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Nonlinear light absorption in GaSe crystals at the fundamental absorption edge
July 1996
ELSEVIER
Optical Materials 6 (1996) 117-120
Nonlinear light absorption in GaSe crystals at the fundamental absorption edge M. Kalafi, H. Bidadi, H. Tajalli, V. Salmanov Centre for Applied Physics Research Universi~ of Tabriz, Tabriz, lran
Abstract The nonlinear light absorption at the fundamental absorption edge for high excitation intensities in GaSe has been investigated experimentally. The bleaching of band-edge absorption which manifests itself as an apparent blue shift of the absorption edge can be interpreted on the base of bandfilling nonlinearities. It is shown that the observed negative absorption change in GaSe crystal is the basis of optical amplification and the semiconductor laser.
1. Introduction GaSe crystals belonging to I I I - V I compounds have received considerable attention recently as an interesting class of nonlinear optical materials. Possessing layered structure, high polarizability, optical homogeneity and naturally mirror-like surfaces, a number of nonlinear optical phenomena such as harmonic generation [1,2], parametric light generation [3,4], electron-hole plasma [5-9] and stimulated emission [10-14], etc., have been observed in these crystals. In this paper, we present the experimental results on nonlinear light absorption in GaSe in the fundamental absorption region at high optical excitation levels. Basically, this phenomenon has previously been studied in narrow-gap semiconductors such as InSb [15], InAs [16], CdHgTe [17] and also in CdS microcrystallites in a polymer film [18] and CdTe quantum dots in glass [19]. The investigation of this effect in a wide band gap semiconductor such as
GaSe seems interesting, as it may extend the possible applications of nonlinear optics.
2. Experimental methods Gallium selenide has a layered structure, where each layer contains two gallium and two selenium close-packed sublayers in the stacking sequence S e G a - G a - S e [20]. The bonding between two adjacent layers is of the Van der Waals type, while within the layer the bonding is predominantly covalent. Band structure calculations [20,21] predict the presence of an indirect minimum of the conduction band at the point M (M~- symmetry) of the Brillouin zone lower than the direct minimum (F~) at the point F. Moreover, the top of the valence band lies at the centre of the Brillouin zone and has the symmetry F3-. The direct and indirect gaps are very close in energy. Measurements of optical absorption and photolumi-
00925-3467/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0925-3467(96)00022-5
118
M. Kalafi et al. / Optical Materials 6 (1996) 117-120
nescence show a difference of about 25 meV between these two minima [22]. The investigated GaSe single crystals were obtained by the Bridgman method. Samples were of E-modification having p-type conductivity. The ingots were cleaved along the planes of layers (_L to the c-axis), obtaining slices about 10-50 ~ m thick. Mobility and concentration of charge carders measured by conventional methods at room temperature were ~ 20 c m 2 / V • s and 1 X 10 j4 cm -3, respectively. The energy gap of GaSe is Eg = 2.02 eV at room temperature. As an excitation source, a Rhodamine 6G dye laser (PRA, LN-107) pumped by the output of a N2-1aser (PRA, LN-1000), tuned through the region 594-643 nm with a repetition frequency of 10 Hz and a pulse width of 1 ns was used. Lower excitation intensities were obtained by means of suitable calibrated neutral filters. Transmission spectra were obtained by shifting filters from the front to the rear of the samples and checking the experimental reproducibility in the region of transparency. The output signals were detected by a silicon photodiode and recorded by a storage oscilloscope (Le Croy 9400).
3. Results
and
2
2
,rE
!oI 1.90
1.95
I
I
I
2.02(Eg)
i
2.10ht,u,eV
Fig. 1. Absorption spectra of GaSe at low (~ 3.5 mW/cm2, curve 1) and high ( ~ 12 mW/cm2, curve 2) intensity excitations.
