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Photocurrent determination of charge transport parameters in KNbO3:Fe3+
February 1994
___________________
PT~CAL F]SFVIER
Optical Materials 3 (1994) 61—64
Photocurrtht determination of charge transport parameters in KNbO3 : Fe3~ J. Garcia M., M.A. MondragOn, J.M. Hernández A., J.L. Maldonado R. Instituto de Fisica, UNAM, P.O. Box 20-364, 01000 Mexico, D.F., Mexico Received 2 April 1993; revised manuscript received 8 September 1993
Abstract From current—voltage measurements, the characteristic parameters for the photovoltaic effect, photoconductivity and dark current were determined for K.Nb0 3~ions. Instead ofa laser, illumination light from a 3 crystals with and 150making ppm ofpossible Fe xenon lamp passed through a monochromator, was300 used, thus the illumination of the samples at several wavelengths. In spite of the low intensity of the exciting light, the obtained parameter values are comparable to others found in the literature. Values for the photosensitivity at different wavelengths were also calculated.
1. Introduction The study of the photorefractive effect in electrooptic crystals has been carried out in the last few years because of the potential applications in volume phase storage, real-time optical information processing and optical phase conjugation [1]. The phenomenon is explained in terms of charge carriers (mainly from the impurities), which are excited into bright regions created by the interference of coherent light beams illuminating the samples. Upon illumination, these charge carriers become mobile and migrate into the lattice due to diffusion drift or photovoltaic effect, and are subsequently retrapped at new sites into dark regions. By this mechanisms, electrical space-charge fields are built up and give rise to a modulation ofthe refractive index through the electro-optic effect. The charge transport in homogeneously illuminated photoconductors, such as photorefractive KNbO3, can be described by [2]
1= ~-“-9-~cxi+(enoii+ —~-~aI”~E hv \ hv I
(1)
The three terms in eq. (1) are due:’to the photovoltaic effect, dark conductivity, and photoconductivity, respectively; I is the light intensity, a the absorption coefficient, 0 the quantum efficiency for exciting a free charge carrier, h v the photon energy, ~ the mobility, r the lifetime ofthe excited carriers, n 0 the carrier density responsible for the dark conductivity, and 1~the mean effective drift length along the polar c axis [3]. The photorefractive sensitivity is defined as the refractive index change per unit absorbed energy density S=dn/dw. This definition of S is a useful figure of merit since it allows us to compare, on an equal basis, materials having different absorption coefficients at a given wavelength [41.For drift recording (E~0), Scan be written as [51
s=
~-~-~-~-
[eØl0+eØjizE~(l+n0/n~)J
,
(2)
2hv where n3 is the refractive index, f33~r33/e3~0 is the polarization optic coefficient (with r33 equal to the
0925-3467/94/$07.OO © 1994 Elsevier Science B.V. All rights reserved SSD10925-3467(93)E0035-A
62
J. GarciaM. eta!. / Optical Materials 3 (1994) 6 1—64
electro-optic coefficient), Ea the applied field and = 0 t al/h v is the photogenerated carrier density. KNbO3 is predicted to have a high photorefractive sensitivity, but its properties have not been fully characterized [6]. The characteristic parameters for the photovoltaic effect (0 10) and photoconductivity (0 ~ r), which determine the photosensitivity and photovoltages of the material, can be deduced from photocurrent measurements. In this paper we present results from optical absorption and photoconductivity measurements for 3~at different illumination wavelengths KNbO3:Fe and impurity concentrations. 2. Experimental
Wove~engtb [nml 20 800
3. Results
600~~
500450
4
—
12
4 <0 15
1~
2~4
21
Photon energy
27
3
LeVI
Fig. 1. Absorption coefficient versus photon energy. (a) 150 ppm, (b) 300 ppm Fe3~concentration, (c) undoped sample with amplification factor shown (data from Ref. [81).
Crystal samples grown by the top-seeded high-ternperature solution method, oriented and sawed with their faces parallel to the c-axis were kindly provided by Dr. Medrano from ETH Zurich. The Fe3~concentrations of the samples were 150 ppm and 300 ppm. These were determined by mass spectroscopy
measure and atomic photocurrents absorptionspectra [7]. the sample was illuminated absorption were taken with a MiltonOptical Roy 3000 Array Spectrophotometer. In order to with monochromatic light coming from a 150 W Xe lamp passed through a 0.25 m Spex monochromator and a filter. The sample was maintained in a l0—~ Ton vacuum cryostat at room temperature. Silver electrodes were painted on the sample, and currents were measured with a 642 Keithley electrometer connected in series with the voltage power supply. The applied electrostatic field E was parallel to the c-axis of the crystal. The light intensity was measured at the sample position for each wavelength with a Spectra Physics 404 power meter.
