Optical and Nanomechanical Properties of Ga₂Se₃ Single Crystals and Thin Films

Abstract

The optical and nanomechanical properties of Ga₂Se₃ single crystals and thin films were investigated using reflection, transmission, and nanoindentation measurements. The reflection spectrum recorded in the 525- to 1100-nm range was analyzed to get the band gap energy of the crystal structure, and derivative analysis of the spectrum resulted in band gap energy of 1.92 eV which was attributed to indirect transition. The band gap energy of thermally evaporated Ga₂Se₃ thin film was determined from the analysis of the transmittance spectrum. The absorption coefficient analysis presented the direct band gap energy as 2.60 eV. The refractive index was investigated in the transparent region using the Wemple–DiDomenico single-oscillator model. Nanoindentation measurements were carried out on the crystal and thin film structures of Ga₂Se₃. Nanohardness and elastic modulus of the Ga₂Se₃ single crystals and thin films were calculated following the Oliver–Pharr analysis method.

Introduction

The III₂–VI₃ (III = Ga, In, and Tl; VI = S, Se, and Te) type semiconducting family has drawn attention particularly because of its remarkable characteristics utilized in photovoltaic and electro-thermal device applications.1,2,^–3 Among the III₂–VI₃ type semiconductors, Ga₂Se₃ may be considered as one of the most attractive compounds due to its suitable electrical and optical characteristics for optoelectronic applications.4,5,6,^–7 Ga₂Se₃ provides an opportunity to form heterostructures with Al₂Se₃, and these heterostructures contribute to the design of optoelectronic devices based upon AlAs, GaAs, and Al_xGa_1−xAs compounds.8 Moreover, Ga₂Se₃ thin films may be inserted at the interface of ZnX (X = Se, Te) to lower the valence band discontinuity in p-ZnTe/p-ZnSe multilayer structures.9,10 The semiconducting Ga₂Se₃ compound has a defect zinc blende structure and has been characterized previously by inductively coupled plasma spectroscopy,11 transmission,12 absorption,11 first principles density functional theory,13 Raman, and infrared reflection14 methods. Analysis of the absorption coefficient detected the presence of direct and indirect transitions with band gap energies of 2.65 eV and 2.06 eV, respectively.12 The photoelectric properties of Ga₂Se₃ single crystals grown by the Bridgman technique have been investigated and dependencies of DC and AC photoconductivity on light intensity, applied voltage, and ambient temperature have been reported.12 Moreover, the forbidden energy gap at room temperature was calculated as 1.87 eV. Ga₂Se₃ single crystals were studied by spectroscopic ellipsometry measurements.15 Analysis of the absorption coefficient indicated that the studied material has a band gap energy of 2.02 eV. Four critical point energies at 2.70, 3.45, 3.83, and 4.45 eV were revealed from analysis of the dielectric function. In recent studies, heterostructures of the Ga₂Se₃ compound, like Yb/Ga₂Se₃/C,6 Ga₂Se₃/GaP,16 and Mo/Cu/In/Ga₂Se₃,17 were investigated to find information about their possible use in technological applications. Copper (Cu)-poor CIGS thin films were obtained from Cu-rich CIGS films by depositing a Ga₂Se₃ layer on the structure.18 The highest conversion efficiency of 10.6% was reported in this study by optimizing the thickness of the Ga₂Se₃ layer.

Nanoindentation is a powerful method for determining mechanical parameters like hardness and elastic modulus of various nanostructured materials19,20 and thin films.21,22,^–23 In the present work reflectivity and nanoindentation techniques were performed to find information about the optical and mechanical characteristics of the Ga₂Se₃ single crystal. The present paper reports for the first time on both transition characteristics (direct and indirect) of the Ga₂Se₃ compound and provides an opportunity to compare the optical characterization results associated with its single crystal and thin film structures. Moreover, the refractive index spectrum obtained from the reflectivity was plotted and analyzed in the transparent region using the Wemple–DiDomenico single-oscillator model. Ga₂Se₃ thin films were grown by the thermal evaporation technique and optical characterization was accomplished by performing transmission measurements. Nanohardness and elastic modulus of semiconducting Ga₂Se₃ single crystals and thin films were calculated following the Oliver–Pharr analysis method and obtained values were compared to understand the effect of the sample type on nanomechanical properties.

