Structural, Optical and Optoelectrical Properties of CuAlSnS₄ Thin Films

The results of the XRD study for the inspected CATS₄ films are provided in Fig. 1. These diagrams reveal the cubic CATS₄ crystal structure, which agrees with the JCPDS 47–1343. The identified peaks coincided with the (222), (224), (400), (422), and (731) crystallographic planes. Additionally, using these relationships, the structural indices of the CATS₄ layers have been evaluated: ^34–36

$$\begin{eqnarray}&&D=\frac{0.9\lambda }{\beta \cos \theta }\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\varepsilon }_{s}=\frac{\beta \cos (\theta )}{4}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{N}_{C}=\frac{t}{{D}^{3}}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\delta =\frac{1}{{D}^{2}}\end{eqnarray} \tag{ 4 }$$

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In these relations, θ indicates the Bragg diffraction angle, D stands for the crystallite size of the CATS₄ layers, and β for the experimental full width at half maximum (FWHM).

The CATS₄ structural characteristics are listed in Table I. It can be noted that when the layer thickness of these samples grew, the D magnitudes of the CATS₄ layers improved, and the N_C of the CATS₄ layers diminished. Figure 2 presents the plot of D, N_C , δ, ε_s , and t for the CATS₄ layers. Based on this graph, we concluded that expanding sheet thickness will boost the D while dropping the N_C , ε_s , and δ values.

Table I. Structural indices of the CATS₄ films.

t (nm)	${\boldsymbol{D}}$ $({\boldsymbol{nm}})$	${{\boldsymbol{N}}}_{{\boldsymbol{C}}}\times {{\bf{10}}}^{-{\bf{3}}}$ $({\boldsymbol{line}}/{{\boldsymbol{nm}}}^{{\bf{3}}})$	${\delta }\times {{\bf{10}}}^{-{\bf{3}}}$ $({{\boldsymbol{nm}}}^{-{\bf{2}}})$	${{\boldsymbol{\varepsilon }}}_{{\boldsymbol{s}}}\times {{\bf{10}}}^{-{\bf{3}}}$
263	28.41	11.47	1.24	1.22
317	34.31	7.84	0.84	1.01
392	41.17	5.61	0.58	0.84
459	48.42	4.04	0.42	0.71

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The EDX spectra of the CATS₄ layers appear in Figs. 3a and 3c. It is clear that Cu, Al, Sn, and S peaks were found in the CATS₄ layers, and their atomic ratios are approximately 1:1:1:4. Furthermore, the FESEM technique was used to analyze the surface of the CATS₄ layers, as appears in Figs. 3b and 3d. It can be noted that the surfaces of the CATS₄ samples are homogeneous and uniform.

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The optical transmittance, T, and reflectance, R, of the CATS₄ layers were used to estimate the values of the linear optical indices. Figures 4a and 4b illustrate the relationships between T and R of the fabricated CATS4 layers with λ. It is evident that the increment in film thickness improves the R values of the fabricated CATS₄ layers and reduces the T values of the fabricated CATS₄ layers.

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Based on the T and R data, the absorption coefficient of the CATS₄ layers is estimated through the subsequent Eq: ^37–39

$$\begin{eqnarray}&&\alpha =\frac{1}{t}\mathrm{ln}\left[\frac{{\left(1-R\right)}^{2}}{2T}+{\left(\frac{{\left(1-R\right)}^{4}}{{4T}^{2}}+{R}^{2}\right)}^{1/2}\right]\end{eqnarray} \tag{ 5 }$$

Figure 5a describes the of the α of the CATS₄ layers with the λ and film thickness. It is noticeable that the values of α of the CATS₄ layers are increased by expanding the film thickness. This performance agrees with other semiconductor materials. ⁴⁰

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Furthermore, the energy gap (E_g ) of the CATS₄ layers could be calculated through the Tauc's relations: ^41,42

$$\begin{eqnarray}&&\alpha h\nu \,=\,P{\left(h\nu \,-\,{E}_{g}\right)}^{h}\end{eqnarray} \tag{ 6 }$$

Here, h detects the kind of optical transition of the CATS₄ layers. It may be indirect at h = 2 or direct at h = 0.5. and P is a constant.

