias voltage step; and (2) field enhancement of the thermal emissiori rate, Schottky-barrier diodes were formed on Bridgmangrown CdTe, which had been doped from the melt with Cl or Ga and annealed at 800°C under saturated
Te
1 ~ C~ C~ dt
.
.
±
where C
=
—
+ ~
\
(1)
Ni’,!
4 is the capacitance just after applying a voltage step (at t = 0). C,.. is the new steady-state capacitance and (dCldt)~~0~ is the rate of charge of the
Cd pressure. Hall coefficient measurements showed room-temperature carrier concentrations of 6.5 X 1017 819
820
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
capacitance just after t = 0. The factor (1 +N~/N,)’ reflects the nonlinear dependence of capacitance on charge density. Consider first the low-temperature behavior. At 77°Kapplying a voltage step 0.6 V to junctions on either Cl- or Ga-doped material, we find an upper bound on the rate of emission at this temperature, 1/re < l0~sec1.(Thiscorresponds to less than 0.0! pF change in C over a 16 hr interval.) This upper bound allows an estimate of the mixing of a supposed non-F donor wave function with conduction-band wave functions. We apply Fermi’s ‘Golden Rule’ in a Wannier representation and require I
1016.
/ /
/
10,000
t
// or / EzO.5~eV / / /1 hr
Vol. 13, No. 7
At higher temperatures, thermally activated emission from the slow states is observed. The measurement of the emission rate with reverse bias applied to the junction is complicated slightly by the effect of the strong electric field acting on the centers. We observe, however, that only the Cl-doped samples show a field enhancement of emission rate. The emission rate, defined by equation (I) and measured with a reverse bias step equal to —0.6 V, is shown as a function of 1/Tin Fig. 1. For Ga-doped material, the slow centers empty with an activation energy of 0.31 eV, precisely equal to that determined for the photoconductive decay and the photocapacitance decay. The emission rate activation energy for Cl must be corrected for the effect of the strong electric field acting on the center. When this is done, the zero-field emission-rate activation energy is found to be 0.49 eV, only slightly below the photoconductive (and photocapacitative) activation energy 0.51 eV. The emission rate, normalized to the zero-field limit, is shown as a function of magnitude of the reverse bias voltage step in Fig. 2 for Cl- and Ga-doped samples. The rate for the Ga centers is constant, even in the
-Photoconductiv~ty —Photocapacitonce o - Transient Capacitance
0pholoca~7’
bOo-
/ %
b
E~O.47eV CdTe:C1
ioo-
e~
..._E=O.3IeV CdTe:Ga
Jo
A
J5.0
6,0
70
8.0
9.0
10 0
O~/T(OKH) FIG - 1. Time constants for emission,
Te, and photoconductive and photoca~acitativedecay. Te is determined by application of—0.6V to the Schottky barrier diode at time t = 0. From C’ vs Vwe find for doping with Cl: N~=2.6X1017,N,=’8.2X10’7withGa:N 17,N 82.4X 10 1=4.OX l0’~(seetext).
Vol. 13, No. 7
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
Here z_ and z4 are depletion layer widths just before and just after application of the voltage step, = z, and r’(V) is the measured rate of emission defined by equation (1). The factor ‘y is a correction for the local field acting on a center. ‘y varies between 1 and (2/3 + c/3c~)depending on the size of tile center involved and the ionicity and structure of the material. With equation (1) we obtain a good fit to the data with an effective interaction radius of(4.9 ±0.1) A for Cl using the Lorentz local field approximation (~y= 3.88). The effective radius of the Ga center is found to be (0 ±0.02) A. The fIt is indicated in Fig. 2. If a coulombic potential well is assumed instead of the localized well approximation, 6 predicts a then the strong increase usual Poole—Frenkel in the ionizationexpression rate of the center. This can be included in the calculation of the transient capacitance decay but a noticeably inferior fit to these data is obtained for Cl-doped material andexhibits no fit atnoall is given for the Ga-doped material (which effect of electric field). These results also are inconsistent
/
/
-
-
—
9/ /o
~
~/ / / /
3 .
~
o—~ aI AiG~
/
O
-
/ ,-J —Localized
2~-
Po~enliolWell Model lLorentz Field Approx,)
/‘ /7 /
-~
/
,~‘-
-——-
Poole-Frenkel Model
.
