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.

©2010 Optical Society of America

1. Introduction

Solar energy related materials of I-III-VI2 (I = Cu, III = In, Ga, Al, and VI = S, Se) family crystals (chalcopyrite phase) are of potential interest for employed in photovoltaic application due to their very high absorption coefficient under sunlight [1,2]. Among these chalcopyrites, sulfide compounds such as Cu(Al,In)S2, Cu(Al,Ga)S2, and Cu(Ga,In)S2 are more environmentally friendly to be free of selenium [3].

Energy band gap is the most important parameter which dominates the main optical-absorption peak of semiconductors. Band-edge structure also determines the optical-absorption behavior in materials. For the sulfide chalcopyrite compounds, CuInS2 is a smallest-gap material (~1.54 eV) with an absorption peak in the near infrared (NIR) region [4]. On the other hand, CuAlS2 possesses a largest gap of ~3.55 eV [5] with its main absorption peak located near ultra-violet (UV) region. To improve photoelectric-conversion efficiency of the solar-cell devices, cascaded thin-film solar cell made by I-III-VI2 family with different band gaps may present high conversion yield due to the combination of absorption peak responses in the NIR, UV, and visible portions. For a cascaded thin-film solar cell by using the Cu(Al,In)S2 series, CuInS2 may employ in the NIR region, CuAlS2 should be dominant in the UV portion, while Cu(AlIn)S2 may play a best role for optoelectronic conversion in the visible range due to its middle-composition characteristic in between the end members of CuInS2 and CuAlS2. Although Cu(AlIn)S2 is expected to have an absorption-peak response in the visible region the experimental evaluation on the band-edge structure of the mixed-crystal chalcopyrite has not yet been reported.

This paper characterizes the experimental band-edge structure of Cu(Al0.5In0.5)S2 chalcopyrite crystal by performing polarized-thermoreflectance (PTR) spectroscopy in the temperature range between 30 and 320 K. The PTR had been proven to be a powerful tool for studying band-edge characteristic of anisotropic crystalline materials [6]. In this study, the PTR measurements were carried out on as-grown {112} face of the chalcopyrite. Two transition features of EA and EB that corresponding to the interband transitions of Γ4V→Γ1C and Γ5V→Γ1C are respectively detected in the PTR spectra of E || <111¯> and E ⊥ <111¯> polarizations. The optical selection rule of Cu(AlIn)S2 crystal clearly indicates that the EA feature is forbidden with the E ⊥ <111¯> polarization, whereas the EB feature is not allowed with the optical measurement along E || <111¯> polarized orientation. The energies of band-edge transitions of E0 (EA) and E0 + Δ0 (EB) are determined to be 2.192 and 2.267 eV at 300 K. Temperature dependence of transition energies of E0 and E0 + Δ0 from the temperature-dependent analysis of PTR spectra for Cu(AlIn)S2 is evaluated. The dependency shows an abnormal S-shape energy variation with increasing the temperatures from 30 to 320 K. This result also renders a maximum turnover temperature of Cu(AlIn)S2 located at 170 K. The occurrence of anomalous temperature-energy shift of the chalcopyrite may closely related to the native defects inside Cu(AlIn)S2.

2. Experiment

Single crystals of Cu(Al0.5In0.5)S2 solid solution were grown by chemical vapor transport (CVT) method using ICl3 as a transport agent. All the starting materials (by stoichiometric weight of each element) and the transport agent were sealed in an evacuated quartz ampoule. The growth temperature was set as 850 °C → 750 °C with a gradient of −5°C/cm. The reaction kept 280 hrs for producing large single crystals. Detailed procedure of CVT was described elsewhere [7]. The as-grown crystals showed slightly dark-red colored and transparent with a maximum size up to 8 × 1.5 × 1 mm3. Figure 1 shows the crystal morphology of the as-grown Cu(AlIn)S2 crystal. The {112} face seems to be the favorite as-grown surface of the crystals. Electron probe microanalysis showed a slight chalcogen deficiency in the crystals. The stoichiometric composition for all elements inside the crystal is matched to a reasonable standard error of the original stoichiometry. X-ray diffraction measurements confirmed the chalcopyrite phase of the solids. The X-ray pattern was analyzed and the lattice parameters were determined to be a = 5.44 Å and c = 10.80 Å, respectively.

