We present the optical function spectra of Cu2SnSe3 determined from 0.30 to 6.45 eV by spectroscopic ellipsometry (SE) at room temperature. We analyze the SE data using the Tauc-Lorentz model and obtain the direct-bandgap energy of 0.49 ± 0.02 eV, which is much smaller than the previously known value of 0.84 eV for the monoclinic-phase Cu2SnSe3. We also perform density-functional theory calculations to obtain the complex dielectric function data, and the results show good agreement with the experimental spectrum. Finally, we discuss the electronic origin of the main optical structures.

The diamond-like I2-IV-VI3 ternary compound1 Cu2SnSe3 has long been of much interest for its applications in acousto-optic2,3 and thermoelectric4,5 devices. Recently, study of Cu2SnSe3 was intensified owing to its connection to thin-film photovoltaic (PV) technologies: Cu2SnSe3 was considered a potential PV absorber material,6,7 but also identified8 as one of the harmful secondary phases present in the emerging PV material, Cu2ZnSnSe4.9,10 Despite the increasing interests in Cu2SnSe3, its optical properties have yet to be well characterized.

Fundamental bandgap energy E0 is a key parameter of a material that directly influences the functionality and performance of resultant devices. For example, to be a high-performance single-junction solar cell, the E0 of the absorber material is expected to lie between 1.0 and 1.5 eV.11 For Cu2SnSe3, however, a large discrepancy exists among the E0 values determined experimentally, which range from 0.84 to 2.10 eV.6,7,12,13 On the other hand, recent electronic structure calculations14,15 predicted more consistent, but much smaller, E0 values of 0.35–0.4 eV. Existence of the Cu2SnSe3 phase in Cu2ZnSnSe4 thin films has been speculated8 mainly based on the room-temperature photoluminescence (PL) signal appearing at around 0.82 eV that was assumed to be the E0 of Cu2SnSe3. Therefore, it is of great importance to acquire accurate optical information, including the E0, of Cu2SnSe3 to evaluate its potential for high-performance solar cells and to identify its contribution to the complicated PL spectrum of the Cu2ZnSnSe4 quaternary compound.

Here, we apply spectroscopic ellipsometry (SE)16 to characterize the room-temperature optical properties of Cu2SnSe3. The SE-determined dielectric function ε = ε1 + 2 spectrum of Cu2SnSe3 is modeled by using a series of Tauc-Lorentz (T-L) oscillators,17 and we obtain the direct-bandgap energy (E0) and absorption onset, represented by the Tauc gap (Eg). For comparison, the ε data are also obtained by density-functional theory (DFT) calculations, which are in a good agreement with the SE results.

A 2.6-μm-thick polycrystalline Cu2SnSe3 thin film was deposited on the roughened surface of a soda-lime glass substrate at 455 °C by co-evaporating elemental Cu, Sn, and Se source materials. Structural properties of the grown film were characterized by X-ray diffraction (XRD) and Raman scattering (RS) spectroscopy.18 Results from the XRD data analysis show that our Cu2SnSe3 polycrystalline film formed with the monoclinic phase in no single preferential growth orientation. Our RS spectrum is in a good agreement with the data reported in previous studies,6,7,19 and both XRD and RS results confirm that no secondary phase is present in the Cu2SnSe3 film used in our study.

A thin film grown on a roughened surface becomes “optically bulk” because the rough surface suppresses the reflection of probing light from the film/substrate interface. The main benefit here is that no thickness fringe appears in the raw SE data, and thus, the optical information around the bandgap can be assessed directly with no mathematical correction of data in the ideal case. Details of this pseudo-bulk approach are given in Ref. 20. Prior to the SE measurements, the surface of the Cu2SnSe3 film was chemo-mechanically polished21 using a colloidal silica suspension with 0.02-μm particles to reduce the root-mean-square (RMS) roughness of the surface from 64.1 down to 2.2 nm, which was determined by atomic force microscopy (AFM) of a 5 μm × 5 μm scan area.

SE data were recorded from 0.30 to 6.45 eV with the sample at room temperature using two different systems. A Fourier-transform infrared variable-angle SE (FTIR-VASE model, J. A. Woollam, Co., Inc.) was used in the spectral range of 0.30 to 0.98 eV, and a rotating compensator-type SE (M2000-DI model, J. A. Woollam, Co., Inc.) was employed to take data from 0.73 to 6.45 eV. The incident angle was 60°. The two SE data sets were numerically merged into a single spectrum for the analysis.

