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Ultimate detectivity of (CdHg)Te infrared photoconductors
ULTIMATE DETECTIVITY OF (CdHg)Te INFRARED PHOTOCONDUCTORS E. IGRAS,J. PIOTROWSKIand T. PIOTROWSKI Military
Technical (Received
Academy,
Warsaw,
Poland
21 June 1978)
Abstract-Dependence of ultimate detectivity ot,.,, on cutoff wavelength and detector ture for photoconductive (CdHg)Te infrared detectors have been calculated. The expression has been obtained: 7100
temperafollowing
+ 0.616
RLX = 4.5 x JO’T-3’21~~8 exp TI’ c,, 3&. 21,, + 0.247 > Calculations experimental
have been made for intrinsic data have been compared.
1.
and
n-type
material.
Theoretical
calculations
and
INTRODUCTION
A number of studies on performance limits for photoconductive (CdHg)Te detectors of optimal construction have been carried out since 1971. The key problem is to determine the dominating mechanism of recombination which limits the upper value of recombination time. Borrello et al.“’ calculated detectivity as a function of temperature and cutoff wavelength assuming a linear recombination model. Recent studies revealed, however,‘2*3’ that Auger recombination dominates in most cases. The ultimate D* value of a (CdHg)Te photoconductor assuming Auger recombination was calculated by M. A. Kinch and S. R. Borrello for n-type 0.1 eV material. (3) Previously such calculations were performed for cooled (8-14) prnc4) and room temperature (2-14) prnc5’ detectors. In this paper we give generalized expressions for ultimate D* values.
2. EVALUATION
OF (CdHg)Te
DETECTOR
PARAMETERS
2.1. Voltage responsivity We consider the detector schematically shown in Fig. 1. The element is made from homogeneous intrinsic or weakly n-type material. We suppose that electron and hole lifetime are equal and that surface recombination may be neglected. Because of the high ratio of electron to hole mobility we consider only the influence of electrons on the conductivity and photoconductivity. If the detector is current-biased and the illumination is weak, the following relation can be obtained for voltage responsivity: R,=
Vqd
tlwhcn,(l + 4n2f%2)“2
where V is bias voltage; 7 is recombination time; r] is effective quantum yield; no is equilibrium electron concentration; 1, w, t are the detector dimensions as shown in Fig. 1; f is modulation frequency.
In the optimum case, i.e. when reflection coefficients from frontal and rear surfaces are R, = 0 and R2 = 1, effective quantum yield is given by: rj = qo[l - exp( - 2at)] 19/2-- R
143
(2)
E. IGRA~ J. PIOTROWSKI and
144
Fig. 1. P~otoconductive
1.
P~OTROWSKI
(CdHg)Te detector
where so is internal quantum efficiency, i.e. number of electron-hole an absorbed photon. Then the expression for voltage responsivity takes the form: R, =
pairs generated
I/@[1 - exp(-Zo(t)@ hClWrn~(1 + 47?f%2)“2
by
(3)
Equatibn 3 shows that voltage responsivity increases monotonically with the increase of bias voltage. Bias voltage, however, is limited by thermal conditions, and we introduce the density of dissipated power P/wZ. Then from (3) we obtain: 1 - expf - 2ar) + 4n2f2s2)1’t
;391
(4)
where e is electronic charge: p,, is electron mobility, 2.2. Noise Four types of noise play an important role in photoconductive detectors: (1) Johnson-Nyquist noise, (2) generation-recombination noise, (3) l/f noise, and (4) radiation noise. The root mean square of Johnson-Nyquist noise voltage in the bandwidth 4f is given by: v,_, = (4kTRAf)“2
(5)
where k is Boltzman’s constant:
T is temperature;
R is resistance.
Generation-recombination noise is the result of the statistical character and recombination processes in semiconductors. Generation-recombination age is given by the following formula:‘3’ POGf V,;, = 2V n&o + po)lwt(l + 47@Vj
of generation noise volt-
1’2
(6)
where no. PO are the equilibrium carrier concentrations. The expression is valid for arbitrary interband generation-recombination processes. In the case of Shockley-Read generation-recombination it is valid for low density of recombination centers (n, e no). Equation 6 shows that spectral distribution of generation-recombination noise is constant for low frequencies v e 1/27cr) and decreases for high frequencies.
