Investigation Optical Properties of the Orthorhombic System CsSnBr 3-x I x : Application for Solar Cells and Optoelectronic Devices

In this work, to study the optical properties of orthorhombic perovskites of the CsSnBr 3-x I x system, spin-orbital and spin-polarized quantum chemical calculations were carried out in the framework of the density functional theory. The effects of electron exchange correlation were taken into account by the modified Becke-Jones exchange-correlation potential ( mBJ ). It has been established that with an increase in the iodine concentration, the absorption capacity and photoconductivity of these semiconductors increase. Other optical properties were also calculated, such as the real and imaginary parts of the dielectric function, refractive indices, energy loss spectrum, extinction coefficients, and reflection coefficients. The high absorption of these compounds in the infrared, visible and ultraviolet energy ranges allows the use of these perovskites in optical and optoelectronic devices operating in all spectral ranges by controlling and changing their content.


Introduction
The family of perovskite nanocrystals with the general formula ABX3 (where A is a positive ion, B is a metal ion, X is a halogen anion) is of considerable interest to the scientific community and is a promising class of materials due to many interesting physical and chemical properties such as high thermal and photoelectric power, superconductivity, ferroelectricity, spin-dependent transport, charge ordering, colossal magnetoresistance and other excellent structural, magnetic and optical properties [1][2][3]. These materials are often used as sensors, substrates, catalytic electrodes in fuel cells, photonic devices such as lasers, LEDs and especially solar cells due to their high absorption of visible light with a narrow bandgap, excellent charge carrier mobility, high dielectric constant, high conductivity, reduced reflectivity, reduced charge carrier recombination rate, and low excitation energy binding. They are promising candidates for optoelectronics [4].
A new application of perovskites has been found in a hybrid organo-inorganic material that has been used in thin film solar cells and transistors [5]. On the other hand, metal halide semiconductor materials are currently more efficient and beneficial for use in photovoltaic applications compared to silicon-based technologies. It is reported that the conversion efficiency of a perovskite solar cell already reaches 26% [6]. In addition, perovskite materials are available at low cost and therefore research on these materials has shown rapid progress in the scientific community as 405 well as their potential use in photovoltaic applications. Halide perovskites have generated considerable interest among other perovskite compounds, due to their excellent energy conversion efficiency in photovoltaic devices. Compounds based on the CsSnBr3-xIx system have interesting optical and electrical properties. Pure CsSnBr3 was found by Clark et al. to undergo a semimetal-semiconductor phase transition [7]. The structural and electronic properties of CsSnBr3 have been repeatedly studied experimentally and theoretically [8][9][10][11][12][13][14][15][16][17], but there are no data in the literature on the optical properties of orthorhombic CsSnBr3 and iodine-doped CsSnBr3 (CsSnBr3-xIx). In this paper, we report on the optical properties of orthorhombic perovskites based on CsSnBr3-xIx.

Materials and Methods
Ab initio quantum chemical calculations within the framework of the density functional theory [6] were implemented in the Wien2k package [18] taking into account spin-orbital and spin-polarized effects. DFT is a method based on quantum chemical calculations, originally proposed by Hohenberg [19], Kohn and Sham [20], which has the advantage that it does not depend on any experimental parameters. The modified Becke-Johnson potential (TB-mBJ) [21] was used to take into account the exchange-correlation energy (XC). The objects of study were orthorhombic structures (Pnma, 62) of nanocrystals of the CsSnBr3-xIx family. The Mufftin sphere radius (RMT) for Cs, Sn, and I was taken to be 2.5a0, and for Br, 2.07a0, where a0 is the Bohr radius. The valence wave functions inside the MT sphere were expanded to lmax = 10, and the charge density was expanded in a Fourier series up to Gmax (boron-1). For the wave function in the interstitial region, the plane wave cutoff value kmax = 7/RMT was chosen. For integration in kspace in the Brillouin zone (BZZ), a grid of 1000 k-points was used. The energy cutoff was chosen to be -6.0 Ry, which determines the separation of the valence and core states. The charge convergence was chosen to be 0.0001e during self-consistency cycles.