Experimental Details

Ga₂Se₃ semiconducting single crystals were grown by the Bridgman method using high-purity elements taken in stoichiometric proportions. The grown optically qualified ingots were red-brown in color. The surface dimensions of the crystal with a thickness of 4 mm were 14 × 11 mm². Ga₂Se₃ thin films were grown on soda-lime glass substrates using the thermal evaporation technique in which the powder form of single crystals was used for the evaporation source. The crystalline characteristics were revealed using XRD experiments carried out in the diffraction angle (2θ) range of 20–90° using a Rigaku miniflex diffractometer with CuKα radiation (λ = 0.154049 nm). The lattice constants of the sample were determined using the least-squares computer program DICVOL 04. The mechanical characteristics of the crystals and thin films were investigated by nanoindentation conducted with a CSM instruments nano/micro-combi tester. The load was applied with a Berkovich tip and a loading–unloading curve was obtained. The data processing software of the tester was used to analyze the indentation data according to the Oliver–Pharr method. The visualization of the indentation test on the crystal surface was performed using a Zeiss EVO 15 scanning electron microscope (SEM). The optical properties of the crystal were studied by reflection measurements using a Perkin-Elmer Lambda 45 UV/Vis spectrophotometer in the wavelength range of 525–1100 nm. Ga₂Se₃ thin films were optically investigated by performing transmission experiments via a Jenway 6400 model spectrophotometer with a resolution of 0.1 nm and accuracy of ± 1 nm. The thickness of the Ga₂Se₃ single crystal was not suitable for carrying out the transmission experiments, and experimental conditions did not allow us to make reflection measurements on Ga₂Se₃ thin films.

Results and Discussion

Figure 1 shows the XRD diffractogram of the studied samples and pattern of standard data of JCPDS Card No: 76-0975 recorded for Ga₂Se₃. As seen from the figure, the peak positions are consistent with each other. Relative intensities of the single crystal also indicate similar behavior for experimental and standard data. The XRD pattern of the Ga₂Se₃ thin film exhibits only one diffraction peak at around 28.60°. This peak is consistent with a (111) plane, as seen from the figure. The lattice constant of the cubic structure was determined from the analysis of the XRD pattern of the Ga₂Se₃ single crystal to be a = 0.540 nm which is very close to that (a = 0.5396 nm) of the standard data. Since the XRD pattern of the thin film presents one peak which is insufficient for analysis, this pattern was not taken into consideration to determine its lattice parameter(s). The reason there are fewer peaks in the XRD pattern of thin films compared to that of the powder form of the bulk crystal is associated with orientations of both samples. Since the powders can be oriented in various positions throughout the XRD measurements, the XRD patterns of the powder forms can exhibit more peaks. However, this is not feasible for thin film structures, and accordingly a few diffraction peaks generally appear in XRD patterns of thin films.

Fig. 1

XRD diffractogram of thin film, single crystal, and standard data of Ga₂Se₃.

The band gap determinations of Ga₂Se₃ single crystals and thin films were accomplished by reflection and transmission measurements, respectively. The thickness of the grown single crystals was not sufficiently thin enough to carry out the transmission measurements. Moreover, the experimental facilities did not allow us to perform reflection measurements on the thin film structure. Due to these reasons, only the reflection spectrum of the Ga₂Se₃ crystal and the transmission spectrum of the Ga₂Se₃ thin film are presented in the following parts. The reflectance spectrum of the Ga₂Se₃ single crystal in the 525–1100 nm spectral range is presented in Fig. 2. As seen from the figure, strong absorption takes place below the 650-nm region in which reflectivity changes sharply. There are some analysis techniques that are used to get the band gap energy from the reflectance spectrum. One of these methods is derivative spectrophotometry, utilizing the first wavelength derivative of transmittance and/or reflectance spectra. The inset in Fig. 2 indicates the dR/dλ spectrum around the strong absorption region. According to the derivative spectrophotometry method, the peak maximum wavelength value corresponds to the band gap energy of the sample. The band gap energy of the Ga₂Se₃ single crystal was found to be 1.92 eV by using this method. In the literature, there are papers that calculate the gap energy of Ga₂Se₃ by various experimental and theoretical methods. The reported gap energies for bulk Ga₂Se₃ generally take values between 1.95 and 2.3 eV. Bletskan et al. found indirect and direct gap energies using photoconductivity measurements of 1.95 and 2.05 eV, respectively.24 Theoretical first-principles calculations resulted in a gap energy of ~ 1.99 eV at 0 K and the authors predicted the room temperature gap energy to be 0.1 eV less (~ 1.89 eV) using data from previously published papers.25 Taking into account the reported band gap energies, the revealed energy value of 1.92 eV is consistent with these values and associated with indirect transition characteristics.

Fig. 2

Room temperature reflection spectrum of Ga₂Se₃ single crystal. Inset indicates the first wavelength derivative of the reflection spectrum.