700
200
-~ ~
I
: :: :: ©
~ 00 50
>< ~
0
200
400
too
600
I
E~ectdc fle~d [v/cm
Fig. 2. Photocurrent density versus applied electric field in KNbO 3~150 ppm. 3: Fe
one and a half hour. Straight lines were fitted by a least-squares method. The dark conductivity a~was obtained from the slope of the dark current straight lines, according to Eq. (1). 0 10 and 0 ~.tt parameters were obtained for each wavelength from the intersection with the Y axis and the slope of the corresponding line, respectively. Tables 1 and 2 summarize all these results.
The absorption coefficient versus photon energy for the two samples are shown in Fig. 1. Data for an undoped sample, from Ref. [8], are included. Figs. 2 and 3 show photocurrent density versus applied electrostatic field at different wavelengths. In
4. Discussion
order to get steady-state current values, we had to wait
Fe
As Fig. 1 shows that KNbO 3 samples with 3 + have an optical absorption in the doped wavelength
J. GarciaM. et a!. / Optical Materials 3(1994)61—64
pyroelectric currents, a filter was used to remove infrared light harmonics.
100 ~ A 450 nm
~
0-)
E
0
515
U
633
).~)
~
75 50
63
etervalues for the photovoltaic effect (01w) and photoconductivity (Ø~vr)lie between those reported in Refs. From Tables and photon [8]. 1isand 2,energy. itcomparison is observed isthat clearly the current paramshown in density Fig.[5] 4versus which aThis plot of theThe photovoltaic dark conductivity
0 dark
0~
2:
0
200
400
600
800
Electric tield [V/cm] Fig. 3. Photocurrent 3~300 ppm.density versus applied electric field in KNbO3 : Fe
region from 400 to 650 nm which is absent in pure KNbO 3. Also shown in Fig. 1 is the increase in the absorption band edge for the dopedwith samples. Bythe il 3~samples light in luminating KNbO3: Fe 400—650 nm region, carriers can be photoexcited to the conduction (or valence) band; any wavelength in this region could be used to measure charge transport parameters. chose light of 515 and to compare withWeprevious experiments and488 two nm other wavelengths (450 and 633 nm) to obtain new data. The experiments were performed in a vacuum atmosphere (~l0~ Torr) since the photocurrents generated by the light source were very low (10—12 2), and at these levels, the pyroelectric currents A/cmgreater than the photocurrents. As a result of were pyroelectricity the measured current increased slowly but steadily with time. To eliminate interference from
values (ad) we measured are similar to those from Ref. [8], although the value from Ref. [5 1 for KNbO3:Fe 300 ppm is higher. Thus, even with the low intensity of the light used here, we found cornparable parameter values to those obtained usinglaser light. The refractive index (n3) calculated data from Ref. [71 and a values two-oscillator Smeillerwith dispersion relation [9] are included in Table 1. For KNbO 2/C [10]. Following Wemple this parameter should not change 3 at 2~=[11], 633 nm,f33 = 0.13 m appreciably in a specific material. Considering the samef 33 value for the four wavelengths, and with data from Tables 1 and 2, the photosensiti~iitywas calculated from Eq. (2) and included in these tables. For KNbO3: Fe 300 ppm at )~=488nm the value is cornparable to that from Ref. [5]. et al.by[12] de3/JReeves indirectly diffracterminedS=0.41 x l0~cm tion efficiency and this result is lower than the one found here, as Tables 1 and 2 show, but the impurity concentration is not known. They also obtained çi~ur=5.3xl0~cm2/V at )~=633nm that is cornparable to our result for K.Nb0 Fe 300 ppm. We observed a memory effect in our3: samples, consisting in the following. After having obtained one current density versus electric field curve, its repetition under the same conditions in less than two days, gave rise to a
Table 1 Absorption coefficient a, photovoltaic Øio and photoconductivity Ø~irparameters, and photosensitivities S determined from optical absorption and photoconductivity measurements for KNbO 3 : Fe 150 ppm. A (nm) 633 515
I
a (cm~)
Ø!o (A)
x lO~ (cm2/V)
E~=l0/pr (V/cm)
n3
xS
l0~ (W/cm 3.65 3.65
0.12 1.68
2.17 2.21
7.6 0.6
2.81 1.94
2.59 5.82
23.38 4.52 (4.2~) 7.14 5.36
36.41 21.34
488 450
0.85 0.10 (l.64~) 0.58 0.49
81.50 90.85
2.23 2.26
3.6 2.8
x
ad=3.3X
~Ref. [8].