Calculation of Optical Properties
All kinds of solids are characterized by optical characteristics such as absorption, photoconductivity, reflection and transmission spectra, and can be quantified at the microscopic and macroscopic levels. At the microscopic or quantum mechanical level in bulk materials, the complex dielectric function is closely related to the band structure. The calculated optical parameters, such as absorption coefficient and refractive indices, indicate what type of response these materials will exhibit when hit by photons. The real part indicates the stored energy of a material that can be output at zero energy or zero frequency and is considered an intrinsic characteristic of any material. The expression for the complex imaginary permittivity ε2(ω) was obtained by summing over the conduction bands according to [22]: According to Equation 1, electrons pass from the occupied to the unoccupied states only within the first Brillouin zone, the wave vectors are fixed k. The real and imaginary parts of the analytical permittivity are related by the Kramers-Kronig relation as: Taking into account expression 1 and 2, it is possible to determine the photoconductivity spectrum (σ), energy loss spectrum (L), refractive index (n), reflection coefficient (R), absorption coefficient (α) and extinction coefficient (k) as a function of ω in form: Absorption coefficient reflects the measurement of light absorption ability of ceramics. When light propagates in the medium, the phenomenon of the intensity of light decreases with the propagation distance (penetration depth) is called light absorption. The absorption of light follows the Beer-Lambert law, and its equation is: where I is the outgoing Light Intensity; Io is the incidental light intensity; K is the molar absorption coefficient, which is dependent on the nature of the absorbent or the wavelength of the incident light and the absorption coefficient is a constant in the Beer-Lambert law; C is the absorbent concentration and L is the absorbent thickness.
Thus, the dielectric function serves as a bridge between the microphysical transition and the electronic structure of a solid, and on the other hand, the main dielectric function can also be used to evaluate other spectral properties of materials.

Results and Discussion
The optical properties of the material, according to Maxwell's equations, are based on the characteristic constants of the substance, such as permittivity, magnetic permeability, and electrical conductivity, which are functions of the frequency (ω) of the incident photon [23]. The incident photon interacts with the constituent atoms, and hence the dielectric function ε(ω) describes the optical response of the material. Figure 1 (a, b) shows the calculated real ε1(ω) and imaginary ε2(ω) parts of the dielectric functions depending on the photon energy in the range of 0-14 eV from the results of mBJ calculations. The real part indicates the stored energy of a material that can be output at zero energy or the zero frequency limit, and is considered an intrinsic characteristic of any material. Figure 1(a) shows that at sufficiently high incident photon energies these materials exhibit metallic behavior. The negative value of ε1 for these systems indicates their metallic nature. That is, it is possible to investigate and evaluate the metallicity of materials according to a real function. On fig.  1(a) shows that ε1(ω) increases when Br is replaced by I. This is indicated by the inverse relationship between the band gap and ε1(ω).
On the other hand, the imaginary part represents the absorptivity and the behavior of these materials shows the energy gain for photovoltaic devices. The imaginary part of the function ε2(ω) is related to the band structure and describes its behavior upon absorption [24]. An increase in the value of ε2 and its shift towards long-wavelength radiation in Figure 1(b) indicates that these materials can absorb the maximum amount of energy in a wide range of photon energies and, coincidentally, can retain this energy, and since this ability increases with an increase in the iodine content in the system. In this case, the optical band gap has an inverse relationship between them. Broad spectra of the dielectric function show high absorption in various regions of the energy spectrum. Similar features are found below in the spectra of extinction coefficients (k), absorption coefficients (α).

Photon Energy (eV) a)
When light propagates in a medium due to the processes of absorption and scattering, dissipation (weakening) of light occurs -a phenomenon known as light quenching. If scattering plays no role compared to absorption, then the extinction coefficient becomes the same as the absorption coefficient. The measure of light attenuation is the light extinction coefficient (k). On the other hand, the extinction coefficient of materials means how actively a substance absorbs light at a given wavelength. This optical property of the material is also related to the refractive index of the material. Figures 2 to 4 show the extinction, absorption, and photoconductivity spectra for the CsSnBr3, CsSnIBr2, CsSnI2Br, and CsSnI3 systems, respectively, as functions of the photon energy (in the IR range).