,~
~
A
~
A
~
/ /
c0
0.2
~
~ o~0.6
0.8
.0
V
2. Relative emptying rates for tile slow centers as a function of magnitude of the voltage step. Each set of data is normalized to the zero field limit (at 173 and 110 K for Cl and Ga respectively). We measure barrier heights 0.81 and 0.69 V for Cl and Ga doped material respectively (from C’2 vs V). At —0.6 V the electric field at time = 0+ is 6 X i0~and 4 X iO~V/cm respectively. The data have been fit to the localized potential model of equation (2). The fitted value of potential well radius is 4.9 ±0.1 and 0.0 ±.02 A for Cl and Ga respectively. For comparison an attempt to fit a Poole—Frenkel model to the Cl data is shown, FIG.
presence of high fileds (> i0~V/cm). In the limit of low fields, for either donor, the emptying rate is nearly equal to the photoconducting decay rate. If one assumes a localized potential well for the slow center, the electric field should increase the emptying rate by a factor exp [Ea/kT] where E is the local electric field and a is an effective radius of the potential well. A relatively straightforward calculation including the field distribution in the Schottky barrier then yields -2 -1 -2 ~ l 2[(~j +zi~ ) exp~~z)—(~j ,
~
Te(V)
Te(0)
—
(2) where 2~
ekT
821
with a non-F donor picture in that the potential must asymptotically approach coulombic even for a non-F donor center The complete localization for the Ga center indicated by the absence of a field dependence is actually inconsistent with any electronic mechanism as the rate-limiting step in the excitation process. Thus .
.
2
particularly for this center, a double-acceptor model must also be ruled out. A double-acceptor center also seems unlikely in Cl-doped material because of the lack of sensitivity to holes generated by band-gap irradiation.4 Other models, such as the clustered defect model suggested by Eernisse and Norris7 to explain slow recombination kinetics in epitaxial Si, do not seem likely because of(1) the simplicity of the activation (for the Ga centers the rate is given by a simple exponential over ten decades8), (2) the absence of a field dependence and (3) rough agreement between total center concentrations and mass spectrographic analysis of Cl and Ga concentrations.4 In separate experiments, attempts were made to increase the free-carrier concentration (and hence raise the Fermi level) by doubly doping CdTe with Cl and Ga. Melt-grown samples (Cd-annealed), however, have free carrier concentrations approximately 8 X 1016 cni’~’3,a factor of nearly 10 lower than singly doped samples. Mass spectrographic analysis showed large concentrations of Cl and Ga and mobility data indicate
822
SLOW PHOTOCONDUCTIVE KINETICS IN Cl- AND Ga-DOPED CdTe
that these samples are closely compensated. Although the photoconducting behavior of these samples is rather complex, persistent photoconductivity is observed with components that can be attributed to Cl and Ga separately. Here the magnitude of the persistent photoconductivity is not consistent with the non-F donor picture and the assignments previously made for the donor-level energies.’ ‘~
High-temperature equilibrium transport measurements on CdTe show that there is a strong tendency for formation of donor complexes.9 These facts indicate that the slow kinetics in Cl- and Ga-doped
1.
Vol. 13, No. 7
CdTe may in fact be due to a donor complex. Simple pairing is ruled out on the basis of the asymetry in the field dependence of Te for the two donors. Complexing with a native defect could explain the difference between cation- and anion-substituted donors. To summarize, we have measured emission rates from the slow Ga and CI centers in CdTe. The results are inconsistent with both models proposed previously. Similar slow kinetics have been observed for other donors in compound semiconductors.1°This suggests that previous interpretations of transport data in these materials may require reexamination.
REFERENCES ISELER G.W., KAFALAS J.A., STRAUSS A.J., MACMILLAN H.F. and BUBE R.H., Solid State Commun. 10, 619 (1972).
2.
LORENZ M.R., SEGALL B. and WOODBURY H.H.,Phys. Rev. 134, A75l (1964).
3. 4.
SAH C.T., FORBES L., ROSIER L.L. and TASCH A.F., Jr., Solid State Electron. 13, 759 (1970). MACMILLAN H.F. PhD Thesis, Stanford University, unpublished (1972).
5.
KAPLAN H.,J. Phys. Chem. Solids 24,1593(1963).
6. 7.
FRENKEL J., Phys. Rev. 54, 647 (1938). EERNISSE E.P. and NORRIS C.B., Solid State Electron. 16, 315 (1973).
8.
LOSEE D.L., to be published.
9.
SMITH F.T.J, Bull. Am. Phys. Soc. 18, 325 (1973).
10.
For example, CRAFORD M.G., STILLMAN G.E., ROSS! J.A. and HOLYONYAK N.,Phys. Rev. 168, 867 (1968).
Die langsame Kinetik der Photoleitung in CdTe, dotiert mit Ga oder Cl Donatoren, wird mit der Methode der Schottky-Barrieren Kapazitdt untersucht. Die Ergebnisse weisen darauf hin, dass der geschwindigkeitsbestimmende Schritt beim Abklingen der Photoleitung em nicht-elektronischer Prozess ist.