Abstract

Polarization dependence of band-edge excitonic transitions in Cu(Al0.5In0.5)S2 [denoted as Cu(AlIn)S2] has been characterized using polarized-thermoreflectance (PTR) measurements with E || <111¯> and E ⊥ <111¯> polarizations in the temperature range between 30 and 320 K. The measurements were done on as-grown {112} surface of the chalcopyrite crystal. The polarization dependence of the band-edge transitions of Cu(AlIn)S2 clearly showed that the EA exciton is present prominently with E || <111¯> polarization while the EB exciton appears significantly only in the E ⊥ <111¯> polarized spectra. For the unpolarized spectra, both EA and EB features were combined. The EA feature is closely related to the E0 transition, while the EB feature is that of E0 + Δ0 transition in the chalcopyrite. The crystal-field splitting energy of Δ0 of Cu(AlIn)S2 at the valence-band top is determined accurately by PTR experiments. Temperature dependences of transition energies of EA and EB transitions were analyzed. The band-edge excitons reveal an anomalous temperature-energy shift with increasing the temperatures from 30 to 320 K due to the variation of Cu d electrons’ contribution to valence band that affected by the native defects inside Cu(AlIn)S2. The PTR technique is more effective in studying the band-edge structure of the chalcopyrite crystal.

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  1. M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
    [CrossRef]
  2. S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
    [CrossRef]
  3. S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
    [CrossRef] [PubMed]
  4. K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
    [CrossRef]
  5. C. H. Ho, “Thermoreflectance characterization of the band-edge excitonic transitions in CuAlS2 ultraviolet solar-cell material,” Appl. Phys. Lett. 96(6), 061902 (2010).
    [CrossRef]
  6. C. H. Ho, “Optical study of the structural change in ReS2 single crystals using polarized thermoreflectance spectroscopy,” Opt. Express 13(1), 8–19 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-8 .
    [CrossRef] [PubMed]
  7. C. H. Ho and S. L. Lin, “Optical properties of the interband transitions of layered gallium sulfide,” J. Appl. Phys. 100(8), 083508 (2006).
    [CrossRef]
  8. D. E. Aspnes, in Handbook on Semiconductors, edited by M. Balkanski, (North Holland, Amsterdam, 1980).
  9. C. H. Ho, J. H. Li, and Y. S. Lin, “Optical characterization of a GaAs/In(0.5)(AlxGa(1-x))(0.5)P/GaAs heterostructure cavity by piezoreflectance spectroscopy,” Opt. Express 15(21), 13886–13893 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-21-13886 .
    [CrossRef] [PubMed]
  10. J. E. Jaffe and A. Zunger, “Electronic structure of the ternary chalcopyrite semiconductors CuAlS2, CuGaS2, CuInS2, CuAlSe2, CuGaSe2, and CuInSe2,” Phys. Rev. B 28(10), 5822–5847 (1983).
    [CrossRef]
  11. J. E. Jaffe and A. Zunger, “Theory of the band-gap anomaly in ABC2 chalcopyrite semiconductors,” Phys. Rev. B 29(4), 1882–1906 (1984).
    [CrossRef]
  12. T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
    [CrossRef]
  13. C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
    [CrossRef]
  14. I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
    [CrossRef]

2010 (2)

C. H. Ho, “Thermoreflectance characterization of the band-edge excitonic transitions in CuAlS2 ultraviolet solar-cell material,” Appl. Phys. Lett. 96(6), 061902 (2010).
[CrossRef]

C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
[CrossRef]

2009 (1)

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

C. H. Ho and S. L. Lin, “Optical properties of the interband transitions of layered gallium sulfide,” J. Appl. Phys. 100(8), 083508 (2006).
[CrossRef]

2005 (2)

C. H. Ho, “Optical study of the structural change in ReS2 single crystals using polarized thermoreflectance spectroscopy,” Opt. Express 13(1), 8–19 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-8 .
[CrossRef] [PubMed]

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

2001 (1)

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

1998 (1)

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

1993 (1)

I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
[CrossRef]

1990 (1)

T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
[CrossRef]

1984 (1)

J. E. Jaffe and A. Zunger, “Theory of the band-gap anomaly in ABC2 chalcopyrite semiconductors,” Phys. Rev. B 29(4), 1882–1906 (1984).
[CrossRef]

1983 (1)

J. E. Jaffe and A. Zunger, “Electronic structure of the ternary chalcopyrite semiconductors CuAlS2, CuGaS2, CuInS2, CuAlSe2, CuGaSe2, and CuInSe2,” Phys. Rev. B 28(10), 5822–5847 (1983).
[CrossRef]

Aksenov, I.

