- Email: [email protected]
Polariton emission from CuGaSe2 crystals
ARTICLE IN PRESS
Physica B 365 (2005) 43–46 www.elsevier.com/locate/physb
Polariton emission from CuGaSe2 crystals N.N. Syrbua, I.M. Tiginyanub, V.V. Ursakib, V.E. Tezlevanb, V.V. Zalamaib, L.L. Nemerencoa, b
a Technical University of Moldova, Chisinau, MD-2012, Moldova Institute of Applied Physics, Academy of Sciences of Moldova, Chisinau, MD-2028, Moldova
Received 23 March 2005; received in revised form 19 April 2005; accepted 27 April 2005
Abstract The value of longitudinal–transverse splitting oLT equal to 2.5–2.8 meV and the translation mass M ¼ 2:5 m0 were determined for the A exciton as a result of investigation of the reflectivity and luminescence spectra of CuGaSe2 crystals. The emission from the upper and lower polariton branches of the long-wavelength exciton was observed. r 2005 Elsevier B.V. All rights reserved. PACS: 78.40.Fy; 78.55.Hx; 71.35.Cc Keywords: Reflectivity; Exciton; Polariton; Luminescence; Polarization
1. Introduction CuGaSe2 compound crystallizes into the chalcopyrite structure with the space group I42d–D12 2d . I–III–VI2 materials present interest from the point of view of applications in optoelectronic devices [1–4]. In some materials of this group stimulated emission was observed, as well as second harmonic generation at 10.6 mm and IR generation in the 4.6 and 12 mm spectral range [1,4]. Biexcitons [5], interference of exciton additional waves [6], resonant Raman scattering [7–9] and intensive
emission of exciton–polaritons and bound excitons were observed from these crystals [10–12]. Solar cells are successfully developed on the basis of CuGaSe2 and CuInSe2 materials. In this paper, excitonic reflectivity spectra and exciton–polariton luminescence are investigated. Contours of reflectivity spectra are calculated using dispersion relations. The main parameters of excitons and the energy band structure of CuGaSe2 crystals are determined.
2. Experiment Corresponding author. Tel.: +037322237508;
fax: +037322235405. E-mail address: [email protected] (L.L. Nemerenco).
CuGaSe2 single crystals grown from the gas phase in closed quartz ampoules, represented
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.04.033
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
2–3 mm thick plates with smooth surfaces of 2.5 1.0 cm2 sizes. Surfaces of some plates contain the ~ c-axis. The reflectivity and luminescence spectra were measured using double DFS-32 and SDL-1 spectrometers with a 10 A˚/mm dispersion. The samples were mounted on the cold station of a LTS-22 C 330 optical cryogenic system. The luminescence spectra were excited by a He–Ne laser with the power of 50 mW.
27,5
T = 9K
27,0
E||c
ωT
26,5 R, %
44
26,0 ωL
25,5 25,0 24,5 1,718
3. Results and discussion The reflectivity spectra of CuGaSe2 crystals measured in the exciton region at the temperature of 87 K are discussed in detail elsewhere [13–15]. The n ¼ 1 line of the A exciton series is found at 1.711 eV in the EJc polarization. The n ¼ 1 line of the B exciton series is hardly observed in this polarization. The n ¼ 1 line of the A exciton series is not found in the polarization. The n ¼ 1 line of the B exciton series is found at 1.797 eV. The C exciton line is observed at 1983 eV in same polarization [15]. The wavelength modulated reflectivity spectra in the region of ground and excited exciton states in CuGaSe2 crystals were previously reported [15]. The n ¼ 1, 2 and 3 lines of the A and B exciton series were found in these spectra. The exciton binding energy and the band gap values were calculated form the position of n ¼ 1 and n ¼ 2 exciton lines. The investigation of polarized wavelength modulated reflectivity spectra demonstrated that the n ¼ 1 line of the A exciton series is allowed in the EJc polarization and forbidden in the polarization. The n ¼ 1 line of the A exciton series is observed in the wavelength modulated reflectivity spectra in the polarization but with a weaker intensity. Fig. 1 presents reflectivity (R) spectra of CuGaSe2 crystals measured in EJc polarization. The experimental data are presented in Fig. 1 by the full curve and the dot curve corresponds to calculations according to the dispersion relations. The dielectric constant near the exciton resonance in the frame of a model taking into account the presence of a Thomas–Hopfield dead-layer and the Pekar additional boundary conditions [16–19]
1,720
1,722 E, eV
1,724
1,726
Fig. 1. Measured (solid line) and calculated (dot line) contour of reflectivity spectra of CuGaSe2 crystals. Polarization EJc. Temperature T ¼ 9 K.