2)
l0’~(ccm)~ (2.3x l0’~ (Lcmy~)
l0~ (cm3/J)
64
J. Garcia M. eta!. / Optical Materials 3 (1994) 6 1—64
Table 2 a, O!o, Ø~rrand S parameters for KNbO
3 : Fe 300 ppm.
A (nm) 633 515
I l0~ (W/cm 0.86 0.90
2)
a(cm1) 0.47 1.26
488
0.70
2.13
x
0!o (A)
Ø~1T x lO~ (cm~/V)
Ea=lo/3rL1 (V/cm)
0.66 0.25 (l.36~) 0.12
9.21 8.97 (2.la) 7.98
71.28 28.28
9.1 2.2
14.60
0.9
Sx l0—~(cm3/J)
(
450
0.49
12.54 4.OX i0’~(Q cm)’ (5.6x
Od=
aRef [8].
10—Id
005b)
(06b)
0.06
2.71
0.4
(~cm)’~, 320x l0~~(~2cm)~’”)
bRef [5].
Wavelength 800
r~
700
600
5.Conclusions
[nm]
500
400
~30
/
-
3~ Weahave measured in ~bO3: Fe with system using a photocurrents white light source and a monochromator. We noted that care should be taken to avoid pyroelectricity and memory effects. The results obtained indicated that even with a low intensity light source, the obtained values for photovol-
/
I
-,
flu
(14b
22.43
-
20
/
I
/
-
/
/
/
-
taic, photoconductivity and dark conductivity parameters are comparable to those reported using
/ //
10
0 0 -c
1.5
1.8
2.1
Photon
2,4
energy
2.7
3.0
33
to measure these parameters even at wavelengths at laser illumination. Thus we have shown it is possible which lasers do not exist or are not available. Finally, photosensitivity values were calculated and found to be comparable to these reported in the literature.
[eV I
Fig. 4. Photoinduced current density versus photon energy in KNbO 3~,X 150 ppm, 0 300 ppm, ——data from Ref. [5]. 3:Fe
curve above the first one, that is, the newly measured photocurrents were bigger than those previously obtamed. So, we observed that in order to have reproducibility we had to leave the samples in the dark at room temperature for at least 48 hours. This procedure could be related to the randomization ofthe carrier distribution after the set up of a preferred direction of movement, caused by the external electric field When the sample was illuminated with wavelengths shorter than 450 nm, the current increased continuously, never reaching a steady state value. At these wavelengths, there can be a contribution from band-to-band transitions from lattice electrons, since these wavelengths are close to the absorption band edge as Fig. 1 shows.
References [1] P. Gunter, Phys. Rep. 93(1982)199. [2] P. Günter and F. Micheron, Ferroelectrics 18 (1987) 27. [3] D. von der Linde and AM. Glass, Appl. Phys. 8 (1975) 85. [4] G.C. Valley and MB. Klein, Opt. Eng. 22 (1983) 704. [5] Ferroelectrics 22 (1978) 671. [6] P. P. Gunter, Günter and J.P. Huignard, in: Photorefractive materials and their applications I, eds. P. Günter and J.P. Huignard (Springer, Berlin, 1988) p. 65. [7] E. Voit, Ph. D. Thesis, ETH Zurich, unpublished (1988). [8] Phys. C. Medrano, 64 (1988) E. Voit, 4668.P. Armhein and P. GUnter, J. Appl. [9] M. Di Domenico Jr. and S.H. Wemple, J. Appi. Phys. 40 (1969) 720. [10] P. Günter, Optics Comm. 11(1974) 285. [11] S.H. Wemple and M. DiDomenico, Applied Solid State Science, Vol. 3, ed. R. Wolfe (Academic, New York, 1972). [12] R.J. Reeves, M.G. Jani, B. Jassemnejad, R.C. Powell, G.J. Mizell and W. Fay, Phys. Rev. B 43 (1991) 71.