A three-phase model was used to analyze the SE data. The model consists of the ambient, a surface overlayer, and the bulk Cu2SnSe3, which is similar to modeling SE data of bulk crystals. Because the reflections from the film/substrate interface were effectively removed by using the controlled scattering from the substrate surface, the optical function data of soda-lime glass substrate and the thickness information of Cu2SnSe3 film are not required in our model. However, artifacts from a surface overlayer need to be taken into account, which is presumably composed of residual microscopic roughness and native oxides in various chemical forms. The optical response of the surface overlayer is often represented by the Bruggeman effective medium approximation (BEMA)22 using a 50–50 mix of the underlying material and void. The effects of microscopic roughness and other contributions, including native oxide, are practically indistinguishable in SE measurements for a thin surface overlayer in this spectral range.23 The best result was obtained with a 4.1-nm-thick BEMA layer, which is apparently greater than the AFM-determined RMS surface roughness. A small discrepancy observed in the roughness values estimated by AFM and SE measurements is not surprising because the surface roughness is calculated differently by the two methods. The BEMA roughness in SE measurements is an average of peak-to-valley variations of surface topography whereas RMS roughness in AFM measurements is a mean-square-deviation relative to the halfway line of average peak-to-valley variations.

The ε spectrum of Cu2SnSe3 was constructed by the sum of nine T-L oscillators and the fit-determined ε1(∞). The ε2 of each T-L oscillator is expressed by17 

ε2={ AE0C(EEg)2(E2E02)2+C2E21E(E>Eg)0(EEg),
(1)

where A is the oscillator amplitude, C is a broadening parameter, E0 is the resonance energy, and Eg is the Tauc gap (the onset of absorption). The Eg was set to be the same for all nine oscillators and constrained to be smaller than the E0 by definition. The mathematical expression for the corresponding ε1 can be calculated by the Kramers-Kronig (K-K) integration of ε2.17 The modeled ε spectrum for Cu2SnSe3 is presented in Fig. 1(a) with the nine constituent T-L oscillators. Experimental data and best-fit curves for the ε are compared in Fig. 1(b), and are in excellent agreement. The best-fit parameters (A, C, and E0) for all the oscillators are listed in Table I. We note that the E0 of the last oscillator (no. 9) resides outside the spectral range of our data and it serves mainly as the background correction for the spectrum. The root-mean-square error is 2.36 and is defined as24 

RMSError=13nmi=1n[ (NEiNGi)2+(CEiCGi)2+(SEiSGi)2 ]×1000,
(2)

where n is the number of wavelengths, m is the number of fit parameters, N is cos(2Ψ), C is sin(2Ψ)cos(Δ), and S is sin(2Ψ)sin(Δ). The subscripts E and G indicate the experimental data and model-generated data, respectively.

FIG. 1.

(a) Real (thin solid line) and imaginary (thick solid line) parts of the ε = ε1 + 2 spectrum for Cu2SnSe3 constructed by a sum of nine Tauc-Lorentz oscillators (dashed color lines). (b) Data (dashed color lines) and the best-fit model (solid gray lines) for the ⟨ε⟩ of Cu2SnSe3. The model is the constructed ε spectrum (shown in (a)) with a surface roughness of 4.1 nm.

FIG. 1.

(a) Real (thin solid line) and imaginary (thick solid line) parts of the ε = ε1 + 2 spectrum for Cu2SnSe3 constructed by a sum of nine Tauc-Lorentz oscillators (dashed color lines). (b) Data (dashed color lines) and the best-fit model (solid gray lines) for the ⟨ε⟩ of Cu2SnSe3. The model is the constructed ε spectrum (shown in (a)) with a surface roughness of 4.1 nm.

Close modal
TABLE I.

Best-fit parameters for the nine T-L oscillators used to model the ε spectrum of Cu2SnSe3. The Tauc gap Eg in Eq. (1) is set to be the same, 0.46 ± 0.02 eV, for all the T-L oscillators, and the ε1(∞) is fixed at 1.0. Root-mean-square error is 2.36.