is determined by the relation: ~ ¼ b þ ðo; kÞ
20 oLT o0 , o20 o2 igo þ _2 k2 o0 =2M
where b is the background dielectric constant, caused by the contribution of all the mechanisms of interaction except for the considered oscillator; o0 is the transverse exciton frequency, M ¼ mC þ mV is the exciton translation mass, k is the wave vector, oLT ¼ oL o0 is the longitudinal–transverse splitting, and oL is the longitudinal exciton frequency. At finite value of M and oLT g one can write " # o LT ~ ¼ 0 1 þ ðo; kÞ . o20 o2 þ _2 k2 =2M For g ¼ 0 taking into account the Pekar’s additional boundary conditions we have 1 n21;2 ¼ 0 (2
2Mc2 ðo o0 Þ 0 þ _o20
"
2Mc2 ðo o0 Þ 0 _o20
2
8Mc2 0 oLT þ _o20
#1=2 91=2 = ;
,
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
1 n 2 , R¼ 1 þ n
For the case of ga0 we have o2 go Mc2 o0 2 ðn1 n2 Þ ¼ 0 1 2 i 2 _o2 o0 o0 2
2oLT 0 Mc , _o2 o2 go Mc2 o0 2 ðn1 þ n2 Þ ¼ 0 1 2 i 2 _o2 o0 o0
2 o go Mc2 o0 þ 2 0 1 2 i 2 _o2 o0 o0 1=2 2oLT 0 Mc2 . _o2
For an isotropic crystal at normal incident light the reflectivity coefficient is determined by the relation ð1 n0 =1 þ n0 Þ þ ðn0 n =n0 þ n Þei2kn0 t 2 , R ¼ 1 þ ð1 n0 =1 þ n0 Þðn0 n =n0 þ n Þei2kn0 t pffiffiffiffi where n0 ¼ 0 , n ¼ ðn1 n2 þ 0 Þ=ðn1 þ n2 Þ, t is the dead layer thickness, k is the exciton wave vector, n1 , n2 are the refractive indexes of transverse waves taking into account the dependence on the damping parameter g. The results of calculation show (Fig. 1) that the best correspondence between the experiment and calculations is achieved with the following parameters: the longitudinal exciton energy E L ¼ 1:7230 eV, the transverse exciton energy E 0 ¼ 1:7205 eV, the background dielectric constant b ¼ 6:2, the damping parameter g ¼ 0:8 meV, the exciton mass M ¼ 2:5 m0 , the longitudinal– transverse splitting oLT ¼ 2; 5 meV and the dead( layer thickness t ¼ 54 A. Two maxima at the energies of 1.7198 eV (oT ) and 1.7226 eV (oL ) are observed in the luminescence spectra of CuGaSe2 crystals measured at the temperature of 10 K under the excitation of 6328 A˚ He–Ne laser line. The luminescence peak at 1.7198 eV differs by 0.7 meV from the transverse exciton energy o0 (1.7205 eV) determined from the
UPB
Ex. He - Ne, 6328 Å
LPB
12
LA
10 IPL (rel. units)
n21 n22 2Mðo oL Þ c ¼ ¼ ; _ o0 0 n1 n2 þ 0 . n ¼ n1 þ n2 n23
45
6
1
8
ETO
6
ELO 5
2 6
ETO 3
A-excition
4
4
x10
2 1,7254
1,7207
1,7161
1,7116
E, eV
Fig. 2. PL spectra of CuGaSe2 crystals measured at T ¼ 9 K in the region of exciton polaritons.