0.0
discussion
The absorption spectra of GaSe at low (curve 1) and high (curve 2) excitation intensities are given in Fig. 1. As it is seen from the figure, at high excitation levels, the absorption coefficient is decreased, and along with the onset of absorption is also shifted towards higher energies. The change in the absorption coefficient A a can be obtained by direct subtraction of curves 1 and 2 in Fig. 1. The result is plotted in Fig. 2. It is seen that the maximum absorption change takes place in the vicinity of the band gap. The observed nonlinear absorption near the band gap at high excitation intensities can be attributed to optical saturation effects in GaSe, i.e. electrons and holes generated by absorption of light which relax rapidly to a thermal distribution, blocking absorption states near the band edge. Effectively, this is like a shift of the band edge to higher energies with increasing laser intensity, which causes the absorption at the vicinity of the band edge to decrease. From Fig. 2, it is clear that, the absorption
1
-1-
°z-200 0 I,D_ rv" 0 t.~ m
<
-450''' 1.90
1.95
202 (Eg) 2.10hw,eV
Fig. 2. The change in the absorptioncoefficient Aa.
M. Kalafi et aL/ Optical Materials 6 (1996) 117-120 change becomes negative. Negative absorption means amplification as can be seen from Beer-Lambert's law
l ( t ) =10e -"~.
119
0.12
f
(1)
For a < 0, the transmitted intensity is higher than the input intensity. This optical gain can give a possibility of producing a semiconductor laser based on GaSe crystals. The bandfilling effect predicts that the change in absorption coefficient due to free carriers (neglecting exciton interaction) at photon energy h to' above the band-gap energy is given by [17]
o
i°t
A~(hto') = - o % ( h t o ' ) 2 1 / 2 ( rrh ]3/2
× [ n e m ~ 3 / 2 e x p ( - A E c / k B T ) + nhm; 3/2
-0.12 ~
w
,
e
V
(2)
Fig. 3. The change in the refractiveindex An(w).
A E c = (hto' - E'g)/(1 + m e / m h ) ,
(3)
AE v = ( h t o ' - E'g)/(1 + m i m e ) ,
(4)
account which can eventually lead to the enhancement of the nonlinear absorption. Such saturation leads both to nonlinear absorption and to a strong intensity dependence of the refractive index. From the Kramers-Kronig relation [24] we may write the change in refractive index at photon energy h to as
×exp( - A E v / k B T ) ] , where
o%(hto') is the low-power absorption coefficient at photon energy h to', m e is the effective mass of an electron, m h is the effective mass of a hole, n e, n h are the integrated population density of free-electron and free-hole, respectively, E'g is the renormalized band gap which results from exchange and correlation effects at high carrier densities [23]. Taking m e = 0.3 m 0, m h = 0.2 m 0 and calculated values of n e, nh, E'g, AE c, A E v from Eqs. (4)-(11) of Ref. [18], the percentage relative absorbance change A a 1 0 0 % / a 0 is evaluated to be ~ 12% in GaSe. This is in good agreement with the corresponding observed value of 15%. The small difference between these values can be due to the fact that, the exciton interactions were neglected in Eq. (2), while in wide-band-gap materials (such as GaSe), Coulomb electron-hole correlation effects should be taken into
hc A.(h,o)
- T,0
!
hto') ' - , 2 - 2 - - - - 2 d ( h to') • (hto) - (hto)
(5)
Using Eq. (5) to compute the index change related to the absorption change of Fig. 2, we obtain the result plotted in Fig. 3. As can be noted from Fig. 3 the change in the refractive index leading to nonlinear effects, An(to) is negative at frequencies below the absorption edge and positive on the high-energy side. The laser-induced negative index change is referred to as a self-defocusing optical nonlinearity. The positive An(hto) on the high-energy side of the band gap corresponds to a self-focusing optical nonlinearity.
120
M. Kalafi et a l . / Optical Materials 6 (1996) 117-120
4. Conclusion
The observed nonlinear absorption near the band gap edge of the layered GaSe crystal is due to the bandfilling effect. The change in absorption affects the refractive index through the Kramers-Kronig relations, leading to nonlinear effects. Bandfilling nonlinearity can give possibility to produce semiconductor laser on the base of GaSe crystals.