Ultimate
detectivity
of (CdHg)Te
infrared
photoconductors
145
Equation 6 for intrinsic material takes the form:
W
v,, = v
[ tIilWf(l
+
112
47r2~2r2)1
where ni is intrinsic concentration. For low frequencies an important role can be played by l/f noise. Its voltage cannot be calculated theoretically. It depends on surface and contact phenomena. In many cases l/fvoltage can be neglected in comparison with other kinds of noise. Radiation noise plays a role only at high signal or background radiation levels and is neglected in the case of small signal and highly reduced background radiation. 2.3. Ultimate detectivity Detectivity
D* is defined by the relation: D*
KA”2(W”2
=
(8)
V” where V, is root mean square noise voltage; A is detector
area.
Taking into account only Johnson-Nyquist and generation-recombination intrinsic or n-type material at low frequency (27rfr 6 1) we obtain :
noise, for
where 1 -
F(S, C) =
s=
e-2S
F2(SC + 1)“2 at,
c = WWP)
*(no/W. (no + POVPO,
P = rate of power dissipation in the detector. SC product is the square of the ratio of Johnson-Nyquist noise to generation-recombination noise. The graph of the F(S,C) function is given in Fig. 2. It is seen that for each C value, the optimum detector thickness can be found for which F(S,C) reaches its maximum. The F(S,C) value increases with decrease of the C value and reaches its absolute maximum value, equal to 0.903, for S = 0.625.“’ This is just the case of detectivity limitation by generation-recombination noise. In this case the detectivity limit can be expressed by:
(10)
WA,,=
The detectivity limit depends on carrier concentration, recombination time and absorption coefficient. It is independent of detector geometry. For not too high photon energy, typical for (CdHg)Te detector application, one can take internal quantum yield value ‘lo equal to unity. Because the detectivity limit is obtained in almost intrinsic material, then the following relation can be obtained:
(11) The maximum value of recombination
time is limited by Auger recombination
ti = ZAi.
146
E. IGRAS,~. PIOTROWSKI and T. PIOTROWSKI
S
Fig, 2. The graph
of function
F(S.CI.
This is the case of the uttimate detectivity. The value (ff~~i~~i~ depends on material composition, temperature and wavelength. For each wavelength there is an optimum composition ~l,,~,, when the ultimate detectivity is obtained. To determine the dependence of ultimate detectivity it is necessary to know the following relations: n,(i,,,, 77, s~~~(&,~.T) and c((A,,,,T). In the case of parabolic bands the dependence of intrinsic carrier concentration II, on temperature T and energy gap E, is given by the following expression?’ ni = 4.3 x 10’” Ei’“T3”
2
3
4
6
IO
x Fig. 3. Recombination
time in (CdHg)Te
exp
ccl1
15
(12)
20
30
40
Pm
vs cutoff wavelength to Eqn (151.
at various
temperatures
according
Ultimate detectivity of (CdHg)Te infrared photoconductors
147
where k is Boltzman’s constant. Equation
12 can be written as: (13)
(mm31
(W(ccm)
(m) W
Recombination time investigations revealed that Auger recombination dominates in (CdHg)Te with high electron concentration (n > 3 x f02’m-3f, i.e. for high intrinsic concentrations or in n-doped samples. (2*4,7)For low electron concentration, i.e. in some cooled or p-type (CdHg)Te detectors, Shockley-Read recombination dominates. Then, most often. in practically important (CdHg)Te detectors Auger recombination determines the detector parameters. We will deal further with this case. For intrinsic, parabolic band material,(4*8’ when Auger recombination dominates, the recombination time is given by the expression: 3.8 x lO-‘s~~(l + r)l12(1 + *l)exp[(+$$)z] ?Ai
(14)
=
where mx/mo is effective mass of an electron to a mass of a free electron ratio; E is static dielectric constant; r is electron to hole effective mass ratio; F,F2 is the product of two wave-function-overlap integrals.
Taking Eqn 14 and m,*/mo = O.O7E,, IF, F2/ = 0.1, mean E value as in Ref. 9, the dependence of ~~~~ on detector temperature T and cutoff wavelength has been obtained : ~~~= 1.92 x 1016T-3’2;1,‘!2
exp[(qs)(iI
] ~$)].
(15)
(IQ aW-4
(s)
There is no general expression for absorption coefficient dependence on temperature and energy gap. For (CdHg)Te, however, as for direct gap semiconductors, the following approximation can be assumed: hc
for
a=0
Y < E, hc 7 > E R’
for
In calculations of detector parameters we took tl = 5 x 104m-‘. This value was taken to estimate the energy gap from absorption measurement.“” Using Eqns 11-15 the following relation for ultimate detectivity can be obtained: O*,,, = 4.5 x 107T-3’2~~~8 exp (mHz”2W-‘)
(IQ
The graph of this dependence
(pm)
is given in Fig. 4.