calculation of reflectivity spectra. The luminescence peak at 1.7226 eV labeled as oL differs by 0.3 meV from the longitudinal exciton energy oL (1.7230 eV) determined from the calculation of reflectivity spectra. These data show that the luminescence spectra presented in Fig. 2 are due to the emission from the upper (oL ) and lower (oT ) exciton–polariton branches. A series of weak PL bands labeled as 1–18 are observed in the long-wavelength spectral range (see Figs. 2 and 3). Taking into account the energy position of these bands and the form of spectra one can assume that this emission is caused by the exciton–polaritons annihilation with the participation of phonons. The PL peaks 1–4 observed near the oT energy are weaker than the bands 6, 7, 8, 10, and 13. The distance between the 1–18 PL peaks and the oT band is consistent with the energy of one- and two-phonon vibrational modes at the center of the Brilloin zone determined from the IR reflectivity spectra [20–23]. The interpretation of PL bands presented in Figs. 2 and 3 is one of the most probable variants. However, the big number of phonons inherent to CuGaSe2 crystal does not exclude the participation of other vibrational modes in the emission processes. One can suggest that the annihilation of exciton–polaritons is due to the increase of population of the lower polariton branch. In conclusion, the value of longitudinal–transverse splitting oLT equal to 2.5–2.8 meV and the translation mass M ¼ 2:5 m0 were determined for
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
46
Ex. He - Ne 6328 Å T = 9K 24 6 7 8 PL (rel. units)
10
18
13
20 11 9 16
5
14 15
12
17 16
12
8
1,7093
1,7047
1,7002 E, eV
1,6957
1,6912
Fig. 3. PL spectra of CuGaSe2 crystals measured at T ¼ 9 K in the long-wavelength spectral range.
the A exciton as a result of investigation of the reflectivity and luminescence spectra of CuGaSe2 crystals. The emission from the upper and lower polariton branches of the long-wavelength exciton was observed. References [1] G.D. Boyd, H. Kasper, J.H. Mc Fee, IEEE J. Quantum Electron. 7 (1971) 563. [2] J.L. Shay, S. Wagner, H.M. Kasper, Appl. Phys. Lett. 27 (1975) 89. [3] A.M. Gabor, J.R. Tuttle, D.S. Albin, A.L. Tennant, M.A. Contreras, R. Noufi, A.M. Hermann, AIP Conf. Proc. 306 (1994) 59. [4] Y.X. Fan, R.C. Eckardt, R.L. Byer, R.K. Route, R.S. Feigelson, Appl. Phys. Lett. 45 (1984) 313. [5] K. Tanaka, H. Uchiki, S. Iida, T. Terasako, S. Shirakata, Solid State Commun. 114 (2000) 197. [6] N.N. Syrbu, V.V. Ursaki, J.M. Tiginyanu, V.E. Tezlevan, M.A. Blaje, J. Phys. Chem. Solids 64 (2003) 1967. [7] M. Susaki, N. Yamamoto, K. Wakita, in: JPAP Book series 1 Japanese Research Review and Ternary and Multinary Compounds for Pioneering the 21 st. Century, Mai, 2001. [8] N.N. Syrbu, M. Blaje, J.M. Tiginyanu, V.E. Tezlevan, Opt. Spectrosc. 92 (2002) 395.
