The Effect on the Electric Structure and Optical Properties of Ca2Ge Bulk with Sr-Doping

The electronic structure and the optical properties of Ca2Ge have been calculated by the first-principles pseudo potential method. The results of the electric structure show that Ca2Ge bulk is a direct semiconductor with the band gap of 0.306 eV, the conduction band is mainly composed of Ca 3d, the valence band is mainly composed of Ge 3p. With Sr-doping, Ca2Ge bulk is a direct semiconductor with the band gap of 0.350 eV, the conduction bands are mainly composed of Ca 3d and Sr 3d, the valence bands are mainly composed of Ge 3p and Sr 3d. The results of the optical properties show that the dielectric constant of Ca2Ge bulk is reduced from 21.52 to 13.94, the reflectivity is decreased, and the absorption is increased with Sr-doping. The optical properties are improved with Sr-doping, the results offer theoretical guide for the optical properties control of Ca2Ge.


Introduction
The alkaline-earth metal of Ca 2 Ge is a new environmental friendly semiconductor material, the existence of multiple germander phases in the Ca-Ge system leads to the simultaneous formation of Ca 2 Ge, Ca 5 Ge 3 , CaGe, Ca 3 Ge 4 , CaGe 2 , Ca 7 Ge 6 and so on during growth process.However, Ca 2 Ge is a direct semiconductor, has a simple orthorhombic structure and a cubic structure (The orthorhombic structure, which is a stable phase with an energy band gap of is 0.26 eV) [1] [2] [3] [4] [5].Ca 2 Ge has attracted much attention for its potential to create new classes of environmentally conscious elec-tronics [6].Recently, the study of Ca 2 Ge has a definite progress while is started relativity late, so the related literature reports and data available for reference.In 2003, the abinito method was used to study the geometric construction of Ca 2 Ge by D. B. Migas, the results showed that Ca 2 Ge was demonstrated had an orthorhombic and a cubic crystal system [3].In 2010, Yang used the first-principles method based on the density functional theory to study the electric structure of Ca 2 Ge, the results showed that Ca 2 Ge was a direct band gap semiconductor material with the band gap of 0.265 eV [4].In 2015, Jun used the first-principles method base on the density functional theory to study the photon correlation spectroscopy of Ca 2 Ge, the results showed that the photon frequency of Ca 2 Ge was lower than Ca 2 Si in the low energy region; the results provide reference for the photoelectric properties of Ca 2 Ge in the next phase study [6].The dielectric function is described the polarization response of the material under the condition of the electric field, it as a bridge establish the connection between microscopic photon excitation, electronic transmission associate and macroscopic visible optical properties, revealing the macroscopic dielectric properties of the micro mechanism.While, in order to improve the optical properties of Ca 2 Ge, using the first principles pseudo-potential method to study the electric structure of Ca 2 Ge with Sr-doping, discuss the influence of dielectric function of Ca 2 Ge with Sr-doping, and study the regulated mechanics of the optical properties of Ca 2 Ge.

Calculation Method
The simple orthogonal Ca 2 Ge bulk belongs to the space group of Pnma (No.62), the lattice constant are a = 7.804 Å, b = 4.896 Å, c = 9.204 Å.Each primitive cell contains 8 Ca atoms and 4 Ge atoms [7]. Figure 1 shows that the position of Ca atom has been the replace by one Sr atom in the internal coordinate of (0.522, 0.250, 0.676).All the possible structures are optimized by the BFGS algorithm (proposed by Broyden, Fletcher, Goldfarb and Shannon) [8] [9] [10] [11], which provides a fast way of finding the lowest energy structure and supports cell optimization in the CASTEP code [12] [13] [14].The optimization is performed until the forces on the atoms are less than 0.01 eV/Å, and all the stress components are less than 0.02 GPa, the tolerance in the self-consistent field (SCF) calculation is 1.0 × 10 −6 eV/atom.Ultra-soft pseudo-potentials (USPP) is expanded within a plane wave basis set with 330eV, the iteration convergence accuracy is 1.0 × 10 −6 eV.The energy of Ca 2 Ge have been calculated based on the optimization of structural system, the minimum energy made to be chosen stable structure, the electronic structure and polarization of the dielectric function were calculation.The ionic and electronic interaction was calculated, the Ca 3p 4s, Ge 3p 4s electron made to be chosen valence electron, the k-point sampling are 4 × 5 × 3 according to the Monkhorst-Pack method in the Brillouin Zone (BZ) [15].shows that the lattice constants a, b, c and the original cell volume V are slightly changed with Sr-doping.Comparing with the results of Ca 2 Ge bulk it shows that the lattice constant and volume of Ca 2 Ge were increased, slightly.The reason is that the atom radius of Sr is larger than Ge and the bond length of Sr-Ge is longer than the Ca-Ge (the atomic radius of Sr is 2.45 Å, the atomic radius of Ge is 1.52 Å).