___________________
PT~CAL F]SFVIER
Optical Materials 3 (1994) 61—64
Photocurrtht determination of charge transport parameters in KNbO3 : Fe3~ J. Garcia M., M.A. MondragOn, J.M. Hernández A., J.L. Maldonado R. Instituto de Fisica, UNAM, P.O. Box 20-364, 01000 Mexico, D.F., Mexico Received 2 April 1993; revised manuscript received 8 September 1993
Abstract From current—voltage measurements, the characteristic parameters for the photovoltaic effect, photoconductivity and dark current were determined for K.Nb0 3~ions. Instead ofa laser, illumination light from a 3 crystals with and 150making ppm ofpossible Fe xenon lamp passed through a monochromator, was300 used, thus the illumination of the samples at several wavelengths. In spite of the low intensity of the exciting light, the obtained parameter values are comparable to others found in the literature. Values for the photosensitivity at different wavelengths were also calculated.
1. Introduction The study of the photorefractive effect in electrooptic crystals has been carried out in the last few years because of the potential applications in volume phase storage, real-time optical information processing and optical phase conjugation [1]. The phenomenon is explained in terms of charge carriers (mainly from the impurities), which are excited into bright regions created by the interference of coherent light beams illuminating the samples. Upon illumination, these charge carriers become mobile and migrate into the lattice due to diffusion drift or photovoltaic effect, and are subsequently retrapped at new sites into dark regions. By this mechanisms, electrical space-charge fields are built up and give rise to a modulation ofthe refractive index through the electro-optic effect. The charge transport in homogeneously illuminated photoconductors, such as photorefractive KNbO3, can be described by [2]
1= ~-“-9-~cxi+(enoii+ —~-~aI”~E hv \ hv I
(1)
The three terms in eq. (1) are due:’to the photovoltaic effect, dark conductivity, and photoconductivity, respectively; I is the light intensity, a the absorption coefficient, 0 the quantum efficiency for exciting a free charge carrier, h v the photon energy, ~ the mobility, r the lifetime ofthe excited carriers, n 0 the carrier density responsible for the dark conductivity, and 1~the mean effective drift length along the polar c axis [3]. The photorefractive sensitivity is defined as the refractive index change per unit absorbed energy density S=dn/dw. This definition of S is a useful figure of merit since it allows us to compare, on an equal basis, materials having different absorption coefficients at a given wavelength [41.For drift recording (E~0), Scan be written as [51
s=
~-~-~-~-
[eØl0+eØjizE~(l+n0/n~)J
,
(2)
2hv where n3 is the refractive index, f33~r33/e3~0 is the polarization optic coefficient (with r33 equal to the
0925-3467/94/$07.OO © 1994 Elsevier Science B.V. All rights reserved SSD10925-3467(93)E0035-A
62
J. GarciaM. eta!. / Optical Materials 3 (1994) 6 1—64
electro-optic coefficient), Ea the applied field and = 0 t al/h v is the photogenerated carrier density. KNbO3 is predicted to have a high photorefractive sensitivity, but its properties have not been fully characterized [6]. The characteristic parameters for the photovoltaic effect (0 10) and photoconductivity (0 ~ r), which determine the photosensitivity and photovoltages of the material, can be deduced from photocurrent measurements. In this paper we present results from optical absorption and photoconductivity measurements for 3~at different illumination wavelengths KNbO3:Fe and impurity concentrations. 2. Experimental
Wove~engtb [nml 20 800
3. Results
600~~
500450
4
—
12
4 <0 15
1~
2~4
21
Photon energy
27
3
LeVI
Fig. 1. Absorption coefficient versus photon energy. (a) 150 ppm, (b) 300 ppm Fe3~concentration, (c) undoped sample with amplification factor shown (data from Ref. [81).
Crystal samples grown by the top-seeded high-ternperature solution method, oriented and sawed with their faces parallel to the c-axis were kindly provided by Dr. Medrano from ETH Zurich. The Fe3~concentrations of the samples were 150 ppm and 300 ppm. These were determined by mass spectroscopy
measure and atomic photocurrents absorptionspectra [7]. the sample was illuminated absorption were taken with a MiltonOptical Roy 3000 Array Spectrophotometer. In order to with monochromatic light coming from a 150 W Xe lamp passed through a 0.25 m Spex monochromator and a filter. The sample was maintained in a l0—~ Ton vacuum cryostat at room temperature. Silver electrodes were painted on the sample, and currents were measured with a 642 Keithley electrometer connected in series with the voltage power supply. The applied electrostatic field E was parallel to the c-axis of the crystal. The light intensity was measured at the sample position for each wavelength with a Spectra Physics 404 power meter.