In this relation, h denotes the type of optical transition directly allowed (h = 1/2) or indirectly allowed (h = 2), and P is a constant. Figure 5b depicts the relationship between the photon energy and αhv of the CATS₄ layers. It can be estimating the E_g values of the CATS₄ layers from the intercepts with the x-axis of this plot. According to Table II, the direct E_g values of the CATS₄ layers decreased from 1.42 eV to 1.31 eV. This trend related to the emergence of localized states within the gap was the cause of this tendency. ^43,44

Table II. The linear optical indices and dispersion parameters of the CATS₄ samples.

t (nm)	${E}_{g}^{{dir}}({eV})$	${E}_{u}({eV})$	Ed (eV)	Eo (eV)	no	εs	f
263	1.42	0.12	15.39	2.87	2.52	6.36	44.16
317	1.39	0.13	16.57	2.81	2.62	6.89	46.57
392	1.35	0.15	17.28	2.73	2.71	7.32	47.19
459	1.31	0.17	19.14	2.64	2.87	8.25	50.52

Conversely, the Urbach energy (E_u ) of the CATS₄ layers is evaluated through the subsequent expressions: ^45,46

$$\begin{eqnarray}&&\alpha ={\alpha }_{{\rm{o}}}\exp \left({\rm{h}}{\rm{\upsilon }}/{{\rm{E}}}_{{\rm{u}}}\right)\,\end{eqnarray} \tag{ 7 }$$

Figure 5c illustrates the relationship between the photon energy and ln (α) of the CATS₄ layers. The Eu values of the CATS4 layers can be estimated from the slope of this plot. On the other hand, the E_u values of the fabricated CATS₄ layers can be observed in Table II. It seems that the CATS₄ sheets' E_u expanded along with their thickness. This trend was linked to a rise in localized states as thickness increased. ⁴⁷

Furthermore, the following relation could be used to compute the refractive index (n) of the fabricated CATS₄ layers: ^48,49

$$\begin{eqnarray}&&n=\frac{1+R}{1-R\,}+{\left(\frac{4R}{{\left(1-R\right)}^{2}}-{k}^{2}\right)}^{1/2}\end{eqnarray} \tag{ 8 }$$

Figure 6a describes the refractive index (n) alteration as a function of λ. It is noticeable that the increment in film thickness improves the n values of the fabricated CATS₄ layers. This performance may be related to enhanced R values by expanding the layer thickness. ^50–52

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Moreover, to deduce the extinction coefficient, k, of the fabricated CATS₄ layers, the following relationship was used: ^53,54

$$\begin{eqnarray}&&k=\frac{\alpha \lambda }{4\pi }\end{eqnarray} \tag{ 9 }$$

Figure 6b reveals the variation of the extinction coefficient, k, of the fabricated CATS₄ layers with λ. Expanding the layer thickness improved the estimated k values of the fabricated CATS4 layers. These results agree with other chemically deposited semiconductor materials. ^55,56

Also, the dispersion indices of the fabricated CATS₄ layers are estimated through the subsequent expression: ^57,58

$$\begin{eqnarray}&&{n}^{2}=1+\frac{{E}_{o}{E}_{d}}{{E}_{o}^{2}-{\left(h\upsilon \right)}^{2}}\end{eqnarray} \tag{ 10 }$$

Here, E_o demonstrates the oscillator energy, and E_d presents the dispersion energy of the fabricated CATS₄ layers.

The correlation between ${({n}^{2}-1)}^{-1}$ and ${(h\upsilon )}^{2}$ of the fabricated CATS₄ layers can be observed in Fig. 7. The slopes and intercepts of the curves' straight lines yield the magnitudes of E_o and E_d for the fabricated CATS₄ sheets (see Table II). Increasing the layer's thickness lowers the estimated magnitudes of E_o and enhances the estimated magnitudes of E_d of the fabricated CATS₄ sheets.

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Conversely, the high-frequency dielectric constant ε_s , oscillator strength f and static refractive index n_o of the fabricated CATS₄ sheets are assessed using the following formulas: ^59–61

$$\begin{eqnarray}&&f={E}_{o}{E}_{d}\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{n}_{o}=\sqrt{1+\frac{{E}_{d}}{{E}_{o}}}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&{\varepsilon }_{s}={{n}_{o}}^{2}\end{eqnarray} \tag{ 13 }$$

The CATS₄ layers' ε_s , n_o, and f magnitudes are given in Table II. It is evident that the improvement in ε_s , n_o, and f coincided with the thickness expansion.