I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
[CrossRef]

Aloni, S.

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

Chi, P. C.

C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
[CrossRef]

Chichibu, S.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Connor, S. T.

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

Cui, Y.

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

Fons, P. J.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Hiramatsu, K.

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

Ho, C. H.

C. H. Ho, “Thermoreflectance characterization of the band-edge excitonic transitions in CuAlS2 ultraviolet solar-cell material,” Appl. Phys. Lett. 96(6), 061902 (2010).
[CrossRef]

C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
[CrossRef]

C. H. Ho, J. H. Li, and Y. S. Lin, “Optical characterization of a GaAs/In(0.5)(AlxGa(1-x))(0.5)P/GaAs heterostructure cavity by piezoreflectance spectroscopy,” Opt. Express 15(21), 13886–13893 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-21-13886 .
[CrossRef] [PubMed]

C. H. Ho and S. L. Lin, “Optical properties of the interband transitions of layered gallium sulfide,” J. Appl. Phys. 100(8), 083508 (2006).
[CrossRef]

C. H. Ho, “Optical study of the structural change in ReS2 single crystals using polarized thermoreflectance spectroscopy,” Opt. Express 13(1), 8–19 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-8 .
[CrossRef] [PubMed]

Hsu, C. M.

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

Hsu, T. M.

T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
[CrossRef]

Hwang, H. L.

T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
[CrossRef]

Ikari, T.

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

Jaffe, J. E.

J. E. Jaffe and A. Zunger, “Theory of the band-gap anomaly in ABC2 chalcopyrite semiconductors,” Phys. Rev. B 29(4), 1882–1906 (1984).
[CrossRef]

J. E. Jaffe and A. Zunger, “Electronic structure of the ternary chalcopyrite semiconductors CuAlS2, CuGaS2, CuInS2, CuAlSe2, CuGaSe2, and CuInSe2,” Phys. Rev. B 28(10), 5822–5847 (1983).
[CrossRef]

Kijatkina, O.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Krunks, M.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Kurafuji, T.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Lee, J. S.

T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
[CrossRef]

Li, J. H.

Lin, S. L.

C. H. Ho and S. L. Lin, “Optical properties of the interband transitions of layered gallium sulfide,” J. Appl. Phys. 100(8), 083508 (2006).
[CrossRef]

Lin, Y. S.

Lo, S. F.

C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
[CrossRef]

Mere, A.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Mikli, V.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Miyake, H.

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

Mizutani, T.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Murakami, K.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Nakanishi, H.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Niki, S.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Nishikawa, N.

I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
[CrossRef]

Oja, I.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Sato, K.

I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
[CrossRef]

Shioda, T.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Shirakata, S.

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

Varema, T.

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Weil, B. D.

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

Yamada, A.

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

Yoshino, K.

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

Zunger, A.

J. E. Jaffe and A. Zunger, “Theory of the band-gap anomaly in ABC2 chalcopyrite semiconductors,” Phys. Rev. B 29(4), 1882–1906 (1984).
[CrossRef]

J. E. Jaffe and A. Zunger, “Electronic structure of the ternary chalcopyrite semiconductors CuAlS2, CuGaS2, CuInS2, CuAlSe2, CuGaSe2, and CuInSe2,” Phys. Rev. B 28(10), 5822–5847 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

K. Yoshino, T. Ikari, S. Shirakata, H. Miyake, and K. Hiramatsu, “Sharp band edge photoluminescence of high-purity CuInS2 single crystals,” Appl. Phys. Lett. 78(6), 742–744 (2001).
[CrossRef]

