Sn-doped CdS: A New Intermediate Band Material for Solar Cells

In this paper, the electronic structure and optical properties of CdS doped by Sn with different concentrations were investigated by rst principles. The calculation results of electronic structure show that the doping of Sn can produce a deep impurity level band in the band structure of CdS. The calculation results of optical property show that Sn doping can increase the light absorption coecient and conductivity of CdS. The overall calculation results show that Sn doping can produce stable intermediate band structure and signicantly improve the optical property of CdS.


Introduction
At present, the rapid development of industrialization leads to the global energy shortage, and a large number of toxic and harmful chemical pollutants are discharged into the environment. Semiconductor optoelectronic material is one of the solar energy fuels to solve the global energy shortage and environmental pollution. On the one hand, semiconductor optoelectronic technology can utilize solar energy to produce electric energy [1][2][3][4][5], such as obtaining current through photovoltaic materials [6], producing uorescence and phosphorescence by photoluminescent materials [7,8]; on the other hand, photovoltaic technology can replace various toxic and harmful chemical fossil energy to purify the environment [9][10][11]. CdS is a direct band gap semiconductor [12][13][14][15], which has excellent photoelectric performance, such as high photoelectric conversion e ciency, low cost, long service life, rich lightemitting color and so on [16][17][18]. However, due to its large band gap (2.42 ev) [19], CdS can only absorb a little energy from the visible light and can not make full use of the visible light. Therefore, it is necessary to adjust the band structure of CdS to expand its visible light response range. Scholars have used a variety of means to expand its spectral range, such as composite [20], sensitization [21], nanosizing [22] and doping [23]. Among those methods, doping is the simplest method with the lowest cost. If a deep impurity level intermediate band structure (shown as Fig. 1) can produce in the band structure of CdS by doping, which is equivalent to inserting a transit station of photon absorption, the idea of doping will be changed. It can be equivalent to the parallel connection of three different band gap semiconductors as shown in Fig. 1, which can not only greatly increase the spectral absorption range of CdS, but also keep its band gap width unchanged, making the theoretical limit photoelectric conversion as high as 63% [24].

Calculation Model And Method
First principles based on density functional theory were adopted to study Sn doped CdS intermediate band material, and all the calculations were performed by MS (Material Studio). The local-density approximation (LDA) is used as the exchange correlation function. In order to obtain the accurate electronic structure, the U value provided through a series of tests, the LDA + U (U Cd =U S = 5.0 eV) method is used to overcome the shortcomings of LDA. The adopted supercell of CdS is 2×2×2 which contains 64 atoms, including 32 Cadmium atoms and 32 sulfur atoms. The energy cutoff was set for 400 eV, and the grid of point K was set for 4 × 4 × 4, respectively. The adopted supercell of CdS is cubic phase structure, which has a space group of F43 m (216) and a lattice constant of a = b = c = 0.583 nm. The valence electrons involved in the calculation are Cd: 4d 1 5s 2 , S: 3s 2 3p 4 , Sn: 5s 2 5p 2 , respectively.