[9] M. Susaki, K. Wakita, N. Yamamoto, E. Niwa, K. Masumoto, Jpn. J. Appl. Phys. 37 (1998) 847. [10] T. Terasako, H. Umiji, K. Tonaka, S. Shiratata, H. Uchiki, S. Jsomura, Jpn. J. Appl. Phys. 38 (1998) 805. [11] M. Susaki, K. Wakita, N. Jamamoto, Jpn. J. Appl. Phys. 38 (1999) 2287. [12] N.N. Syrbu, M. Blaje, V.E. Tezlevan, V.V. Ursaki, Opt. Spectrosc. 92 (2002) 402. [13] B. Tell, P.M. Bridenbaugh, Phys. Rev. B 12 (1975) 3330. [14] J.L. Shay, B. Tell, H.M. Kasper, L.M. Schiavone, Phys. Rev. B 5 (1972) 5003. [15] N.N. Syrbu, M. Bogdanash, V.E. Tezlevan, I.G. Stamov, J. Phys: Condens. Matter 9 (1997) 1217. [16] J.J. Hopfield, D.G. Thomas, Phys. Rev. 132 (1963) 563. [17] S.I. Pekar, Zh. Eksp. Teor. Fiz. 34 (1958) 1176. [18] E.L. Ivchenko, Exitons, in: E.I. Rashba, M.D. Sturge (Eds.), North-Holland Publishing Company, Amsterdam, 1982, p. 141. [19] V.M. Agranovich, V.L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons, Nauka, Moscow, 1979, Springer, New York, 1984. [20] H. Neuman, W. Kissinger, H. Sobbota, W. Rirde, J. Phys. 84 (1984) 69. [21] N.N. Syrbu, Opt. Spectrosc. 79 (1995) 249. [22] A.M. Andriesh, N.N. Syrbu, M.S. Iovu, V.E. Tezlevan, Phys. Status Solidi (B) 187 (1995) 83. [23] N.N. Syrbu, M. Bogdanas, V.E. Tezlevan, I. Mushcutariu, Physica B (Condens. Matter) 229 (1997) 199.
Physica B 365 (2005) 43–46 www.elsevier.com/locate/physb
Polariton emission from CuGaSe2 crystals N.N. Syrbua, I.M. Tiginyanub, V.V. Ursakib, V.E. Tezlevanb, V.V. Zalamaib, L.L. Nemerencoa, b
a Technical University of Moldova, Chisinau, MD-2012, Moldova Institute of Applied Physics, Academy of Sciences of Moldova, Chisinau, MD-2028, Moldova
Received 23 March 2005; received in revised form 19 April 2005; accepted 27 April 2005
Abstract The value of longitudinal–transverse splitting oLT equal to 2.5–2.8 meV and the translation mass M ¼ 2:5 m0 were determined for the A exciton as a result of investigation of the reflectivity and luminescence spectra of CuGaSe2 crystals. The emission from the upper and lower polariton branches of the long-wavelength exciton was observed. r 2005 Elsevier B.V. All rights reserved. PACS: 78.40.Fy; 78.55.Hx; 71.35.Cc Keywords: Reflectivity; Exciton; Polariton; Luminescence; Polarization
1. Introduction CuGaSe2 compound crystallizes into the chalcopyrite structure with the space group I42d–D12 2d . I–III–VI2 materials present interest from the point of view of applications in optoelectronic devices [1–4]. In some materials of this group stimulated emission was observed, as well as second harmonic generation at 10.6 mm and IR generation in the 4.6 and 12 mm spectral range [1,4]. Biexcitons [5], interference of exciton additional waves [6], resonant Raman scattering [7–9] and intensive
emission of exciton–polaritons and bound excitons were observed from these crystals [10–12]. Solar cells are successfully developed on the basis of CuGaSe2 and CuInSe2 materials. In this paper, excitonic reflectivity spectra and exciton–polariton luminescence are investigated. Contours of reflectivity spectra are calculated using dispersion relations. The main parameters of excitons and the energy band structure of CuGaSe2 crystals are determined.