Osc. no.A [eV]C [eV]E0 [eV]
2.84 ± 3.50 0.06 ± 0.02 0.49 ± 0.02 
0.94 ± 0.70 0.12 ± 0.03 0.58 ± 0.01 
9.41 ± 2.42 1.13 ± 0.12 0.75 ± 0.07 
1.55 ± 0.26 0.53 ± 0.04 1.57 ± 0.01 
3.21 ± 0.98 0.90 ± 0.14 2.10 ± 0.04 
1.84 ± 0.51 0.57 ± 0.05 2.44 ± 0.01 
7.16 ± 3.01 2.12 ± 0.23 4.20 ± 0.11 
16.06 ± 4.92 2.56 ± 0.29 5.21 ± 0.05 
33.09 ± 2.96 5.12 ± 0.42 8.23 ± 0.10 
Osc. no.A [eV]C [eV]E0 [eV]
2.84 ± 3.50 0.06 ± 0.02 0.49 ± 0.02 
0.94 ± 0.70 0.12 ± 0.03 0.58 ± 0.01 
9.41 ± 2.42 1.13 ± 0.12 0.75 ± 0.07 
1.55 ± 0.26 0.53 ± 0.04 1.57 ± 0.01 
3.21 ± 0.98 0.90 ± 0.14 2.10 ± 0.04 
1.84 ± 0.51 0.57 ± 0.05 2.44 ± 0.01 
7.16 ± 3.01 2.12 ± 0.23 4.20 ± 0.11 
16.06 ± 4.92 2.56 ± 0.29 5.21 ± 0.05 
33.09 ± 2.96 5.12 ± 0.42 8.23 ± 0.10 

Cu2SnSe3 is known to form with the monoclinic crystal structure.12 Therefore, anisotropic optical responses (εaεbεc) are anticipated. However, because of the polycrystalline nature of the sample used in this study,18 anisotropy is not observed in our SE data and the ε spectrum shown in Fig. 1 is a close approximation to the average of three ε components. Nevertheless, our pseudodielectric functionε⟩ = ⟨ε1⟩+ iε2⟩ spectrum25 represented as dashed lines in Fig. 1(b) unambiguously show the absorption onset at around 0.5 eV, which is much smaller than the values of 0.84–2.10 eV reported in previous experimental studies.6,7,12,13 In the previous optical study of Cu2SnSe3 single crystals,12 the E0 was determined by analyzing the optical absorption coefficient α spectrum. Even though the α decreases sharply below 0.85 eV, the α value found at the low-energy limit (0.70 eV) in the reported spectrum12 is still quite large (in the low 103 cm−1). We note that our ε2 spectrum also exhibits an optical structure at 0.79 eV that may have been mistakenly understood as the fundamental bandgap in the previous study,12 probably due to the limited spectral range (0.7–0.9 eV).

The fundamental bandgap (E0 of oscillator no. 1) at 0.49 ± 0.02 eV obtained in our study is in good agreement with the results from recent electronic structure calculations14,15 of Cu2SnSe3. First-principles total energy and band-structure calculations predicted14 the direct-bandgap energies of Cu2SnS3 and Cu2SnSe3 to be 0.8–0.9 eV and 0.4 eV, respectively. The bandgap of Cu2SnSe3 being smaller by ∼0.5 eV of that of Cu2SnS3 was explained14 by the following: (1) the higher Se 4p level than S 3p level that lifts up the valence-band maximum, and (2) the larger size of Se than S that lowers the antibonding anion s and Sn s conduction-band minimum state in Cu2SnSe3. A similar argument can also be adopted for understanding the observed difference in bandgap energy of ∼0.5 eV between Cu2ZnSnS4 and Cu2ZnSnSe4 quaternary compounds.20,26–28 The E0 of 0.49 eV for Cu2SnSe3 obtained in this study suggests that the E0 for Cu2SnS3 would be around 1.0 eV, which indeed is consistent with the theoretical prediction14 and the results from recent experimental studies29,30 of Cu2SnS3. The N and α spectra calculated from the modeled ε data are presented in Figs. 2(a) and 2(b), respectively.

FIG. 2.

(a) Complex refractive index N = n + ik and (b) absorption coefficient α (log scale) spectra for Cu2SnSe3, which are calculated from the modeled ε spectrum. The fundamental absorption edge is clearly seen in the α spectrum.

FIG. 2.

(a) Complex refractive index N = n + ik and (b) absorption coefficient α (log scale) spectra for Cu2SnSe3, which are calculated from the modeled ε spectrum. The fundamental absorption edge is clearly seen in the α spectrum.