3. COMPARISON
OF
EXPERIMENTAL
CALCULATIONS
WITH
RESULTS
Dependence of recombination time ZAion cutoff wavelength and detector temperature from (15) is given in Fig. 3. For high detector temperature and composition
obtained
E.
IGRAS. J. P~OTROWSKIand 7. PIOTROWSKI
A
I
I
3
4
I 6
IO
I5
I 20
30
I
40
Fig. 4. Ultimate detectivity LIZ,,,,for photoconductive (CdHg)Te detectors as a function of cutoff wavelength at different temperatures. Results of our measurements: for 77K are indicated by filled circles: for ZOOKare indicated by open circles; for 300K are indicated by triangles. Data for 77K according to 11 indicated by x Data for 77K according to 12 indicated by C.
HgTe (x S 0.3). i.e. for i,,, > 4flm, calculated ialues of T\, are consistent with experimental data for epitaxial (CdHg)Te layers.“’ For low temperatures as well as for relatively CdTe-rich alloys experimental recombination time is much lower than theoretical because of the additional effect of Shockley-Read and radiative recombination. In Fig. 4 the theoretical relation f3*,,,(&,) for different detector temperatures is presented. Our experimental data of D*m,x(A,,) for epitaxial (CdHg)Te layers are also given. For uncooled detectors the best accordance of theoretical and experimental data are observed at 3, = 4-6 pm. For A,, < 4 pm experimental values are lower than predicted. This is probably caused by the effect of surface and Shockley-Read recombination and deviations from intrinsic concentration observed in samples. For I,, > 6pm the effect of l/‘noise (especially for high bias current) and sometimes amplifier noise are observed. Misfit between ultimate detectivity and experimental results in the short-wave region increases with temperature decrease. This is caused by the fact that experimental results of recombination time are rising slower with temperature decrease than theoretical values. near
Ultimate detectivity of (CdHg)Te infrared photoconductors
149
Equation 16 has been obtained when Auger recombination prevails. Comparing it with the expression obtained in Ref 1 for linear recombination model, one can see that in our case the dependence of P&,x (E,) is stronger than in Ref. 1, 4. SUMMARY 1.
When Auger recombination tor is expressed by:
(mHz”*W-
’)
prevails, ultimate detectivity of a (CdHg)Te photoconduc-
6)
(w)
2. For uncooled detectors the best accordance of theoretical and experimental data occurs at 1 = 4-6 grn. 3. Misfit between ultimate detectivity and experimental rest&s in the short-wave region increases with temperature decrease. This is caused by the fact that experimental results of recombination time are rising slower with temperature decrease than theoretical values. 4. The region of the best agreement of ultimate detectivity with experimental results shifts towards the long waves when temperature is lowered. REFERENCES 1. 2. 3.
EORRELLO,5. R., C. G. ROBERTS, B. H. BREAZEALE & G. R. PRUETT,Injwed KINCH M. A., M. J. BRAU & A. SIMMONS,J. appl. Phys. 44, 4 (1973). KINCH M, A., & S. R. BOORRELLO, Infrared Phy.s.IS, 1t 1 (1975).
4. LONG D. & J. L. SCHNT, S~~jc~~~~ro:s nnd ~~rnjrn~~~u1.s~
Phys. 11; 225 (1971).
Voi. 5, ps 175.Academic Press, New York
g1970). 5. 6. 7. 8. 9. 10.
ltix~s E., & J. PIOTROWSKI, Optica Appficuru, Wroclaw Vfl, I ($977). SCHMIT,J. L. J. appl. Phys. 41, 2876 (1970). GALUS, W., J. PIOTROWSKI & T. PIOTROWSKI, A’%“’ Compounds Symposium, Jaszowiec (1976). LUBCZENKO,A. W., L. E. PROKOPCZUK& E. A. SALKOW,Ukruiniun Phys. J. 20, 7 (1975). BAARS,J. & F. SORGER,Solid Store Commun. 10, 875 (1972). SCHMIT.J. L. & E. L. STELZER,+I. appt. Phys. 40, 4865 (1969).