2. Experiment Corresponding author. Tel.: +037322237508;
fax: +037322235405. E-mail address: [email protected] (L.L. Nemerenco).
CuGaSe2 single crystals grown from the gas phase in closed quartz ampoules, represented
0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.04.033
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
2–3 mm thick plates with smooth surfaces of 2.5 1.0 cm2 sizes. Surfaces of some plates contain the ~ c-axis. The reflectivity and luminescence spectra were measured using double DFS-32 and SDL-1 spectrometers with a 10 A˚/mm dispersion. The samples were mounted on the cold station of a LTS-22 C 330 optical cryogenic system. The luminescence spectra were excited by a He–Ne laser with the power of 50 mW.
27,5
T = 9K
27,0
E||c
ωT
26,5 R, %
44
26,0 ωL
25,5 25,0 24,5 1,718
3. Results and discussion The reflectivity spectra of CuGaSe2 crystals measured in the exciton region at the temperature of 87 K are discussed in detail elsewhere [13–15]. The n ¼ 1 line of the A exciton series is found at 1.711 eV in the EJc polarization. The n ¼ 1 line of the B exciton series is hardly observed in this polarization. The n ¼ 1 line of the A exciton series is not found in the polarization. The n ¼ 1 line of the B exciton series is found at 1.797 eV. The C exciton line is observed at 1983 eV in same polarization [15]. The wavelength modulated reflectivity spectra in the region of ground and excited exciton states in CuGaSe2 crystals were previously reported [15]. The n ¼ 1, 2 and 3 lines of the A and B exciton series were found in these spectra. The exciton binding energy and the band gap values were calculated form the position of n ¼ 1 and n ¼ 2 exciton lines. The investigation of polarized wavelength modulated reflectivity spectra demonstrated that the n ¼ 1 line of the A exciton series is allowed in the EJc polarization and forbidden in the polarization. The n ¼ 1 line of the A exciton series is observed in the wavelength modulated reflectivity spectra in the polarization but with a weaker intensity. Fig. 1 presents reflectivity (R) spectra of CuGaSe2 crystals measured in EJc polarization. The experimental data are presented in Fig. 1 by the full curve and the dot curve corresponds to calculations according to the dispersion relations. The dielectric constant near the exciton resonance in the frame of a model taking into account the presence of a Thomas–Hopfield dead-layer and the Pekar additional boundary conditions [16–19]
1,720
1,722 E, eV
1,724
1,726
Fig. 1. Measured (solid line) and calculated (dot line) contour of reflectivity spectra of CuGaSe2 crystals. Polarization EJc. Temperature T ¼ 9 K.
is determined by the relation: ~ ¼ b þ ðo; kÞ
20 oLT o0 , o20 o2 igo þ _2 k2 o0 =2M
where b is the background dielectric constant, caused by the contribution of all the mechanisms of interaction except for the considered oscillator; o0 is the transverse exciton frequency, M ¼ mC þ mV is the exciton translation mass, k is the wave vector, oLT ¼ oL o0 is the longitudinal–transverse splitting, and oL is the longitudinal exciton frequency. At finite value of M and oLT g one can write " # o LT ~ ¼ 0 1 þ ðo; kÞ . o20 o2 þ _2 k2 =2M For g ¼ 0 taking into account the Pekar’s additional boundary conditions we have 1 n21;2 ¼ 0 (2
2Mc2 ðo o0 Þ 0 þ _o20
"
2Mc2 ðo o0 Þ 0 _o20
2
8Mc2 0 oLT þ _o20
#1=2 91=2 = ;
,
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
1 n 2 , R¼ 1 þ n
For the case of ga0 we have o2 go Mc2 o0 2 ðn1 n2 Þ ¼ 0 1 2 i 2 _o2 o0 o0 2
