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First-principles calculations of electronic and optical properties in the bulk and on the (001) surface of CsPbCl3

We perform density functional theory using first-principles calculations in order to investigate the band structure, density of states, the real and imaginary part of dielectric function, refractive index and optical absorption of CsPbCl3 in the bulk and (001) surface structure. Energy bands exhibits wide and direct bandgap. When CsPbCl3 is extended to (001) surface a decrease of band gap is observed with increasing thickness. The optical constants observed exhibits optimal properties in the ultraviolet and visible range indicating its usefulness in photonic, optoelectronic, photovoltaic and optomagnetic devices.


Introduction
Perovskite which have general formula AMX3 where, A and M can be cations like Pb, Cs, Sn, Rb, organic material viz. CH3NH3, CH3CH2NH2 and X be a halide, possess unique properties like strong light absorption, high charge carrier mobility, long carrier diffusion lengths and small exciton binding energies and hence are promising materials for use in optoelectronic, photo detectors and photonic devices [1][2][3][4][5][6][7]. Moreover, they exhibit physical properties like colossal magneto-resistance, spin dependent transport properties, superconductivity, high thermoelectric power, ferroelectricity and charge ordering [8][9][10]. The practical applications of perovskites in optoelectronics often require such materials to be in the form of thin films, hence its surface study would assist in analyzing the electronic and optical properties.
In our present work using the first principles approach of the density functional theory (DFT) as in WIEN2k code, we have analyzed the structural, electronic and optical properties of bulk CsPbCl3 as well as its (001) surface texture.

Computational detail
To perform the full potential linearized augmented plane wave (FP-LAPW) method of the density functional theory, we have used WIEN2k software package by Peter and Blaha [11] for the calculation of structural, electronic and optical properties of CsPbCl3 bulk and its 001 surface. Our calculations was performed using exchange correlations treated by using Perdew, Burke, and Ernzerhof (PBE-sol) generalized gradient approximation (GGA) and was corrected using a more advanced technique called modified Becke Johnson (mBJ) potential [12]. Using PBE-sol exchange correlations, we optimized the lattice constants and atomic positions of unit cell of bulk CsPbCl3. The muffin tin sphere radius (RMT) value was chosen to be 2.5a.u for Cs, Pb and Cl. The plane-wave cut off value, energy threshold, Fourier expansion (Gmax), angular momentum, energy convergence and charge convergence was set to 7, −6.0 Ry, 12 (a.u.) -1 , 10, 0.0001 Ry and 0.0001e respectively. Also, CsPbCl3 (001) surface with different thickness were modelled with 2D slabs using Structeditor program implemented in WIEN2k code. Surface terminated by CsX was considered in order to avoid direct exposure of Pb at the surface alongwith spacing of 30Å vacuum. Studies were done by creating surface with different thickness which was taken to be the distance between 2 Pb atoms and their multiples. The thicknesses used for this purpose were 10.628 bohr, 21.256 bohr and are refered to as S1 and S2 in the rest of the paper.

Structural Properties
The volume of unit cell of CsPbCl3 is optimized to obtain structural properties like lattice constant a(Aº), ground state energy E0, bulk modulus B(GPa) and pressure derivative Bp . The optimization curve is given in figure 1 Figure 2 shows the band structure diagram. The electronic band gap is described by difference between the states at the conduction band minimum (CBM) and valence band maximum (VBM).   Figure 2. Band structure of (a) bulk CsPbCl3 (b) S1 CsPbCl3 (c) S2 CsPbCl3.

Optical Properties
Study of optical properties play a significant role in materials which are been used for optoelectronics, photonics, photovoltaic applications, etc. The optical parameters of the solids can be calculated by frequency dependent dielectric function ε(ω) obtained through Kramers-Kronig relation [15]. Figure 4(a) exhibits the real part of dielectric function ε1(ω) and can be seen that the zero frequency limit ε1(0) is highest for bulk CsPbCl3 and with increasing thickness, ε1(0) increases. It can be observed that ε1(ω) firstly increases and reaches a maximum value and then goes on decreasing. In bulk CsPbCl3 the wave is attenuated at higher energies i.e. 12.31 eV since ε1(ω) becomes negative [16]. Attenuation is not observed for surfaces. The imaginary part of the dielectric constant ( figure 4(b)) gives information about the absorption behaviour of free electrons and has a direct relation with the band gap of the material. Comparing the CsPbCl3 bulk and (001) surface, it is observed that the edge of ε2(ω) starts at 2.84 eV, 2.70 eV and 2.38 eV related to their band gap of 2.85 eV, 2.83 eV and 2.40 eV for bulk CsPbCl3, (001) S1 CsPbCl3 and (001) S2 CsPbCl3 respectively. Various peaks are observed for CsPbCl3 and are attributed to inter-band or intra band transitions. Identification of these peaks transition can be done analyzing density of states. For CsPbCl3, 4 peaks at 4.55 eV, 6.43 eV, 9.45 eV and 12.17 eV are observed. The peak at 4.55 is due to the transition of electron from Cl -p state of valence band (VB) to Pb-p state in conduction band (CB). The peak at 6.43 eV arises due to transition from Cl -p state to Cs-d and Pb-p state in CB. 9.45 eV peak originate because of transition from mixed Pb-s and Cl-p to the mixed Pb-p, Cs-d,p states of CB. The last peak at 12.17 eV is due to electronic transition from the semi-core states to the conduction band. Refractive index is an important optical constant which describes the absorption of light. The computed refractive index of CsPbCl3 bulk and surface slabs are presented in figure 4(c). The maximum refractive index nmax and static refractive index n(0) are tabulated in table 3. The spectrum of n(ω) is similar to ε1(ω).It first increases to reach a maximum and then decreases. It is clear from the figure that as the thickness of CsPbCl3 surface is increased the static refractive index also increases. The extinction coefficient presented in figure 4(d) for CsPbCl3 bulk and surface refers to the amount of attenuation caused when light propagates through the material. High value of k(ω) implies that absorption of light has taken place whereas a low value denotes light passing out from material without much loss. From the graph it is observed that value of k(ω) is low. The calculated optical parameter like absorption coefficient of CsPbCl3 bulk and surface compounds relates the response of these materials to the incoming photons. The plot is shown in figure 4(e) and for CsPbCl3 bulk along with their surface structures shows absorption in the range of 2-14 eV. The absorption coefficient for surface films has smaller value than their bulk compound. Optimal absorption is observed in the visible and ultraviolet range which makes these compounds suitable for photonic and optoelectronic devices like LED, solar cell etc. Also, many peaks are observed at different energies or wavelength showing the absorption of maximum light at different wavelengths. This property of the material can be used for wavelength filtering purpose in those regions. Table 3. Optical parameters such as dielectric function ε1(ω) and refractive index n (ω).