It. BORKELLO,S., M. KXNCH6;: D, LAMONT- fnfrnred P@. 17, tll (1977). fZ. KINCH, M. A,, S. R: BORRE~LO& A. SIMMONS, Infrared @s. If, 127 (1477).
Technical (Received
Academy,
Warsaw,
Poland
21 June 1978)
Abstract-Dependence of ultimate detectivity ot,.,, on cutoff wavelength and detector ture for photoconductive (CdHg)Te infrared detectors have been calculated. The expression has been obtained: 7100
temperafollowing
+ 0.616
RLX = 4.5 x JO’T-3’21~~8 exp TI’ c,, 3&. 21,, + 0.247 > Calculations experimental
have been made for intrinsic data have been compared.
1.
and
n-type
material.
Theoretical
calculations
and
INTRODUCTION
A number of studies on performance limits for photoconductive (CdHg)Te detectors of optimal construction have been carried out since 1971. The key problem is to determine the dominating mechanism of recombination which limits the upper value of recombination time. Borrello et al.“’ calculated detectivity as a function of temperature and cutoff wavelength assuming a linear recombination model. Recent studies revealed, however,‘2*3’ that Auger recombination dominates in most cases. The ultimate D* value of a (CdHg)Te photoconductor assuming Auger recombination was calculated by M. A. Kinch and S. R. Borrello for n-type 0.1 eV material. (3) Previously such calculations were performed for cooled (8-14) prnc4) and room temperature (2-14) prnc5’ detectors. In this paper we give generalized expressions for ultimate D* values.
2. EVALUATION
OF (CdHg)Te
DETECTOR
PARAMETERS
2.1. Voltage responsivity We consider the detector schematically shown in Fig. 1. The element is made from homogeneous intrinsic or weakly n-type material. We suppose that electron and hole lifetime are equal and that surface recombination may be neglected. Because of the high ratio of electron to hole mobility we consider only the influence of electrons on the conductivity and photoconductivity. If the detector is current-biased and the illumination is weak, the following relation can be obtained for voltage responsivity: R,=
Vqd
tlwhcn,(l + 4n2f%2)“2
where V is bias voltage; 7 is recombination time; r] is effective quantum yield; no is equilibrium electron concentration; 1, w, t are the detector dimensions as shown in Fig. 1; f is modulation frequency.
In the optimum case, i.e. when reflection coefficients from frontal and rear surfaces are R, = 0 and R2 = 1, effective quantum yield is given by: rj = qo[l - exp( - 2at)] 19/2-- R
143
(2)
E. IGRA~ J. PIOTROWSKI and
144
Fig. 1. P~otoconductive
1.
P~OTROWSKI
(CdHg)Te detector
where so is internal quantum efficiency, i.e. number of electron-hole an absorbed photon. Then the expression for voltage responsivity takes the form: R, =
pairs generated
I/@[1 - exp(-Zo(t)@ hClWrn~(1 + 47?f%2)“2
by
(3)
Equatibn 3 shows that voltage responsivity increases monotonically with the increase of bias voltage. Bias voltage, however, is limited by thermal conditions, and we introduce the density of dissipated power P/wZ. Then from (3) we obtain: 1 - expf - 2ar) + 4n2f2s2)1’t
;391
(4)
where e is electronic charge: p,, is electron mobility, 2.2. Noise Four types of noise play an important role in photoconductive detectors: (1) Johnson-Nyquist noise, (2) generation-recombination noise, (3) l/f noise, and (4) radiation noise. The root mean square of Johnson-Nyquist noise voltage in the bandwidth 4f is given by: v,_, = (4kTRAf)“2
(5)
where k is Boltzman’s constant:
T is temperature;
R is resistance.
Generation-recombination noise is the result of the statistical character and recombination processes in semiconductors. Generation-recombination age is given by the following formula:‘3’ POGf V,;, = 2V n&o + po)lwt(l + 47@Vj
of generation noise volt-
1’2
(6)
where no. PO are the equilibrium carrier concentrations. The expression is valid for arbitrary interband generation-recombination processes. In the case of Shockley-Read generation-recombination it is valid for low density of recombination centers (n, e no). Equation 6 shows that spectral distribution of generation-recombination noise is constant for low frequencies v e 1/27cr) and decreases for high frequencies.