C. H. Ho, “Thermoreflectance characterization of the band-edge excitonic transitions in CuAlS2 ultraviolet solar-cell material,” Appl. Phys. Lett. 96(6), 061902 (2010).
[CrossRef]

J. Am. Chem. Soc. (1)

S. T. Connor, C. M. Hsu, B. D. Weil, S. Aloni, and Y. Cui, “Phase transformation of biphasic Cu2S-CuInS2 to monophasic CuInS2 nanorods,” J. Am. Chem. Soc. 131(13), 4962–4966 (2009).
[CrossRef] [PubMed]

J. Appl. Phys. (4)

I. Aksenov, N. Nishikawa, and K. Sato, “Electron spin resonance of copper vacancy in CuAlS2,” J. Appl. Phys. 74(6), 3811–3814 (1993).
[CrossRef]

T. M. Hsu, J. S. Lee, and H. L. Hwang, “Photoreflectance of sulfur-annealed copper indium disulfide,” J. Appl. Phys. 68(1), 283–287 (1990).
[CrossRef]

S. Chichibu, T. Mizutani, K. Murakami, T. Shioda, T. Kurafuji, H. Nakanishi, S. Niki, P. J. Fons, and A. Yamada, “Band gap energies of bulk, thin-film, and epitaxial layers of CuInSe2 and CuGaSe2,” J. Appl. Phys. 83(7), 3678–3689 (1998).
[CrossRef]

C. H. Ho and S. L. Lin, “Optical properties of the interband transitions of layered gallium sulfide,” J. Appl. Phys. 100(8), 083508 (2006).
[CrossRef]

J. Electrochem. Soc. (1)

C. H. Ho, S. F. Lo, and P. C. Chi, “Electronic structure and E1 excitons of CuInS2 energy-related crystals studied by temperature-dependent thermoreflectance spectroscopy,” J. Electrochem. Soc. 157(2), H219–H226 (2010).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (2)

J. E. Jaffe and A. Zunger, “Electronic structure of the ternary chalcopyrite semiconductors CuAlS2, CuGaS2, CuInS2, CuAlSe2, CuGaSe2, and CuInSe2,” Phys. Rev. B 28(10), 5822–5847 (1983).
[CrossRef]

J. E. Jaffe and A. Zunger, “Theory of the band-gap anomaly in ABC2 chalcopyrite semiconductors,” Phys. Rev. B 29(4), 1882–1906 (1984).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

M. Krunks, O. Kijatkina, A. Mere, T. Varema, I. Oja, and V. Mikli, “Sprayed CuInS2 films grown under Cu-rich conditions as absorbers for solar cells,” Sol. Energy Mater. Sol. Cells 87(1-4), 207–214 (2005).
[CrossRef]

Other (1)

D. E. Aspnes, in Handbook on Semiconductors, edited by M. Balkanski, (North Holland, Amsterdam, 1980).

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Figures (5)

Fig. 1
Fig. 1

The crystal morphology and measurement arrangement of PTR experiments for Cu(Al0.5In0.5)S2.

Fig. 2
Fig. 2

Experimental PTR spectra of Cu(AlIn)S2 at (a) 300 and (b) 30 K along E || <11 1 ¯ > and E ⊥ <11 1 ¯ > polarizations. The dashed lines are experimental data and open-circle lines are least-square fits to Eq. (1). The obtained transition energies are indicated by arrows.

Fig. 3
Fig. 3

The representative scheme of band-edge structure of Cu(AlIn)S2 by PTR experiments at 300 K.

Fig. 4
Fig. 4

Temperature-dependent PTR spectra of Cu(AlIn)S2 between 30 and 320 K. The dashed lines are the experimental data with E || <11 1 ¯ > polarization and solid lines are those of the E ⊥ <11 1 ¯ > polarized spectra.

Fig. 5
Fig. 5

Temperature dependences of transition energies of EA (E0) and EB (E0 + Δ0) in Cu(AlIn)S2.

Equations (1)

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Δ R R = Re [ i=1 2 A i ex e j ϕ i ex ( E-E i ex + j Γ i ex ) 2 ]

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