References [1] G.B. Abdullaev, L.A. Gulevski, A.P. Prokhorov, A.D. Saveliev, E.Yu. Salaev and V.V. Smirnov, JETP Lett. 16 (1972) 130. [2] G.A. Akhundov, A.A. Agaeva, V.M. Salmanov, Ju.P. Scharonov and I.D. Jarochetski, Sov. Phys. Semicond. 7 (1973) 1229. [3] G.B. Abdullaev, K.R. Allakhverdiev, L.A. Gulevski, A.P. Prokhorov, E.Yu. Salaev, A.D. Saveliev and V.V. Smirnov, Quantum Electronics 2 (1975) 1228. [4] E.B. Beregylin, P.M. Valov, T.B. Ribakova, V.M. Salmanov and I.D. Jarochetski, Sov. Phys. Semicond. 9 (1975) 2288. [5] R. Baltramieyunas, V. Narkevicius, E. Skaistys, J. Vaitkus and J. Viscakas, Nuovo Cimento B 38 (1977) 603. [6] A. Frova, Ph. Schmid, A. Grisel and F. Levy, Solid State Commun. 23 (1977) 45. [7] S.S. Yao, J. Buchert and R.R. Alfano, Phys. Rev. B 25 (1982) 6534.
[8] V.S. Dneprovskii, A.I. Furtichev, V.I. Klimov, E.V. Nazvanova, D.K. Okorokov and U.V. Vandishev, Phys. Status Solidi (b) 146 (1988) 341. [9] L. Pavesi and J.L. Staehly, Phys. Rev. B 39 (1989) 10982, [10] R.E. Nahory, K.L. Shaklee, R.F. Leheny and J.C. De Winter, Solid State Commun. 9 (1971) 1107. [11] I.M. Catalano, A. Cingolani, M. Ferrara and A. Minafra, Phys. Status Solidi (b) 68 (1975) 341. [12] X.Z. Lu, R. Rao, B. Willman, S. Lee, A.G. Doukas and R.R. Alfano, Phys. Rev. B 36 (1987) 1140. [13] A.I. Bobrysheva, G.P. Golubev, I.I. Dobinda, E.A. Zhukov, D.G. Luchinskii and Yu.G. Shekun, Phys. Status Solidi (a) 117 (1990) 587. [14] G.B. Abdullaev, I.O. Godzhaev, N.B. Kakhramanov and R.A. Suleimanov, Fiz. Tverd. Tela 34 (1992) 75. [15] D.A.B. Miller, C.T. Seaton, M.E. Prise and S.D. Smith, Phys. Rev. Lett. 47 (1981) 197. [16] C.D. Poole and E. Garmire, Appl. Phys. Lett. 44 (1984) 368. [17] A. Miller, G. Parry and R. Daley, IEEE J. Quantum Electron. QE-20 (1984) 710. [18] F.E. Hilinski, P.A. Lucas and Ying Wang, J. Chem. Phys. 89 (1988) 3435. [19] V. Esch, B. Fluegel, G. Khitrova, H.M. Gibbs, Xu Jiajin, K. Kang, S.W. Koch, L.C. Liu, H. Risbub and N. Peyghambarian, Phys. Rev. B 42 (1990) 7450. [20] M. Schluter, Nuovo Gimento 13B (1973) 313. [21] Y. Depeursinge, Nuovo Cimento 64B (1981) 111. [22] A. Mercier, E. Mooser and J.P. Voitchovsky, Phys. Rev. B 12 (1975) 4307. [23] P. Vashista and R.K. Kalia, Phys. Rev. B 25 (1982) 6492. [24] N. Peyghambarian, S.W. Koch and A. Mysyrovicz, Introduction to Semiconductor Optics, Series in Solid State Physical Electronics (Prentice-Hall, New Jersey, 1993) p. 325.