2oLT 0 Mc , _o2 o2 go Mc2 o0 2 ðn1 þ n2 Þ ¼ 0 1 2 i 2 _o2 o0 o0
2 o go Mc2 o0 þ 2 0 1 2 i 2 _o2 o0 o0 1=2 2oLT 0 Mc2 . _o2
For an isotropic crystal at normal incident light the reflectivity coefficient is determined by the relation ð1 n0 =1 þ n0 Þ þ ðn0 n =n0 þ n Þei2kn0 t 2 , R ¼ 1 þ ð1 n0 =1 þ n0 Þðn0 n =n0 þ n Þei2kn0 t pffiffiffiffi where n0 ¼ 0 , n ¼ ðn1 n2 þ 0 Þ=ðn1 þ n2 Þ, t is the dead layer thickness, k is the exciton wave vector, n1 , n2 are the refractive indexes of transverse waves taking into account the dependence on the damping parameter g. The results of calculation show (Fig. 1) that the best correspondence between the experiment and calculations is achieved with the following parameters: the longitudinal exciton energy E L ¼ 1:7230 eV, the transverse exciton energy E 0 ¼ 1:7205 eV, the background dielectric constant b ¼ 6:2, the damping parameter g ¼ 0:8 meV, the exciton mass M ¼ 2:5 m0 , the longitudinal– transverse splitting oLT ¼ 2; 5 meV and the dead( layer thickness t ¼ 54 A. Two maxima at the energies of 1.7198 eV (oT ) and 1.7226 eV (oL ) are observed in the luminescence spectra of CuGaSe2 crystals measured at the temperature of 10 K under the excitation of 6328 A˚ He–Ne laser line. The luminescence peak at 1.7198 eV differs by 0.7 meV from the transverse exciton energy o0 (1.7205 eV) determined from the
UPB
Ex. He - Ne, 6328 Å
LPB
12
LA
10 IPL (rel. units)
n21 n22 2Mðo oL Þ c ¼ ¼ ; _ o0 0 n1 n2 þ 0 . n ¼ n1 þ n2 n23
45
6
1
8
ETO
6
ELO 5
2 6
ETO 3
A-excition
4
4
x10
2 1,7254
1,7207
1,7161
1,7116
E, eV
Fig. 2. PL spectra of CuGaSe2 crystals measured at T ¼ 9 K in the region of exciton polaritons.
calculation of reflectivity spectra. The luminescence peak at 1.7226 eV labeled as oL differs by 0.3 meV from the longitudinal exciton energy oL (1.7230 eV) determined from the calculation of reflectivity spectra. These data show that the luminescence spectra presented in Fig. 2 are due to the emission from the upper (oL ) and lower (oT ) exciton–polariton branches. A series of weak PL bands labeled as 1–18 are observed in the long-wavelength spectral range (see Figs. 2 and 3). Taking into account the energy position of these bands and the form of spectra one can assume that this emission is caused by the exciton–polaritons annihilation with the participation of phonons. The PL peaks 1–4 observed near the oT energy are weaker than the bands 6, 7, 8, 10, and 13. The distance between the 1–18 PL peaks and the oT band is consistent with the energy of one- and two-phonon vibrational modes at the center of the Brilloin zone determined from the IR reflectivity spectra [20–23]. The interpretation of PL bands presented in Figs. 2 and 3 is one of the most probable variants. However, the big number of phonons inherent to CuGaSe2 crystal does not exclude the participation of other vibrational modes in the emission processes. One can suggest that the annihilation of exciton–polaritons is due to the increase of population of the lower polariton branch. In conclusion, the value of longitudinal–transverse splitting oLT equal to 2.5–2.8 meV and the translation mass M ¼ 2:5 m0 were determined for
ARTICLE IN PRESS N.N. Syrbu et al. / Physica B 365 (2005) 43–46
46
Ex. He - Ne 6328 Å T = 9K 24 6 7 8 PL (rel. units)
10
18
13
20 11 9 16
5
14 15
12
17 16
12
8
1,7093
1,7047
1,7002 E, eV
1,6957
1,6912
Fig. 3. PL spectra of CuGaSe2 crystals measured at T ¼ 9 K in the long-wavelength spectral range.