The optoelectrical indices of the fabricated CATS₄ sheets are estimated through the subsequent relations: ^62,63

$$\begin{eqnarray}&&{\omega }_{p}=\sqrt{\frac{{e}^{2}\,{N}_{{opt}}}{{\varepsilon }_{0}\,{\varepsilon }_{{\rm{\infty }}}\,{m}^{* }}}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{n}^{2}={\varepsilon }_{L}-\left(\frac{{e}^{2}}{4{\pi }^{2}{c}^{2}{\varepsilon }_{0}}\right)\left(\frac{{N}_{{opt}}}{{m}^{* }}\right){\lambda }^{2}\end{eqnarray} \tag{ 15 }$$

In these relations, ${\omega }_{p}$ denotes the plasma frequency, c stands for the light speed, ${\varepsilon }_{L}$ refers to the lattice dielectric constant, ε₀, stands for the free space's electric permittivity, e stands for the electronic charge, and ${N}_{{opt}}/{m}^{* }$ stands for the charge carrier concentration.

In Fig. 8a, the relationship between ${n}^{2}$ and ${\lambda }^{2}$ of the fabricated CATS₄ layers is illustrated. We can estimate the ${\varepsilon }_{L}$ and ${N}_{{opt}}/{m}^{* }\,$ values of the CATS₄ layers from this plot. The ${N}_{{opt}}/{m}^{* }\,$ and ${\varepsilon }_{L}$ values of the fabricated CATS₄ layers can be observed in Table III. According to this table, the increment in film thickness produces an improvement in the ${N}_{{opt}}/{m}^{* }$ and ${\varepsilon }_{L}$ values of the fabricated CATS₄ layers due to a boost in charge carrier concentration. Moreover, the increment in film thickness produces a decrease in ${\omega }_{p}$ magnitudes.

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Table III. The optoelectrical indices of the CATS₄ layers.

t (nm)	${{\boldsymbol{N}}}_{{\boldsymbol{opt}}}/{{\boldsymbol{m}}}^{* }$ $\left(\times {{\bf{10}}}^{{\bf{54}}}\right)$ ${{\bf{K}}{{\bf{g}}}^{-{\bf{1}}}\,{\bf{m}}}^{-{\bf{3}}}$	${{\boldsymbol{\varepsilon }}}_{{\boldsymbol{L}}}$	${\boldsymbol{\tau }}$ $(\times {{\bf{10}}}^{-{\bf{16}}})$ ${\bf{\sec }}$	${{\boldsymbol{\mu }}}_{{\boldsymbol{opt}}}$ $(\times {{\bf{10}}}^{-{\bf{4}}})$ ${\bf{C}}.{\bf{\sec }}/{\bf{kg}}$	${{\boldsymbol{\omega }}}_{{\boldsymbol{p}}}$ $\left(\times {{\bf{10}}}^{{\bf{13}}}\right)$ Hz	${{\boldsymbol{\rho }}}_{{\boldsymbol{opt}}}$ $(\frac{{\bf{Kg}}.{{\bf{m}}}^{{\bf{3}}}}{{{\bf{C}}}^{{\bf{2}}}.{\bf{\sec }}})$
263	1.12	4.98	14.96	1.51	4.49	0.06
317	1.45	5.19	9.08	3.36	4.41	0.09
392	1.87	5.46	8.46	5.68	4.02	0.23
459	1.94	5.54	2.56	6.74	3.69	0.28

Likewise, the relaxation time τ of the fabricated CATS₄ layers is estimated through the subsequent expression: ^64,65

$$\begin{eqnarray}&&{\varepsilon }_{2}=\frac{1}{4{\pi }^{3}{\varepsilon }_{0}}\left(\frac{{e}^{2}}{{c}^{3}}\right)\left(\frac{{N}_{{opt}}}{{m}^{* }}\right)\left(\frac{1}{\tau }\right){\lambda }^{3}\end{eqnarray} \tag{ 16 }$$

Figure 8b describes the alteration in the ε₂ of the fabricated CATS₄ layers versus λ³ . The values of the relaxation time τ can be estimated from the slope of this plot. It is noticeable that the increment in film thickness produces a reduction in the values of the relaxation time τ.