ELSEVIER
Optical Materials 6 (1996) 117-120
Nonlinear light absorption in GaSe crystals at the fundamental absorption edge M. Kalafi, H. Bidadi, H. Tajalli, V. Salmanov Centre for Applied Physics Research Universi~ of Tabriz, Tabriz, lran
Abstract The nonlinear light absorption at the fundamental absorption edge for high excitation intensities in GaSe has been investigated experimentally. The bleaching of band-edge absorption which manifests itself as an apparent blue shift of the absorption edge can be interpreted on the base of bandfilling nonlinearities. It is shown that the observed negative absorption change in GaSe crystal is the basis of optical amplification and the semiconductor laser.
1. Introduction GaSe crystals belonging to I I I - V I compounds have received considerable attention recently as an interesting class of nonlinear optical materials. Possessing layered structure, high polarizability, optical homogeneity and naturally mirror-like surfaces, a number of nonlinear optical phenomena such as harmonic generation [1,2], parametric light generation [3,4], electron-hole plasma [5-9] and stimulated emission [10-14], etc., have been observed in these crystals. In this paper, we present the experimental results on nonlinear light absorption in GaSe in the fundamental absorption region at high optical excitation levels. Basically, this phenomenon has previously been studied in narrow-gap semiconductors such as InSb [15], InAs [16], CdHgTe [17] and also in CdS microcrystallites in a polymer film [18] and CdTe quantum dots in glass [19]. The investigation of this effect in a wide band gap semiconductor such as
GaSe seems interesting, as it may extend the possible applications of nonlinear optics.
2. Experimental methods Gallium selenide has a layered structure, where each layer contains two gallium and two selenium close-packed sublayers in the stacking sequence S e G a - G a - S e [20]. The bonding between two adjacent layers is of the Van der Waals type, while within the layer the bonding is predominantly covalent. Band structure calculations [20,21] predict the presence of an indirect minimum of the conduction band at the point M (M~- symmetry) of the Brillouin zone lower than the direct minimum (F~) at the point F. Moreover, the top of the valence band lies at the centre of the Brillouin zone and has the symmetry F3-. The direct and indirect gaps are very close in energy. Measurements of optical absorption and photolumi-
00925-3467/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved PH S0925-3467(96)00022-5
118
M. Kalafi et al. / Optical Materials 6 (1996) 117-120
nescence show a difference of about 25 meV between these two minima [22]. The investigated GaSe single crystals were obtained by the Bridgman method. Samples were of E-modification having p-type conductivity. The ingots were cleaved along the planes of layers (_L to the c-axis), obtaining slices about 10-50 ~ m thick. Mobility and concentration of charge carders measured by conventional methods at room temperature were ~ 20 c m 2 / V • s and 1 X 10 j4 cm -3, respectively. The energy gap of GaSe is Eg = 2.02 eV at room temperature. As an excitation source, a Rhodamine 6G dye laser (PRA, LN-107) pumped by the output of a N2-1aser (PRA, LN-1000), tuned through the region 594-643 nm with a repetition frequency of 10 Hz and a pulse width of 1 ns was used. Lower excitation intensities were obtained by means of suitable calibrated neutral filters. Transmission spectra were obtained by shifting filters from the front to the rear of the samples and checking the experimental reproducibility in the region of transparency. The output signals were detected by a silicon photodiode and recorded by a storage oscilloscope (Le Croy 9400).
3. Results
and
2
2
,rE
!oI 1.90
1.95
I
I
I
2.02(Eg)
i
2.10ht,u,eV
Fig. 1. Absorption spectra of GaSe at low (~ 3.5 mW/cm2, curve 1) and high ( ~ 12 mW/cm2, curve 2) intensity excitations.