700
200
-~ ~
I
: :: :: ©
~ 00 50
>< ~
0
200
400
too
600
I
E~ectdc fle~d [v/cm
Fig. 2. Photocurrent density versus applied electric field in KNbO 3~150 ppm. 3: Fe
one and a half hour. Straight lines were fitted by a least-squares method. The dark conductivity a~was obtained from the slope of the dark current straight lines, according to Eq. (1). 0 10 and 0 ~.tt parameters were obtained for each wavelength from the intersection with the Y axis and the slope of the corresponding line, respectively. Tables 1 and 2 summarize all these results.
The absorption coefficient versus photon energy for the two samples are shown in Fig. 1. Data for an undoped sample, from Ref. [8], are included. Figs. 2 and 3 show photocurrent density versus applied electrostatic field at different wavelengths. In
4. Discussion
order to get steady-state current values, we had to wait
Fe
As Fig. 1 shows that KNbO 3 samples with 3 + have an optical absorption in the doped wavelength
J. GarciaM. et a!. / Optical Materials 3(1994)61—64
pyroelectric currents, a filter was used to remove infrared light harmonics.
100 ~ A 450 nm
~
0-)
E
0
515
U
633
).~)
~
75 50
63
etervalues for the photovoltaic effect (01w) and photoconductivity (Ø~vr)lie between those reported in Refs. From Tables and photon [8]. 1isand 2,energy. itcomparison is observed isthat clearly the current paramshown in density Fig.[5] 4versus which aThis plot of theThe photovoltaic dark conductivity
0 dark
0~
2:
0
200
400
600
800
Electric tield [V/cm] Fig. 3. Photocurrent 3~300 ppm.density versus applied electric field in KNbO3 : Fe
region from 400 to 650 nm which is absent in pure KNbO 3. Also shown in Fig. 1 is the increase in the absorption band edge for the dopedwith samples. Bythe il 3~samples light in luminating KNbO3: Fe 400—650 nm region, carriers can be photoexcited to the conduction (or valence) band; any wavelength in this region could be used to measure charge transport parameters. chose light of 515 and to compare withWeprevious experiments and488 two nm other wavelengths (450 and 633 nm) to obtain new data. The experiments were performed in a vacuum atmosphere (~l0~ Torr) since the photocurrents generated by the light source were very low (10—12 2), and at these levels, the pyroelectric currents A/cmgreater than the photocurrents. As a result of were pyroelectricity the measured current increased slowly but steadily with time. To eliminate interference from
values (ad) we measured are similar to those from Ref. [8], although the value from Ref. [5 1 for KNbO3:Fe 300 ppm is higher. Thus, even with the low intensity of the light used here, we found cornparable parameter values to those obtained usinglaser light. The refractive index (n3) calculated data from Ref. [71 and a values two-oscillator Smeillerwith dispersion relation [9] are included in Table 1. For KNbO 2/C [10]. Following Wemple this parameter should not change 3 at 2~=[11], 633 nm,f33 = 0.13 m appreciably in a specific material. Considering the samef 33 value for the four wavelengths, and with data from Tables 1 and 2, the photosensiti~iitywas calculated from Eq. (2) and included in these tables. For KNbO3: Fe 300 ppm at )~=488nm the value is cornparable to that from Ref. [5]. et al.by[12] de3/JReeves indirectly diffracterminedS=0.41 x l0~cm tion efficiency and this result is lower than the one found here, as Tables 1 and 2 show, but the impurity concentration is not known. They also obtained çi~ur=5.3xl0~cm2/V at )~=633nm that is cornparable to our result for K.Nb0 Fe 300 ppm. We observed a memory effect in our3: samples, consisting in the following. After having obtained one current density versus electric field curve, its repetition under the same conditions in less than two days, gave rise to a
Table 1 Absorption coefficient a, photovoltaic Øio and photoconductivity Ø~irparameters, and photosensitivities S determined from optical absorption and photoconductivity measurements for KNbO 3 : Fe 150 ppm. A (nm) 633 515
I
a (cm~)
Ø!o (A)
x lO~ (cm2/V)
E~=l0/pr (V/cm)
n3
xS
l0~ (W/cm 3.65 3.65
0.12 1.68
2.17 2.21
7.6 0.6
2.81 1.94
2.59 5.82
23.38 4.52 (4.2~) 7.14 5.36
36.41 21.34
488 450
0.85 0.10 (l.64~) 0.58 0.49
81.50 90.85
2.23 2.26
3.6 2.8
x
ad=3.3X
~Ref. [8].