 

Fig. 1 The crystal morphology and measurement arrangement of PTR experiments for Cu(Al0.5In0.5)S2.

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The PTR experiments were carried out in the energy range of 1.8 to 2.8 eV. An 150 W tungsten-halogen lamp filtered by a PTI 0.2 m monochromator provided the monochromatic light. The reflected light of the sample was detected by an EG&G type HUV-2000B silicon photodiode and the signal was recorded from an EG&G model 7265 dual phase lock-in amplifier. A pair of visible-dichroic-sheet polarizers with the measured range of 700-400 nm was employed in the PTR measurements of Cu(AlIn)S2. The representative scheme for the sample placement and measurement arrangement of PTR is demonstrated in Fig. 1. The experiments were done on the {112} face. The angular-dependent polarized measurements were carried out with the linearly polarized light setting at E || <111¯> (θ = 0°) or E ⊥ <111¯> (θ = 90°) polarized orientation. For thermal perturbation of the samples, a quartz plate acted as the heat sink. The quartz plate was coated with a winding path of golden tracks as the heating element. The shape of the golden path was formed by a copper mask. The detailed experimental procedure of TR was described elsewhere [6]. The measurements were done in the temperature range between 30 and 320 K with a temperature stability of about 0.5 K or better. A RMC model 22 closed-cycle cryogenic refrigerator equipped with a model 4075 digital thermometer controller facilitated the temperature dependent measurement.

3. Results and discussion

Figure 2 shows the PTR spectra of E || <111¯> (θ = 0°) and E ⊥ <111¯> (θ = 90°) polarizations for Cu(AlIn)S2 at (a) 300 K, and (b) 30 K, respectively. The dashed lines are the experimental data and open-circle lines are the least-square fits to a Lorentzian line-shape function appropriate for the interband transitions expressed as [8,9]:

ΔRR=Re[i=12Aiexejϕiex(E-Eiex+jΓiex)2] (1),
where Aiex and ϕiex are the amplitude and phase of the lineshape, and Eiex and Γiex are the energy and broadening parameter of the interband transition. As shown in Fig. 2, two transition features of EA and EB combine together in the unpolarized spectra of Cu(AlIn)S2 at 30 and 300 K. The polarization dependence of band-edge transitions of Cu(AlIn)S2 clearly indicates that the EA feature is merely present in the E || <111¯> polarization while the EB feature appears prominently only in the E ⊥ <111¯> polarized spectra. The unpolarized spectrum can be regarded as the random superposition of the PTR spectra with E || <111¯> and E ⊥ <111¯> polarizations. This situation can be evident from the similar spectral line shape of A + B (i.e. linear combination of two polarized spectra) and unpolarized TR spectra in Fig. 2. Transition energies of the EA and EB features in Fig. 2 can be analyzed by fitting the PTR spectra to Eq. (1) that obtained transition energies are indicated with arrows. The values of EA and EB at 300 K (30 K) are respectively 2.192 ± 0.008 eV (2.222 ± 0.005 eV) and 2.267 ± 0.008 eV (2.292 ± 0.005 eV). This result also determines an uniaxial crystal-field splitting energy (i.e. EB-EA) of Δ0 = 75 meV at 300 K and Δ0 = 70 meV at 30 K, respectively.

 

Fig. 2 Experimental PTR spectra of Cu(AlIn)S2 at (a) 300 and (b) 30 K along E || <111¯> and E ⊥ <111¯> 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.