0.0
discussion
The absorption spectra of GaSe at low (curve 1) and high (curve 2) excitation intensities are given in Fig. 1. As it is seen from the figure, at high excitation levels, the absorption coefficient is decreased, and along with the onset of absorption is also shifted towards higher energies. The change in the absorption coefficient A a can be obtained by direct subtraction of curves 1 and 2 in Fig. 1. The result is plotted in Fig. 2. It is seen that the maximum absorption change takes place in the vicinity of the band gap. The observed nonlinear absorption near the band gap at high excitation intensities can be attributed to optical saturation effects in GaSe, i.e. electrons and holes generated by absorption of light which relax rapidly to a thermal distribution, blocking absorption states near the band edge. Effectively, this is like a shift of the band edge to higher energies with increasing laser intensity, which causes the absorption at the vicinity of the band edge to decrease. From Fig. 2, it is clear that, the absorption
1
-1-
°z-200 0 I,D_ rv" 0 t.~ m
<
-450''' 1.90
1.95
202 (Eg) 2.10hw,eV
Fig. 2. The change in the absorptioncoefficient Aa.
M. Kalafi et aL/ Optical Materials 6 (1996) 117-120 change becomes negative. Negative absorption means amplification as can be seen from Beer-Lambert's law
l ( t ) =10e -"~.
119
0.12
f
(1)
For a < 0, the transmitted intensity is higher than the input intensity. This optical gain can give a possibility of producing a semiconductor laser based on GaSe crystals. The bandfilling effect predicts that the change in absorption coefficient due to free carriers (neglecting exciton interaction) at photon energy h to' above the band-gap energy is given by [17]
o
i°t
A~(hto') = - o % ( h t o ' ) 2 1 / 2 ( rrh ]3/2
× [ n e m ~ 3 / 2 e x p ( - A E c / k B T ) + nhm; 3/2
-0.12 ~
w
,
e
V
(2)
Fig. 3. The change in the refractiveindex An(w).
A E c = (hto' - E'g)/(1 + m e / m h ) ,
(3)
AE v = ( h t o ' - E'g)/(1 + m i m e ) ,
(4)
account which can eventually lead to the enhancement of the nonlinear absorption. Such saturation leads both to nonlinear absorption and to a strong intensity dependence of the refractive index. From the Kramers-Kronig relation [24] we may write the change in refractive index at photon energy h to as
×exp( - A E v / k B T ) ] , where
o%(hto') is the low-power absorption coefficient at photon energy h to', m e is the effective mass of an electron, m h is the effective mass of a hole, n e, n h are the integrated population density of free-electron and free-hole, respectively, E'g is the renormalized band gap which results from exchange and correlation effects at high carrier densities [23]. Taking m e = 0.3 m 0, m h = 0.2 m 0 and calculated values of n e, nh, E'g, AE c, A E v from Eqs. (4)-(11) of Ref. [18], the percentage relative absorbance change A a 1 0 0 % / a 0 is evaluated to be ~ 12% in GaSe. This is in good agreement with the corresponding observed value of 15%. The small difference between these values can be due to the fact that, the exciton interactions were neglected in Eq. (2), while in wide-band-gap materials (such as GaSe), Coulomb electron-hole correlation effects should be taken into
hc A.(h,o)
- T,0
!
hto') ' - , 2 - 2 - - - - 2 d ( h to') • (hto) - (hto)
(5)
Using Eq. (5) to compute the index change related to the absorption change of Fig. 2, we obtain the result plotted in Fig. 3. As can be noted from Fig. 3 the change in the refractive index leading to nonlinear effects, An(to) is negative at frequencies below the absorption edge and positive on the high-energy side. The laser-induced negative index change is referred to as a self-defocusing optical nonlinearity. The positive An(hto) on the high-energy side of the band gap corresponds to a self-focusing optical nonlinearity.
120
M. Kalafi et a l . / Optical Materials 6 (1996) 117-120
4. Conclusion
The observed nonlinear absorption near the band gap edge of the layered GaSe crystal is due to the bandfilling effect. The change in absorption affects the refractive index through the Kramers-Kronig relations, leading to nonlinear effects. Bandfilling nonlinearity can give possibility to produce semiconductor laser on the base of GaSe crystals.