Figure 3 shows the transmission spectrum of Ga₂Se₃ thin film. The spectrum shows that there is strong absorption in the 400–480 nm spectral range. The band gap energy (E_g) of evaporated Ga₂Se₃ thin film can be determined utilizing the absorption coefficient (α) expressed by26

$$ \alpha = \frac{1}{d}{ \ln }\left( T \right) $$

(1)

where T and d symbolize the transmittance and thickness values, respectively. The thickness of the grown thin films was measured electro-mechanically as ~ 0.5 μm. The relation between E_g and α is given by the Tauc formula as26

$$ \left( {\alpha hv} \right) = A\left( {hv - E_{\text{g}} } \right)^{p} $$

(2)

where A is a coefficient and exponent p is equal to either 1/2 for direct transition or 2 for indirect transition characteristics. Figure 4a presents the (αhv)² vs hv plot and linear fitted line in the strong absorption region. The intersection of this fitted line corresponds to the band gap energy according to Eq. 2. The fitted line intersects the energy axis at 2.60 eV and since fitting was successfully performed for p = 1/2, this energy value was related to the direct band gap energy. The band gap characteristics of Ga₂Se₃ thin films deposited by the thermal evaporation method were previously investigated by transmission measurements.12 The analysis showed that grown thin films have a direct band gap energy of 2.65 eV. The revealed energy value in the present paper is in good agreement with this reported energy. Derivative spectroscopy analysis was also used for the transmission spectrum of the Ga₂Se₃ thin film. Figure 4b presents the first wavelength derivative transmission spectrum which exhibited a peak around 473 nm, corresponding to 2.62 eV. The energy values revealed from the absorption coefficient and derivative spectroscopy analysis methods are consistent with each other.

Fig. 3

Transmission spectrum of Ga₂Se₃ thin film.

Fig. 4

(a) (αhv)² versus hv plot and (b) first wavelength derivative of the transmission spectrum of Ga₂Se₃ thin film.

At this point, it is worthwhile discussing the results of applied techniques on Ga₂Se₃ single crystals and thin films. The Ga₂Se₃ single crystal is in the bulk form, having thickness such that αd ≫ 1 (d; thickness of the sample). In the thick samples, the radiated light is almost completely absorbed through direct transitions in a short distance due to a higher photon absorption rate in direct band gap materials. Therefore, it is almost impossible to get direct band gap energies for thick samples by performing transmission and/or reflection measurements. However, film structures are very thin (αd ≪ 1) and this presents an opportunity for radiated light to reach the other side of the samples without being completely absorbed. Moreover, since direct band gap compounds have higher absorption rates, direct transitions are more likely to occur throughout the propagation of the light through thin films. Therefore, indirect and direct transition characteristics were revealed in Ga₂Se₃ single crystal and thin films, respectively. The present paper reports for the first time the presence of both transition characteristics for the Ga₂Se₃ compound.

The refractive index (n) is expressed in terms of reflectivity (R) in the transparent region as26

$$ n = \frac{1 + \sqrt R }{1 - \sqrt R }. $$

(3)

Figure 5 indicates the wavelength dependency of the refractive index in the 550- to 1100-nm region. The refractive index and band gap energy typically have an inverse relation in semiconducting materials. The photon energy dependency of the refractive index was also investigated using the Wemple and DiDomenico single-effective-oscillator model which relates n to hv in the below band gap region (hv < E_g) by27

$$ n^{2} = 1 + \frac{{E_{so} E_{d} }}{{E_{so}^{2} - \left( {h\upsilon } \right)^{2} }} $$

(4)

where E_so and E_d represent the single oscillator and dispersive energies, respectively. The values of E_d and E_so were obtained from the intercept on the vertical axis and slope of the linearly fitted line (inset of Fig. 5) as 25.1 and 4.2 eV, respectively. The zero-frequency refractive index ($n_{0}$) and dielectric constant ($\varepsilon_{0}$) were also calculated as n₀ = 2.7 and $\varepsilon_{0} = n_{0}^{2} = 7.2$.

Fig. 5

Wavelength dependent refractive index plot of Ga₂Se₃ single crystal. Inset shows the plot of (n²−1)⁻¹ versus (hv)². The solid line indicates the linear fit according to Eq. 4.

Two mechanical parameters, hardness and elastic modulus, are important for device applications of the materials. The mechanical properties of the Ga₂Se₃ semiconducting compounds were determined using nanoindentation measurements. Figure 6 and its inset indicate the typical nanoindentation load–displacement curves for the crystal and thin film structures, respectively. The indentation plot presents two different profiles; loading (plastic) and unloading (elastic).

Fig. 6

Load versus indenter displacement for indentation measurements carried out on Ga₂Se₃ single crystal and (inset) the same plot for Ga₂Se₃ thin film.