Results And Discussion
In order to evaluate the accuracy of the method, the supercell optimization calculations were carried out.
Firstly, CdS primitive cell was optimized, and the lattice constant was a=b=c=0.5832 nm after optimization, which I s very consistent with the experimental data of a=b=c=0.5818 nm [28], and ensures the reliability of the method. Therefore, the same conditions are used to calculate the electron structure and optical property of Sn doped CdS.
In order to determine the stability of the Sn doped CdS system under different crystal growth conditions, the formation energies of the system with different doping positions are calculated as follows: Where E d and E p represent the total energy of Sn doped CdS system and pure CdS respectively; m Sn and m Cd represents the chemical potential of Sn, respectively; m is doped atom number. The chemical potential can be obtained from the ground state energy of bulk materials m Cd . The chemical potential of Cd and S in CdS structure is as follows: m CdS m Cd m S Where m Cd and m S denote the chemical potential of pure Cd and S atoms, respectively. The populations and energies of CdS doped by Sn are listed in table 1. It can be seen from table 1 that with the decrease of Sn doping concentration, the value of the formation energy ΔE from -2.86 eV decrease to -21.65 eV which means the lower the doping concentration is, the lower the formation energy is, and the higher the stability is. The population can be used to analyze the strength of covalent properties of chemical bonds. Table 1 shows that the maximum bond population of various doping concentrations have little change.
From the bond population data, it can be seen that with the increase of Sn doping ion concentration, the bond population decreases steadily, which also indicates that the stability of Sn doped CdS at low doping ratio. Fig. 2 shows the energy band structure diagrams of the supercells of CdS of doped by Sn. Fig.2a shows the calculated band gap of pure CdS. Fermi level is set as zero, and the top of the valence band is mainly composed of S-3p orbital while the bottom of the conduction band is composed of Cd-5s and Cd-4p orbitals, and it can be seen that pure CdS is a N typed semiconductor with a band gap (E g ) of 2.45 eV by LDA+U method, which is consistent with the experimental results and more accurate than that of LDA and GGA method [29,30]. Fig.2b-e are the energy band gap diagram of Sn doped CdS. It can be seen obviously that there is an impurity band in the Fermi level, while the valence band is below it and conduction band is above it, which makes the absorption of photons have three ways: one is from the valence band directly to the conduction band, the other is from the valence band to the intermediate band, Charge density difference diagrams of CdS doped by Sn are shown Fig.4, and it is an effective method to study the redistribution of electrons when materials are doped. The gain, loss and transfer of electrons around doped atoms can be clearly seen by charge density difference diagram, by which the bonding characteristics and interaction between atoms can be judged. In order to further study the mechanism of the effect of doped atoms on the electronic structure, the charge density difference diagram along the (001) crystal plane is shown in g. 4. Due to the complexity of the relative position of doped atoms in the crystal cell, we only discuss the charge density difference changes of CdS before and after doping (Sn doping concentration is 1/16) here. The value of the scale bar represents the value of the charge density difference contour, which re ects the bonding type, charge distribution and charge transfer between atoms. The blue area indicates the area where electrons are obtained, the red area indicates the area where electrons are lost. The darker the color, the more electrons are gained or lost. It can be seen from g. 4 that Sn doping provides more free electrons than Cd. The charge density difference around the Sn doped atoms increases obviously. The Sn atom is surrounded by yellow color, indicating that Sn atoms lose electrons and are donor atoms. The dark blue represents S, indicating that S atoms get electrons and are acceptor atoms. The color between Sn and Cd atoms is yellow and evenly distributed, the gain and loss of surface electrons are relatively large, thus there are more free electrons in Sn doping system than that of pure CdS. The number of electrons at the top of the valence band and the bottom of the conduction band decrease, resulting in the decrease of the photon absorption capacity. Therefore, from the results of photoabsorption coe cient and re ectivity, the optimum Sn doping ratio is 1/16.
Dielectric function is a common index to study the optical properties of materials. The macroscopic optical property of solids is generally expressed by complex dielectric functions: Where ω is the frequency, and ε 1 (ω) and ε 2 (ω) are the real and imaginary parts of the dielectric function, respectively. The imaginary part ε 2 (ω), which means the power loss, is directly related to optical absorption, and the real part ε 1 (ω) can be calculated by Kramers-Krönig relation calculation. Absorption coe cients and re ectivity can be given by ε 1 (ω) and ε 2 (ω): Where α(ω) and R(ω) are the absorption coe cient and re ectivity, respectively. Fig. 7 shows the curves of imaginary parts of the dielectric function of Sn doped ZnS with different doping concentration. As we can see, the imaginary part of the dielectric function in the UV-visible region increases in intensity after Sn doping. The imaginary part of the dielectric function is the largest when the Sn doping ratio to Zn is 1/16, and it has two wide peak in visible region, indicating that the power loss is biggest, the trend of which is the same as the conductivity in g.8. By comparison with g. 3 and g. 4, it can be seen that when the doping ratio is 1/16, the impurity level has an intermediate band structure, but the power loss and conductivity are both large, and the conductivity also increases sharply as shown in g. 8 Declarations Figure 1 model of intermediate band.