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The crystal structure of I-III-VI2 family is a chalcopyrite form. The chalcopyrite lattice crystallizes in a tetragonal structure with its unit cell approximately doubles the size of a zinc-blende unit cell (e.g. ZnS) along the c-axis. The sub-unit cells of chalcopyrite are essentially the zinc-blende type. The main difference in between a zinc-blende and an I-III-VI2 unit cell is the unequal bond lengths of RI-VI ≠ RIII-VI due to different atomic sizes of I and III cations contributed to the I-VI and III-VI bonds. Therefore copper incorporation to the valence band (EV) is the main distinction in chalcopyrite [CuInS2, CuAlS2, and Cu(AlIn)S2] with respect to the general zinc-blendes [10,11]. The main contribution of valence band for the chalcopyrite is coming from Cu 3d – S 3p hybridizations. One consequence of p-d hybridization is p-d repulsion. The p-d repulsion makes a substantial upward repulsion to lift up S p-like Γ15(p) states, which also reduces the band gap of the chalcopyrite compounds relative to their II-VI zinc-blende binary analogs. Because the raise of the S 3p states by p-d repulsion, the sulfur p electrons are hence entering into the conduction band [10]. The band-gap transition of Cu(AlIn)S2 is therefore determined by the pp transition of sulfur. The sulfur pp transition is an “intra-atomic” transition in the I-III-VI2 compounds. This type of band gap differs from that of the binary II-VI zinc-blendes, which belong to the “inter-atomic” transition. A compound with band gap of “intra-atomic” transition has a special character in contrast to that of the “inter-atomic” band gap. The specialty is very high absorption coefficient for the chalcopyrite to be utilized as the solar-cell material. The p-d hybridization in valence band also achieves the separation of S 3p Γ15 band into Γ4V(p) and Γ5V(p) located at the EV maximum by crystal field splitting. For CuInS2, the EV top is Γ5V (i.e. Γ5V > Γ4V) [10]. It is claimed to be contradict to the other chalcopyrites (i.e. CuGaS2, CuAlS2) with the EV maximum located at Γ4V [10]. The Γ4V and Γ5V bands at the EV top can be respectively identified by the polarization-dependent optical measurements using E || <111¯> and E ⊥ <111¯> polarizations [2]. The PTR spectra of Cu(AlIn)S2 shown in Fig. 2 clearly indicates that the transition energy of EA with E || <111¯> polarization is lower than that of EB with E ⊥ <111¯> polarization. It lends an evidence that the band-edge nature of EV for Cu(AlIn)S2 is similar to that of CuAlS2 with Γ4V > Γ5V located at the valence-band top [5]. Figure 3 depicts the band-edge structure of Cu(AlIn)S2 determined by PTR measurement at 300 K. The band gap is determined by S pp transition. The presence of EA (E0) and and EB (E0 + Δ0) is attributed to the valence-band splitting in Cu(AlIn)S2, which caused by the uniaxial crystal field. The crystal-field splitting Δ0 is 75 meV for Cu(AlIn)S2, which is dissimilar to Δ0 ≈154 meV for CuAlS2 [5] and |Δ0| ≈22 meV for CuInS2 [12,13] due to different amount of uniaxial stress (i.e. different crystal field) existed in the chalcopyrites with the stoichiometric variation of aluminum and indium composition from CuAlS2 to CuInS2. For the conduction band (EC) of Cu(AlIn)S2, the lowest band is Γ1C, and which is determined by the antibonding S 3p* [11]. The EC edge usually exists an excitonic level starting from the principal quantum number of n = 2 below Γ1C due to its p-state character. The E0 and E0 + Δ0 are assigned as the band-edge transitions of Γ4V→Γ1C and Γ5V→Γ1C, respectively.

 

Fig. 3 The representative scheme of band-edge structure of Cu(AlIn)S2 by PTR experiments at 300 K.

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Temperature dependent PTR spectra of Cu(AlIn)S2 in the temperature range of 30-320K are shown in Fig. 4 . The dashed lines are the PTR spectra with E || <111¯> polarization and the solid lines are the experimental data of E ⊥ <111¯> polarized spectra. The optical selection rule applied to the valence band of Γ4V and Γ5V clearly indicates that the EA transition is forbidden in the E ⊥ <111¯> polarization while the EB feature is not allowed in the E || <111¯> polarized spectra. The temperature-dependent PTR spectra of Cu(AlIn)S2 in Fig. 4 can be analyzed by the Lorentzian line-shape function using Eq. (1) (not showing fitted curves) and the obtained transition energies of EA and EB are indicated by arrows and are interconnected by dotted lines to show their temperature-variation trace from 30 to 320 K. As the temperature is raised, the EA and EB features demonstrate a slowly energy red-shift behavior with increasing the temperatures from 30 to 140 K. Whereas the EA and EB features reveal anomalous blue shift with the temperatures increased from 140 to 170 K. For T > 170 K, the temperature-energy variation of the band-edge transitions in Cu(AlIn)S2 recovers to normal behavior of general semiconductors. An anomalous S-shape temperature-energy shift for EA and EB is found with the increase of temperatures from 30 to 320 K (see Fig. 4), where a maximum turnover temperature of about 170 K is occurred. The occurrence of abnormal temperature-energy shift of Cu(AlIn)S2 may come from the native defects such as VCu and VS inside Cu(AlIn)S2 to alter the symmetry center of the chalcopyrite lattice points when the temperature is changed. This consequence reduces the contribution of copper d electrons in the valence band, which increases the band gap of Cu(AlIn)S2 near the turnover temperature. Although the temperature of Cu(AlIn)S2 increases from 140 to 170K the energies of the EA and EB features still present anomalous blue shift due to somewhat reduction of p-d repulsion in the temperature range to increase band gap. This situation had also been found in an as grown sulfur-deficient CuInS2 crystal (Eg ≈1.54 eV) with the turnover temperature of 120 K [12]. For the sulfur-annealed sample, the anomalous blue-shift effect is small [12]. The anomalous temperature-energy shift of the band gap of Cu(AlIn)S2 may cause by copper vacancy (VCu) and sulfur vacancy (VS) inside the crystal to reduce the d electrons’ contribution in the valence band (i.e. reduce the p-d repulsion to enlarge gap). The VS may come from sulfur deficiency of the crystal while VCu is caused by the deficiency of copper similar to the native copper vacancies that frequently detected in CuAlS2 [14]. For the CuAlS2, the maximum turnover temperature had been evaluated to be about 210 K [5], which is higher than those of Cu(AlIn)S2 and CuInS2.