the A exciton as a result of investigation of the reflectivity and luminescence spectra of CuGaSe2 crystals. The emission from the upper and lower polariton branches of the long-wavelength exciton was observed. References [1] G.D. Boyd, H. Kasper, J.H. Mc Fee, IEEE J. Quantum Electron. 7 (1971) 563. [2] J.L. Shay, S. Wagner, H.M. Kasper, Appl. Phys. Lett. 27 (1975) 89. [3] A.M. Gabor, J.R. Tuttle, D.S. Albin, A.L. Tennant, M.A. Contreras, R. Noufi, A.M. Hermann, AIP Conf. Proc. 306 (1994) 59. [4] Y.X. Fan, R.C. Eckardt, R.L. Byer, R.K. Route, R.S. Feigelson, Appl. Phys. Lett. 45 (1984) 313. [5] K. Tanaka, H. Uchiki, S. Iida, T. Terasako, S. Shirakata, Solid State Commun. 114 (2000) 197. [6] N.N. Syrbu, V.V. Ursaki, J.M. Tiginyanu, V.E. Tezlevan, M.A. Blaje, J. Phys. Chem. Solids 64 (2003) 1967. [7] M. Susaki, N. Yamamoto, K. Wakita, in: JPAP Book series 1 Japanese Research Review and Ternary and Multinary Compounds for Pioneering the 21 st. Century, Mai, 2001. [8] N.N. Syrbu, M. Blaje, J.M. Tiginyanu, V.E. Tezlevan, Opt. Spectrosc. 92 (2002) 395.
[9] M. Susaki, K. Wakita, N. Yamamoto, E. Niwa, K. Masumoto, Jpn. J. Appl. Phys. 37 (1998) 847. [10] T. Terasako, H. Umiji, K. Tonaka, S. Shiratata, H. Uchiki, S. Jsomura, Jpn. J. Appl. Phys. 38 (1998) 805. [11] M. Susaki, K. Wakita, N. Jamamoto, Jpn. J. Appl. Phys. 38 (1999) 2287. [12] N.N. Syrbu, M. Blaje, V.E. Tezlevan, V.V. Ursaki, Opt. Spectrosc. 92 (2002) 402. [13] B. Tell, P.M. Bridenbaugh, Phys. Rev. B 12 (1975) 3330. [14] J.L. Shay, B. Tell, H.M. Kasper, L.M. Schiavone, Phys. Rev. B 5 (1972) 5003. [15] N.N. Syrbu, M. Bogdanash, V.E. Tezlevan, I.G. Stamov, J. Phys: Condens. Matter 9 (1997) 1217. [16] J.J. Hopfield, D.G. Thomas, Phys. Rev. 132 (1963) 563. [17] S.I. Pekar, Zh. Eksp. Teor. Fiz. 34 (1958) 1176. [18] E.L. Ivchenko, Exitons, in: E.I. Rashba, M.D. Sturge (Eds.), North-Holland Publishing Company, Amsterdam, 1982, p. 141. [19] V.M. Agranovich, V.L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons, Nauka, Moscow, 1979, Springer, New York, 1984. [20] H. Neuman, W. Kissinger, H. Sobbota, W. Rirde, J. Phys. 84 (1984) 69. [21] N.N. Syrbu, Opt. Spectrosc. 79 (1995) 249. [22] A.M. Andriesh, N.N. Syrbu, M.S. Iovu, V.E. Tezlevan, Phys. Status Solidi (B) 187 (1995) 83. [23] N.N. Syrbu, M. Bogdanas, V.E. Tezlevan, I. Mushcutariu, Physica B (Condens. Matter) 229 (1997) 199.