Ultimate
detectivity
of (CdHg)Te
infrared
photoconductors
145
Equation 6 for intrinsic material takes the form:
W
v,, = v
[ tIilWf(l
+
112
47r2~2r2)1
where ni is intrinsic concentration. For low frequencies an important role can be played by l/f noise. Its voltage cannot be calculated theoretically. It depends on surface and contact phenomena. In many cases l/fvoltage can be neglected in comparison with other kinds of noise. Radiation noise plays a role only at high signal or background radiation levels and is neglected in the case of small signal and highly reduced background radiation. 2.3. Ultimate detectivity Detectivity
D* is defined by the relation: D*
KA”2(W”2
=
(8)
V” where V, is root mean square noise voltage; A is detector
area.
Taking into account only Johnson-Nyquist and generation-recombination intrinsic or n-type material at low frequency (27rfr 6 1) we obtain :
noise, for
where 1 -
F(S, C) =
s=
e-2S
F2(SC + 1)“2 at,
c = WWP)
*(no/W. (no + POVPO,
P = rate of power dissipation in the detector. SC product is the square of the ratio of Johnson-Nyquist noise to generation-recombination noise. The graph of the F(S,C) function is given in Fig. 2. It is seen that for each C value, the optimum detector thickness can be found for which F(S,C) reaches its maximum. The F(S,C) value increases with decrease of the C value and reaches its absolute maximum value, equal to 0.903, for S = 0.625.“’ This is just the case of detectivity limitation by generation-recombination noise. In this case the detectivity limit can be expressed by:
(10)
WA,,=
The detectivity limit depends on carrier concentration, recombination time and absorption coefficient. It is independent of detector geometry. For not too high photon energy, typical for (CdHg)Te detector application, one can take internal quantum yield value ‘lo equal to unity. Because the detectivity limit is obtained in almost intrinsic material, then the following relation can be obtained:
(11) The maximum value of recombination
time is limited by Auger recombination
ti = ZAi.
146
E. IGRAS,~. PIOTROWSKI and T. PIOTROWSKI
S
Fig, 2. The graph
of function
F(S.CI.
This is the case of the uttimate detectivity. The value (ff~~i~~i~ depends on material composition, temperature and wavelength. For each wavelength there is an optimum composition ~l,,~,, when the ultimate detectivity is obtained. To determine the dependence of ultimate detectivity it is necessary to know the following relations: n,(i,,,, 77, s~~~(&,~.T) and c((A,,,,T). In the case of parabolic bands the dependence of intrinsic carrier concentration II, on temperature T and energy gap E, is given by the following expression?’ ni = 4.3 x 10’” Ei’“T3”
2
3
4
6
IO
x Fig. 3. Recombination
time in (CdHg)Te
exp
ccl1
15
(12)
20
30
40
Pm
vs cutoff wavelength to Eqn (151.
at various
temperatures
according
Ultimate detectivity of (CdHg)Te infrared photoconductors
147
where k is Boltzman’s constant. Equation
12 can be written as: (13)
(mm31
(W(ccm)
(m) W
Recombination time investigations revealed that Auger recombination dominates in (CdHg)Te with high electron concentration (n > 3 x f02’m-3f, i.e. for high intrinsic concentrations or in n-doped samples. (2*4,7)For low electron concentration, i.e. in some cooled or p-type (CdHg)Te detectors, Shockley-Read recombination dominates. Then, most often. in practically important (CdHg)Te detectors Auger recombination determines the detector parameters. We will deal further with this case. For intrinsic, parabolic band material,(4*8’ when Auger recombination dominates, the recombination time is given by the expression: 3.8 x lO-‘s~~(l + r)l12(1 + *l)exp[(+$$)z] ?Ai
(14)
=
where mx/mo is effective mass of an electron to a mass of a free electron ratio; E is static dielectric constant; r is electron to hole effective mass ratio; F,F2 is the product of two wave-function-overlap integrals.
Taking Eqn 14 and m,*/mo = O.O7E,, IF, F2/ = 0.1, mean E value as in Ref. 9, the dependence of ~~~~ on detector temperature T and cutoff wavelength has been obtained : ~~~= 1.92 x 1016T-3’2;1,‘!2
exp[(qs)(iI
] ~$)].
(15)
(IQ aW-4
(s)
There is no general expression for absorption coefficient dependence on temperature and energy gap. For (CdHg)Te, however, as for direct gap semiconductors, the following approximation can be assumed: hc
for
a=0
Y < E, hc 7 > E R’
for
In calculations of detector parameters we took tl = 5 x 104m-‘. This value was taken to estimate the energy gap from absorption measurement.“” Using Eqns 11-15 the following relation for ultimate detectivity can be obtained: O*,,, = 4.5 x 107T-3’2~~~8 exp (mHz”2W-‘)
(IQ
The graph of this dependence
(pm)
is given in Fig. 4.