Close modal

Overall, our ⟨ε⟩ spectrum shown in Fig. 1(b) is similar to that reported in a previous SE study of Cu2SnSe3 bulk crystals;31 but our data show more optical structures, in part, because of the extended spectral range. In the previous SE study,31 three interband-transition critical-point (CP) energies were obtained between 1.0 and 4.7 eV from the standard lineshape analysis of second-energy-derivatives of ⟨ε⟩,32,33 which are (1.32, 1.36), (2.34, 2.42), and (3.29, 3.26) eV for the two samples reported. The first two CP structures may correspond to oscillators no. 4 and no. 6 in our results (see Table I), whereas the third structure was not resolved in our study.

Even though a first-principles study14 predicted a fairly accurate E0 of Cu2SnSe3, the previous calculation with a small amount of k-point sampling in the Brillouin zone (BZ) appears to overestimate the strength of transition at around 1.5 eV. The previous SE study31 also shows strong disagreement with the theoretical prediction for the ε2 value of this particular optical structure. To better describe the above-bandgap optical properties, we performed electronic structure calculations using the hybrid nonlocal exchange-correlation functional proposed by Heyd, Scuseria, and Ernzerhof (HSE),34 as implemented in the VASP code.35 The effects of different cation arrangements and symmetries on the ε spectrum are investigated by considering two crystal phases of Cu2SnSe3, structure-I and -II, that are structurally distinguished mainly by their space-group symmetries, Cc and Imm2, respectively. These two phases have the same cation coordination around Se atoms: two-thirds of the Se atoms are coordinated with Cu3Sn, and one-third of them with Cu2Sn2. Detailed structural parameters for these two phases are listed in Ref. 14. The BZ integration was carried out using 12 × 12 × 6 Monkhorst-Pack k-point meshes for the 12-atom unit cell of the structure-I (Cc). The 14 × 14 × 10 k-point meshes were chosen for the 6-atom unit cell of the structure-II (Imm2). To obtain a smooth ε2 spectrum for the given k-point meshes, a broadening of the calculated ε2 was introduced through the K-K transformation of ε1 with a small complex shift of 0.1 eV, which results in the non-zero ε2 below the bandgap.

Our calculated ε spectra for two different phases are shown in Figs. 3(a) and 3(b), which are a mathematical average of the ε components along the three principal axes, (εa + εb + εc)/3, to properly describe the optical properties of the polycrystalline material. We found that the shape of the ε2 spectrum and the strength of optical transitions at the low-energy regime (E < 3 eV) depend sensitively on the number of k-points used in the BZ summation. Our calculations with finer k-point meshes clearly better describe the experimental data—especially the low-energy transitions—than does the previous work.14 In the ε2 spectrum of the structure-II, two noticeable peaks appear at 1.6 and 2.4 eV, which are associated with the transitions from the valence bands characterized by the Cu 3d + Se 4p states to the Sn 5s + Se 4p-derived conduction bands. In the high-energy region ranging from 4 to 6 eV, two different types of transitions occur: either (1) from the Cu 3d +Se 4p valence bands to the Sn 5p-derived conduction bands or (2) from the Cu 3d +Se 4p bands to the Cu 4s-derived conduction bands.

FIG. 3.

Calculated ε spectra for Cu2SnSe3 with (a) structure-I (Cc) and (b) structure-II (Imm2). The two structures have different cation arrangements and symmetries.

FIG. 3.

Calculated ε spectra for Cu2SnSe3 with (a) structure-I (Cc) and (b) structure-II (Imm2). The two structures have different cation arrangements and symmetries.

Close modal

In summary, we used SE to determine the optical function spectra from 0.30 to 6.45 eV and bandgap energy of Cu2SnSe3 at room temperature. Unlike many earlier optical studies, our data clearly show the absorption onset. By modeling the SE data with a series of Tauc-Lorentz oscillators, we obtained the bandgap energy of 0.49±0.02 eV and absorption onset energy of 0.46±0.01 eV. The bandgap energy of 0.49 eV is much smaller than the previously known value of 0.84 eV, but close to theoretical predictions. We also calculated the complex dielectric function data within the density-functional theory. The calculations with a large number of k-point summations in the Brillouin zone significantly improved the accuracy of the data, and described the experimental results much better than in previous theoretical work. The optical information obtained by our study suggests that (1) the energy bandgap of Cu2SnSe3 may be too small for a high-performance photovoltaic absorber material, and (2) the unidentified optical structure shown at around 0.8 eV in the photoluminescence spectrum of Cu2ZnSnSe4 is unlikely to have originated from the Cu2SnSe3 phase.

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory. N.J.P. acknowledges start-up funding support provided by the University of Toledo.

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Supplementary Material