SEM images of the sample surface were recorded for the measured area in the nanoindentation experiments. Figure 7a and b indicate the surface of the crystal before and after nanoindentation measurements. Moreover, Fig. 7c shows the atomic force microscopy (AFM) image of the indented surface as an illustration. As seen, pile-ups and cracking around the indented area were not observed when the nanoindentation load of up to a maximum of ~ 40.1 mN was applied to the single crystal. The total penetration depth into the Ga₂Se₃ crystal throughout the measurements was around 800 nm.

Fig. 7

SEM images of the indented surface (a) before and (b) after indentation measurements for Ga₂Se₃ single crystal. (c) AFM image of the indented surface.

The output data of force (P)—penetration depth (h) plot was analyzed to get hardness (H) and Young’s modulus (E) of the crystal (see Fig. 6). Hardness, which is a measure of resistance of a material to deformation, penetration, and indentation is formulated as28

$$ H = \frac{{P_{\hbox{max} } }}{A} $$

(5)

where P_max is the indenter maximum load and A is the projected contact area. The projected area for a perfect Berkovich indenter as a function of true contact depth (h_c) is given as A = 24.56 h ²_c . Stiffness and h_c values are determined by linearly fitting the initial portion of the unloading curve. The slope (dP/dh) of this region and intersection point of the fitted line on the depth axis give the stiffness and true contact depth, respectively. The Oliver–Pharr analysis used to obtain the reduced elastic modulus (E_r) and elastic modulus (E) of the studied sample used the following expressions29

$$ S = 2\beta E_{\text{r}} \sqrt {\frac{A}{\pi }} $$

(6)

$$ \frac{1}{{E_{\text{r}} }} = \frac{{1 - v_{\text{f}}^{2} }}{E} + \frac{{1 - v_{\text{i}}^{2} }}{{E_{\text{i}} }} $$

(7)

where constant β depends on the indenter geometry (β = 1.034 for Berkovich indenter30), ν_i and ν_f are Poisson’s ratios for crystal and indenter, respectively, E_i is the elastic modulus of the indenter and S is the stiffness. Diamond tip indenter parameters are given as ν_i = 0.07 and E_i = 1141 GPa. The Poisson’s ratio of the crystal was taken as ν_i = 0.3 for analysis. Hardness and elastic modulus were calculated as 4.0 GPa and 60.5 GPa, respectively, for the Ga₂Se₃ crystal and 4.2 GPa and 81.3 GPa for the thin film following the Oliver–Pharr analysis method. As seen from the values, both were lower for the single crystal structure. However, the difference between the hardness values was slight while there was a remarkable difference between elastic modulus values. This point needs further theoretical investigation on the mechanical characteristics of the compound. The similar behavior between hardness and elastic modulus of single crystals and thin films has been observed previously.30,31,^–32 Nanomechanical characterization of Bi₂Se₃ thin films showed that the thin film structure has larger elastic modulus and hardness values compared with the crystal structure. Moreover, when comparison of elastic moduli and hardness values of GaSe crystal and thin film were done, it was seen that the hardness values (2.0 GPa for crystal and 1.8 GPa for thin film) of both structures were nearly equal while the elastic modulus of GaSe thin film (65.8 GPa) was much larger than that (33.0 GPa) of single crystal.31,32 The comparison of the revealed values with those of GaSe is also important because the constituent elements of GaSe and Ga₂Se₃ are the same. When the values were compared, a remarkable variation was observed for elastic moduli and hardness values which were higher for Ga₂Se₃ crystal.

Conclusion

Optical and nanomechanical properties of Ga₂Se₃ crystals and thin films were investigated by room temperature reflection, transmission, and nanoindentation experiments. The lattice constant of the cubic structure of the single crystal sample was determined from the analysis of the XRD pattern as a = 0.540 nm. The derivative spectrophotometry analysis of the reflection spectrum of the Ga₂Se₃ crystal resulted in a band gap energy of 1.92 eV, which is consistent with indirect band gap energy values reported in the literature. The analysis of the transmission spectrum of thermally evaporated Ga₂Se₃ thin film indicated that grown thin film has a direct band gap energy of 2.60 eV. The refractive index spectrum was plotted using the reflectivity spectrum and analyzed in the transparent region by the Wemple–DiDomenico single-oscillator model. The single oscillator and dispersive energies were found from the analysis to be 25.1 eV and 4.2 eV, respectively. Nanoindentation experimental data for Ga₂Se₃ single crystal and thin film structures were analyzed by the Oliver–Pharr method. Nanohardness and elastic modulus of the single crystal were calculated to be 4.0 GPa and 60.5 GPa, respectively, while those of the thin film were determined as 4.2 GPa and 81.3 GPa.