3. COMPARISON
OF
EXPERIMENTAL
CALCULATIONS
WITH
RESULTS
Dependence of recombination time ZAion cutoff wavelength and detector temperature from (15) is given in Fig. 3. For high detector temperature and composition
obtained
E.
IGRAS. J. P~OTROWSKIand 7. PIOTROWSKI
A
I
I
3
4
I 6
IO
I5
I 20
30
I
40
Fig. 4. Ultimate detectivity LIZ,,,,for photoconductive (CdHg)Te detectors as a function of cutoff wavelength at different temperatures. Results of our measurements: for 77K are indicated by filled circles: for ZOOKare indicated by open circles; for 300K are indicated by triangles. Data for 77K according to 11 indicated by x Data for 77K according to 12 indicated by C.
HgTe (x S 0.3). i.e. for i,,, > 4flm, calculated ialues of T\, are consistent with experimental data for epitaxial (CdHg)Te layers.“’ For low temperatures as well as for relatively CdTe-rich alloys experimental recombination time is much lower than theoretical because of the additional effect of Shockley-Read and radiative recombination. In Fig. 4 the theoretical relation f3*,,,(&,) for different detector temperatures is presented. Our experimental data of D*m,x(A,,) for epitaxial (CdHg)Te layers are also given. For uncooled detectors the best accordance of theoretical and experimental data are observed at 3, = 4-6 pm. For A,, < 4 pm experimental values are lower than predicted. This is probably caused by the effect of surface and Shockley-Read recombination and deviations from intrinsic concentration observed in samples. For I,, > 6pm the effect of l/‘noise (especially for high bias current) and sometimes amplifier noise are observed. Misfit between ultimate detectivity and experimental results in the short-wave region increases with temperature decrease. This is caused by the fact that experimental results of recombination time are rising slower with temperature decrease than theoretical values. near
Ultimate detectivity of (CdHg)Te infrared photoconductors
149
Equation 16 has been obtained when Auger recombination prevails. Comparing it with the expression obtained in Ref 1 for linear recombination model, one can see that in our case the dependence of P&,x (E,) is stronger than in Ref. 1, 4. SUMMARY 1.
When Auger recombination tor is expressed by:
(mHz”*W-
’)
prevails, ultimate detectivity of a (CdHg)Te photoconduc-
6)
(w)
2. For uncooled detectors the best accordance of theoretical and experimental data occurs at 1 = 4-6 grn. 3. Misfit between ultimate detectivity and experimental rest&s in the short-wave region increases with temperature decrease. This is caused by the fact that experimental results of recombination time are rising slower with temperature decrease than theoretical values. 4. The region of the best agreement of ultimate detectivity with experimental results shifts towards the long waves when temperature is lowered. REFERENCES 1. 2. 3.
EORRELLO,5. R., C. G. ROBERTS, B. H. BREAZEALE & G. R. PRUETT,Injwed KINCH M. A., M. J. BRAU & A. SIMMONS,J. appl. Phys. 44, 4 (1973). KINCH M, A., & S. R. BOORRELLO, Infrared Phy.s.IS, 1t 1 (1975).
4. LONG D. & J. L. SCHNT, S~~jc~~~~ro:s nnd ~~rnjrn~~~u1.s~
Phys. 11; 225 (1971).
Voi. 5, ps 175.Academic Press, New York
g1970). 5. 6. 7. 8. 9. 10.
ltix~s E., & J. PIOTROWSKI, Optica Appficuru, Wroclaw Vfl, I ($977). SCHMIT,J. L. J. appl. Phys. 41, 2876 (1970). GALUS, W., J. PIOTROWSKI & T. PIOTROWSKI, A’%“’ Compounds Symposium, Jaszowiec (1976). LUBCZENKO,A. W., L. E. PROKOPCZUK& E. A. SALKOW,Ukruiniun Phys. J. 20, 7 (1975). BAARS,J. & F. SORGER,Solid Store Commun. 10, 875 (1972). SCHMIT.J. L. & E. L. STELZER,+I. appt. Phys. 40, 4865 (1969).
It. BORKELLO,S., M. KXNCH6;: D, LAMONT- fnfrnred P@. 17, tll (1977). fZ. KINCH, M. A,, S. R: BORRE~LO& A. SIMMONS, Infrared @s. If, 127 (1477).