 

Fig. 4 Temperature-dependent PTR spectra of Cu(AlIn)S2 between 30 and 320 K. The dashed lines are the experimental data with E || <111¯> polarization and solid lines are those of the E ⊥ <111¯> polarized spectra.

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Temperature dependence of transition energies of EA (E0) and EB (E0 + Δ0) features obtained by the PTR measurements of 30-320 K are depicted in Fig. 5 . The solid lines (above 170 K) are fitted to a Bose-Einstein expression Ei(T) = EiB-aiB⋅{1 + 2/[exp(θiB/T)-1]}, where i is the respective transition feature, aiB represents the strength of the electron (exciton)-phonon interaction and ΘiB corresponds to the average phonon temperature. The fitted values of EiB, aiB and ΘiB of Cu(AlIn)S2 are 2.334 ± 0.003 eV, 28 ± 5 meV, and 240 ± 40 K for E0 + Δ0 transition, and 2.267 ± 0.003 eV, 34 ± 5 meV, and 245 ± 40 K for E0 transition, respectively. These values are available for the estimate of transition energies into higher temperature range when the solar-cell material is operated under sunlight with T>300K. The temperature-energy shift of EA and EB features in Fig. 5 also reveals approximately parallel temperature dependence due to their similar valence-band origin that coming from the sulfur pp transition.

 

Fig. 5 Temperature dependences of transition energies of EA (E0) and EB (E0 + Δ0) in Cu(AlIn)S2.

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4. Conclusions

Polarization-dependent band-edge transitions of Cu(Al0.5In0.5)S2 are evaluated by temperature-dependent PTR measurements in the temperature range between 30 and 320 K. The optical selection rule applied to the valence band of the chalcopyrite is clearly demonstrated in the PTR spectra of Cu(AlIn)S2. The energy values of E0 and E0 + Δ0 at 300 K are respectively determined to be 2.192 ± 0.008 eV and 2.267 ± 0.008 eV. The crystal-field splitting energy between Γ4V and Γ5V is determined to be Δ0 = 75 meV at 300 K, which is lying in between those of CuInS2 and CuAlS2. The temperature-energy shift of the band-edge transitions in Cu(AlIn)S2 shows an anomalous S-shape variation with increasing the temperatures from 30 to 320K. It is due to the native defects such as VCu and VS in Cu(AlIn)S2 to alter the symmetry center of the chalcopyrite lattice points when the temperature is changed. The maximum turnover temperature for the abnormality of Cu(AlIn)S2 is about 170 K. It is lying in between the turnover temperatures of CuInS2 and CuAlS2 in the same chalcopyrite series of Cu(Al,In)S2. From the experimental analyses of PTR, it can be inferred that both the crystal-field splitting energy (Δ0) and maximum turnover temperature for the Cu(Al1-xInx)S2 (0≤x≤1) series may be simultaneously determined by the uniaxial crystal field existed in the chalcopyrite lattice.

Acknowledgments

The authors would like to acknowledge the financial support from the National Science Council of Taiwan under the grant No. NSC 98-2221-E-011-151-MY3.

References and links

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]  

References

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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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