Figure 2. The calculated value of k(ω) for CsSnBr3, CsSnIBr2, CsSnI2Br and CsSnI3 depending on the photon energy (inset: extinction coefficient ranging from 0 to 14 eV)
A positive value of k indicates that there will be absorption, while it indicates that the light is passing directly through the material [39]. According to Figure 2, the graphs of the extinction coefficients have similar features (critical points) with the imaginary part. The absorption coefficient (α) determines how far in the material the propagation of light can drill through the material before it is absorbed and depends on both the incoming light and the intrinsic properties of the material [25,26]. According to Figure 3, with a decrease in the content of bromine and an increase in the concentration of iodine, the absorption capacity of the CsSnBr3-xIx system increases, and therefore CsSnI3 is characterized by maximum absorption in the IR region and will cover the maximum range of the solar spectrum, therefore it is suitable for devices such as solar cells, LEDs and lasers. The maximum extinction and absorption coefficients are in the same range of light, which is consistent with the dispersion theory [27][28][29].
The optical conductivity spectra σ(ω) shown in Figs. 4 show that the optical conductivity starts at about 0.52, 0.46 0.23 and 0.18 eV for CsSnBr3, CsSnIBr2, CsSnI2Br and CsSnI3, respectively. Outside these points, σ(ω) increases and reaches a maximum there, and then decreases again and, finally, dissipates with small variations. The calculated light reflectance spectra R(ω) for IR radiation are shown in Figure 5 for all investigated materials. According to the results, with an increase in the I content in the system, the reflection coefficient tends to decrease ( Figure 5), which is also confirmed by an increase in the absorption coefficients of the materials under study. According to the results of quantum chemical calculations, the maximum reflection occurs when ε1(ω) reaches a negative value, i.e. thus, the material exhibits dielectric properties (ε1(ω)>0); below zero, the material exhibits metallic properties (ε1(ω)<0). The maximum range of R(ω) increased with increasing metallicity, when ε1(ω) became negative.
The electron energy loss functions L(ω) and the refractive index n(ω) were calculated using the real and imaginary components of the permittivity from expressions (4 and 5). The electron energy loss function L(ω) is an important parameter describing the non-adaptable scattering in high accelerated electrons passing through the material, characterizing the plasma frequency (ωp) associated with it. The peaks of the energy loss function represent the combined character of the plasma resonance as well as the plasma frequency (ωp), above which the material acts as a dielectric and below which it exhibits a metallic nature. The calculated spectra of the energy loss function for the systems under study are shown in Figure 6. According to Figure 6, the energy loss function of CsSnI3 is the lowest among these perovskites. This is due to the higher electronegativity of I (2.5 on the Pauling scale) compared to Br (2.8 on the Pauling scale). Figure 7 shows the refractive indices ( ) as a function of the incident photon energy for the systems under study. All sharp peaks are due to exciton transitions at the band gap allowed in the infrared spectrum.  Figure 7 shows that the refractive index ( ) of the material increases with increasing iodine concentration in the CsSnBr3-xIx system. After ( ) reached its maximum value, it decreased below unity in some energy ranges. Moreover, considering = / , it can be concluded that a refractive index value less than one indicates that the phase velocity of the incident radiation is greater than , so the incident radiation can penetrate through the depth. Consequently, the material will become transparent to incoming radiation.
The results of calculations of the optical characteristics can be compared with the experimental data, but, as mentioned above, there are no data in the literature on the optical characteristics of the orthorhombic perovskites considered by us. Thus, the results obtained can contribute to the understanding of some features of their optical properties, which are important for the practical application of the studied systems and may be of interest to researchers searching for materials with desired optical characteristics [28][29][30].

Conclusion
The study of the optical properties of the CsSnBr3-xIx orthorhombic system is very important because of the possibility of its use in LEDs and solar cells. According to the results obtained in this work, it became known that doping with iodine leads to an improvement in the spectral properties of perovskites of the CsSnBr3-xIx system. It became known that with an increase in the iodine content, the coefficient of extinction, absorbed ability, and photoconductivity of these alloys increase, and in a timely manner, the reflectivity decreases. It was also found that with an increase in the iodine concentration as the transition from CsSnBr3 to CsSnI3 decreases, the electron loss energy decreases. The wide absorption range suggests that these compounds can be used for various optical and optoelectronic devices in all regions of the electromagnetic radiation spectrum.

Data Availability Statement
The data presented in this study are available in article.

Funding
The author received no financial support for the research, authorship, and/or publication of this article.

Declaration of Competing Interest
The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the author.