The Energy Band Structure
The energy band structure of Ca 2 Ge bulk for derails see Figure 2. The Figure 2(a) shows that the Ca 2 Ge bulk is a direct semiconductor with the band gap of 0.306 eV at the Γ-point.The Figure 2(b) shows that the top of valence band and the bottom of the conduction are moved to the direction of the high energy with Sr-doped and is formed a direct semiconductor with the band gap of 0.350 eV at the Z-point.The change is that the configuration of extra-nuclear electron of Ca is 3p 6 4s 2 , the configuration of extra nuclear electron of Sr is 4p 6 5s 2 , and the lose electron of Sr is easy than Ca. the results show that Ca 2 Ge is a direct band gap semiconductor material with the band gap of 0.35 eV, with Sr-doping.

The Density of States
The density of states of Ca 2 Ge bulk for derails see Figure 3

The Complex Dielectric Function
Figure 4 is the dielectric function of Ca 2 Ge bulk. Figure 4(a) shows that the dielectric constant of Ca 2 Ge bulk is 21.5 and the dielectric function department is formed two dielectric peaks with the photoelectron energy increasing.The maximum dielectric peak is appeared at 1.3 eV, and the maximum dielectric peak is 42.5.The dielectric function imaginary part is forthcoming when the photoelectron energy is higher than 0.8 eV is formed four dielectric peaks with the photoelectron energy increasing, and it reflected the transition of the electron.dielectric peaks with the photoelectron energy increasing.The maximum dielectric peak is appeared at 2.1 eV, and the maximum dielectric peak is 38.5.The dielectric function imaginary part is forthcoming when the photoelectron energy is higher than 1.8eV is formed two dielectric peaks with the photoelectron energy increasing.The effect of the dielectric function of Ca 2 Ge bulk with Sr-doped is that the dielectric constant and the maximum dielectric peak are decreased, and it due to the configuration of extra-nuclear electron of Sr is active than Ca.The results show that the dielectric constant of Ca 2 Ge bulk is 21.5.The results show that the dielectric constant Ca 2 Ge bulk with Sr-doping is 13.9.

The Absorption Spectrum
Figure 5 is the dielectric function of Ca 2 Ge bulk.direction with Sr-doping.The results show that the absorption coefficient decreased.

The Reflectivity Spectrum
Figure 6 is the dielectric function of Ca 2 Ge bulk. Figure 6 shows that the reflectivity of Ca 2 Ge bulk is exceed 80% is appeared at the photoelectron energy range of 6.3 -8.2 eV.
The reflectivity of Ca 2 Ge bulk with Sr-doping is exceed 80% is appeared at the photoelectron energy range of 7.6 -8.7 eV.Comparing the reflectivity spectrum found that the reflectivity is moved to the high direction and is decreased the high reflection area with Sr-doping.The results show that the reflection spectrum decreased.

Conclusion
The electronic structure and optical properties of orthorhombic Ca 2 Ge bulk are calculated by first-principles pseudo potential method based on density functional theory.
The results show that the forbidden bandwidth is increased, and the optical properties are enhanced with Sr-doping.

Figure 1 .
Figure 1.The atomic structure of Ca 2 Ge.

Table 1 .
Geometric structure of Ca 2 Ge and doping after optimization.