References [1] G.B. Abdullaev, L.A. Gulevski, A.P. Prokhorov, A.D. Saveliev, E.Yu. Salaev and V.V. Smirnov, JETP Lett. 16 (1972) 130. [2] G.A. Akhundov, A.A. Agaeva, V.M. Salmanov, Ju.P. Scharonov and I.D. Jarochetski, Sov. Phys. Semicond. 7 (1973) 1229. [3] G.B. Abdullaev, K.R. Allakhverdiev, L.A. Gulevski, A.P. Prokhorov, E.Yu. Salaev, A.D. Saveliev and V.V. Smirnov, Quantum Electronics 2 (1975) 1228. [4] E.B. Beregylin, P.M. Valov, T.B. Ribakova, V.M. Salmanov and I.D. Jarochetski, Sov. Phys. Semicond. 9 (1975) 2288. [5] R. Baltramieyunas, V. Narkevicius, E. Skaistys, J. Vaitkus and J. Viscakas, Nuovo Cimento B 38 (1977) 603. [6] A. Frova, Ph. Schmid, A. Grisel and F. Levy, Solid State Commun. 23 (1977) 45. [7] S.S. Yao, J. Buchert and R.R. Alfano, Phys. Rev. B 25 (1982) 6534.
[8] V.S. Dneprovskii, A.I. Furtichev, V.I. Klimov, E.V. Nazvanova, D.K. Okorokov and U.V. Vandishev, Phys. Status Solidi (b) 146 (1988) 341. [9] L. Pavesi and J.L. Staehly, Phys. Rev. B 39 (1989) 10982, [10] R.E. Nahory, K.L. Shaklee, R.F. Leheny and J.C. De Winter, Solid State Commun. 9 (1971) 1107. [11] I.M. Catalano, A. Cingolani, M. Ferrara and A. Minafra, Phys. Status Solidi (b) 68 (1975) 341. [12] X.Z. Lu, R. Rao, B. Willman, S. Lee, A.G. Doukas and R.R. Alfano, Phys. Rev. B 36 (1987) 1140. [13] A.I. Bobrysheva, G.P. Golubev, I.I. Dobinda, E.A. Zhukov, D.G. Luchinskii and Yu.G. Shekun, Phys. Status Solidi (a) 117 (1990) 587. [14] G.B. Abdullaev, I.O. Godzhaev, N.B. Kakhramanov and R.A. Suleimanov, Fiz. Tverd. Tela 34 (1992) 75. [15] D.A.B. Miller, C.T. Seaton, M.E. Prise and S.D. Smith, Phys. Rev. Lett. 47 (1981) 197. [16] C.D. Poole and E. Garmire, Appl. Phys. Lett. 44 (1984) 368. [17] A. Miller, G. Parry and R. Daley, IEEE J. Quantum Electron. QE-20 (1984) 710. [18] F.E. Hilinski, P.A. Lucas and Ying Wang, J. Chem. Phys. 89 (1988) 3435. [19] V. Esch, B. Fluegel, G. Khitrova, H.M. Gibbs, Xu Jiajin, K. Kang, S.W. Koch, L.C. Liu, H. Risbub and N. Peyghambarian, Phys. Rev. B 42 (1990) 7450. [20] M. Schluter, Nuovo Gimento 13B (1973) 313. [21] Y. Depeursinge, Nuovo Cimento 64B (1981) 111. [22] A. Mercier, E. Mooser and J.P. Voitchovsky, Phys. Rev. B 12 (1975) 4307. [23] P. Vashista and R.K. Kalia, Phys. Rev. B 25 (1982) 6492. [24] N. Peyghambarian, S.W. Koch and A. Mysyrovicz, Introduction to Semiconductor Optics, Series in Solid State Physical Electronics (Prentice-Hall, New Jersey, 1993) p. 325.