On the other side, both the optical resistivity and mobility of the fabricated CATS₄ sheets are predicated on the relations: ^66,67

$$\begin{eqnarray}&&{\mu }_{{opt}}=\frac{e\tau }{{m}^{* }}\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&{\rho }_{{opt}}=\frac{1}{e}{\mu }_{{opt}}{N}_{{opt}}\end{eqnarray} \tag{ 18 }$$

Table III shows the estimated values of μ_opt and ρ_opt for the fabricated CATS₄ layers. It is noted that, by the increment in film thickness, the calculated μ_opt and ρ_opt improved. ⁶⁰

Additionally, the electrical conductivity (σ_e ) and the optical conductivity (σ_opt ) of the fabricated CATS₄ layers are predicated through the subsequent expressions: ⁶⁸

$$\begin{eqnarray}&&{\sigma }_{{opt}}=\frac{\alpha {nc}}{4\pi }\end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray}&&{\sigma }_{e}=\frac{2{\lambda }{\sigma }_{{opt}}}{{\rm{\alpha }}}\end{eqnarray} \tag{ 20 }$$

In Fig. 9a, the relationships between σ_opt of the fabricated CATS₄ layers with photon energy are illustrated. It is noted that the improvement in σ_opt coincided with enlarging the photon energy and the layer thickness. This trend related to improving the electronic charge excitation is brought about by expanding the hv. The relationship between σ_e of the fabricated CATS₄ layers and photon energy can be observed in Fig 9b. According to this plot, the increment in the photon energy and film thickness produces an improvement in the σ_e values.

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Likewise, to deduce the ${\varepsilon }_{1}\,{\rm{and}}\,{\varepsilon }_{2}$ of the fabricated CATS₄ layers, the following relationships were used: ^69–71

$$\begin{eqnarray}&&{\varepsilon }_{1}={n}^{2}-{k}^{2}\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&{\varepsilon }_{2}=2{nk}\end{eqnarray} \tag{ 22 }$$

Figures 10a and 10b describes the alteration in the ε₁ and ε₂ as a function of λ. It is evident that the increment in film thickness improves the ε₁ and ε₂ values of the fabricated CATS₄ layers. This performance may be related to enhancing the n and k values of the fabricated CATS₄ layers by the thickness growth.

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In this work, Miller's relationships could be exploited to evaluate the nonlinear optical indices of the fabricated CATS₄ layers as follows: ^72,73

$$\begin{eqnarray}&&{\chi }^{(1)}=\frac{{{\rm{n}}}^{2}-1}{4{\rm{\pi }}}\end{eqnarray} \tag{ 23 }$$

$$\begin{eqnarray}&&{\chi }^{\left(3\right)}={\rm{B}}{\left[\frac{{{\rm{n}}}^{2}-1}{4{\rm{\pi }}}\right]}^{4}\end{eqnarray} \tag{ 24 }$$

$$\begin{eqnarray}&&{{\rm{n}}}_{2}=\frac{12{\rm{\pi }}{\chi }^{\left(3\right)}}{{{\rm{n}}}_{0}}\,\end{eqnarray} \tag{ 25 }$$

Figures 11a–11c describes the ${\chi }^{(1)},$ ${\chi }^{\left(3\right)},$ and ${n}_{2}$ dependence on photon energy and layer thickness for the fabricated CATS₄ layers. The increase in film thickness produces an enhancement in the values of the ${\chi }^{(1)},$ ${\chi }^{\left(3\right)},$ and ${n}_{2}.$ This trend is attributed to the growth of the refractive index of the fabricated CATS₄ sheets. ^74,75

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The hot probe approach indicates that the CATS₄ films exhibit p-type conductivity. A sensitive multimeter and a soldering iron were the instruments employed in this process. The multimeter's positive terminal was connected to the heated side of the CATS₄ film, and its negative terminal was connected to its cold side. The voltage sign in the multimeter can be used to assess whether the film is more likely to be n-type or p-type. The film inclination will be an n-type semiconductor if a positive indication is seen. On the other hand, a p-type semiconductor will be the film inclination if a negative sign is detected. ⁷⁶ In our studies, all CATS₄ films produce a negative voltage when the heated probe is used. The hot probe validates the films' propensity to function as p-type semiconductors.