2)
l0’~(ccm)~ (2.3x l0’~ (Lcmy~)
l0~ (cm3/J)
64
J. Garcia M. eta!. / Optical Materials 3 (1994) 6 1—64
Table 2 a, O!o, Ø~rrand S parameters for KNbO
3 : Fe 300 ppm.
A (nm) 633 515
I l0~ (W/cm 0.86 0.90
2)
a(cm1) 0.47 1.26
488
0.70
2.13
x
0!o (A)
Ø~1T x lO~ (cm~/V)
Ea=lo/3rL1 (V/cm)
0.66 0.25 (l.36~) 0.12
9.21 8.97 (2.la) 7.98
71.28 28.28
9.1 2.2
14.60
0.9
Sx l0—~(cm3/J)
(
450
0.49
12.54 4.OX i0’~(Q cm)’ (5.6x
Od=
aRef [8].
10—Id
005b)
(06b)
0.06
2.71
0.4
(~cm)’~, 320x l0~~(~2cm)~’”)
bRef [5].
Wavelength 800
r~
700
600
5.Conclusions
[nm]
500
400
~30
/
-
3~ Weahave measured in ~bO3: Fe with system using a photocurrents white light source and a monochromator. We noted that care should be taken to avoid pyroelectricity and memory effects. The results obtained indicated that even with a low intensity light source, the obtained values for photovol-
/
I
-,
flu
(14b
22.43
-
20
/
I
/
-
/
/
/
-
taic, photoconductivity and dark conductivity parameters are comparable to those reported using
/ //
10
0 0 -c
1.5
1.8
2.1
Photon
2,4
energy
2.7
3.0
33
to measure these parameters even at wavelengths at laser illumination. Thus we have shown it is possible which lasers do not exist or are not available. Finally, photosensitivity values were calculated and found to be comparable to these reported in the literature.
[eV I
Fig. 4. Photoinduced current density versus photon energy in KNbO 3~,X 150 ppm, 0 300 ppm, ——data from Ref. [5]. 3:Fe
curve above the first one, that is, the newly measured photocurrents were bigger than those previously obtamed. So, we observed that in order to have reproducibility we had to leave the samples in the dark at room temperature for at least 48 hours. This procedure could be related to the randomization ofthe carrier distribution after the set up of a preferred direction of movement, caused by the external electric field When the sample was illuminated with wavelengths shorter than 450 nm, the current increased continuously, never reaching a steady state value. At these wavelengths, there can be a contribution from band-to-band transitions from lattice electrons, since these wavelengths are close to the absorption band edge as Fig. 1 shows.
References [1] P. Gunter, Phys. Rep. 93(1982)199. [2] P. Günter and F. Micheron, Ferroelectrics 18 (1987) 27. [3] D. von der Linde and AM. Glass, Appl. Phys. 8 (1975) 85. [4] G.C. Valley and MB. Klein, Opt. Eng. 22 (1983) 704. [5] Ferroelectrics 22 (1978) 671. [6] P. P. Gunter, Günter and J.P. Huignard, in: Photorefractive materials and their applications I, eds. P. Günter and J.P. Huignard (Springer, Berlin, 1988) p. 65. [7] E. Voit, Ph. D. Thesis, ETH Zurich, unpublished (1988). [8] Phys. C. Medrano, 64 (1988) E. Voit, 4668.P. Armhein and P. GUnter, J. Appl. [9] M. Di Domenico Jr. and S.H. Wemple, J. Appi. Phys. 40 (1969) 720. [10] P. Günter, Optics Comm. 11(1974) 285. [11] S.H. Wemple and M. DiDomenico, Applied Solid State Science, Vol. 3, ed. R. Wolfe (Academic, New York, 1972). [12] R.J. Reeves, M.G. Jani, B. Jassemnejad, R.C. Powell, G.J. Mizell and W. Fay, Phys. Rev. B 43 (1991) 71.