The Effect on the Electric Structure and Optical Properties of Ca_{2}Ge Bulk with Sr-Doping

Affiliation(s)

^{1}
College of Big Data and Information Engineering, Guizhou Minzu University, Guiyang, China.

^{2}
College of Big Data and Information Engineering, Guizhou University, Guiyang, China.

^{3}
Special and Key Laboratory of Guizhou Provincial Higher Education for the Analysis and Processing of Photoelectric Information, Guizhou Minzu University, Guiyang, China.

ABSTRACT

The electronic structure and the optical properties of Ca_{2}Ge have been calculated by the first-principles pseudo potential method. The results of the electric structure show that Ca_{2}Ge bulk is a direct semiconductor with the band gap of 0.306 eV, the conduction band is mainly composed of Ca 3d, the valence bands is mainly composed of Ge 3p. With Sr-doping, Ca_{2}Ge 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 Ca_{2}Ge 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 Ca_{2}Ge.

The electronic structure and the optical properties of Ca

1. 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 electronics [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-poten- tial 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.

2. 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] .

3. Calculation Results and Discussion

3.1. The Crystal Structure

The lattice constants and volume of Ca_{2}Ge bulk for derails see Table 1. The Table 1

Figure 1. The atomic structure of Ca_{2}Ge.

Table 1. Geometric structure of Ca_{2}Ge and doping after optimization.

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).

3.2. The Electronic Structure

3.2.1. 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.

3.2.2. The Density of States

The density of states of Ca_{2}Ge bulk for derails see Figure 3. The Figure 3(a) shows that the valence bands are mainly composed of Ge 4p, Ca 3d, the contribution of Ge 3s and Ca 3p are less. The conduction bands are mainly composed of Ca 3d, the contribution of Ge 3p 3s and Ca 3p are less. The Figure 3(b) shows that the valence bands are mainly composed of Ge 4p, Ca 3d, Sr 4d, the contribution of Ge 3s and Ca 3p are less. The conduction bands are mainly composed of Ca 3d, Sr 4d, and the contribution of Ge 3p 3s and Ca 3p are less. The effect of density of states of Ca_{2}Ge bulk with Sr-doped is that the Ge 3p active state is increased in the valence bands and the Ca 3d active state is in-

(a) (b)

Figure 2.The band structure of Ca_{2}Ge. (a) Ca_{2}Ge; (b) Sr-doped Ca_{2}Ge.

(a) (b)

Figure 3. Density of states. (a) Ca_{2}Ge; (b) Sr-doped Ca_{2}Ge.

creased in the conduction bands. The valance bands of Sr-doped Ca_{2}Ge are mainly composed of Ge 4p, Ca 3d and Sr 4d. The conduction bands are mainly composed of Ca 3d, Sr 4d.

3.3. The Optical Properties

3.3.1. 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. Figure 4(b) shows that the dielectric constant Ca_{2}Ge bulk with Sr-doping is 13.9, and the dielectric function department is formed two

(a)(b)

Figure 4. The dielectric function. (a) Ca_{2}Ge; (b) Sr-doped Ca_{2}Ge.

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.

3.3.2. The Absorption Spectrum

Figure 5 is the dielectric function of Ca_{2}Ge bulk. Figure 5 shows that the absorption edge of Ca_{2}Ge bulk is appeared at the photoelectron energy of 0.8 eV, and in the energy range of 1.8 - 7.3 eV the absorption spectrum more than 10,000. The absorption edge of Ca_{2}Ge bulk with Sr-doping is appeared at the photoelectron energy of 1.8 eV, and in the energy range of 2.3 - 10.2 eV the absorption spectrum more than 10,000. The absorption range of Ca_{2}Ge bulk is increased and the absorption edge is moved to high energy

Figure 5. The absorption of Ca_{2}Ge.

Figure 6. Reflectivity spectrum of Ca_{2}Ge.

direction with Sr-doping. The results show that the absorption coefficient decreased.

3.3.3. 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.

4. 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.

Acknowledgements

Project supported by the science and technology foundation of Guizhou Province, China (The contract LH of Guizhou No. [2017]7077).

Cite this paper

Wei, Y. , Yang, Y. , Cen, W. , Li, R. and Lv, L. (2016) The Effect on the Electric Structure and Optical Properties of Ca_{2}Ge Bulk with Sr-Doping. *Journal of Materials Science and Chemical Engineering*, **4**, 20-26. doi: 10.4236/msce.2016.411003.

Wei, Y. , Yang, Y. , Cen, W. , Li, R. and Lv, L. (2016) The Effect on the Electric Structure and Optical Properties of Ca

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[1] Manfrinetti, P., Fornasini, M.L. and Palenzona, A. (2000) Phase Diagram of the Ca-Si System. Intermetallics, 8, 331-334.

http://dx.doi.org/10.1016/s0966-9795(99)00112-0

[2] Palenzona, A., Manfrinetti, P. and Fornasini, M.L. (2002) The Phase Diagram of the Ca-Ge System. Journal of Alloys and Compounds, 345, 144–147.

http://dx.doi.org/10.1016/S0925-8388(02)00326-2

[3] Migas, D.B., Miglio, L., Shaposhnikov, V.L. and Borisenko, V.E. (2003) Comparative Study of Structral, Electronic and Optical Properties of Ca2Si, Ca2Ge, Ca2Sn, and Ca2Pb Structural. Physical Review B, 67, Article ID: 205203.

[4] Yang, Z.W., Shi, D.M., Wena, B., et al. (2010) First-Principle Studies of Ca-X (X = Si, Ge, Sn, Pb) Intermetallic Compounds. Journal of Solid State Chemistry, 183, 136-143.

http://dx.doi.org/10.1016/j.jssc.2009.11.007

[5] Bouderba, H., Djaballah, Y., Belgacem-Bouzida, A. and Beddiaf, R. (2011) First-Principles Investigations of Intermetallics in the Ca-Ge System. Physica B, 406, 2601-2609.

http://dx.doi.org/10.1016/j.physb.2011.03.075

[6] Tani, J. and Kido, H. (2015) Investigation of Structural, Elastic, and Lattice-Dynamical Properties of Ca2Si, Ca2Ge, and Ca2Sn Based on First-Principles Density Functional Theory. Computational Materials Science, 97, 36-41.

http://dx.doi.org/10.1016/j.commatsci.2014.10.002

[7] Eckerlin, P. and Wölfel, E. (1955) Die Kristallstruktur von Ca2Si und Ca2Ge. Zeitschrift Für Anorganische Und Allgemeine Chemie, 280, 321-331.

http://dx.doi.org/10.1002/zaac.19552800509

[8] Broyden, C.G. (1970) The Convergence of a Class of Algorithms the New Algorithm Doublerankminimization. Journal of the Institute of Mathematics and Its Applications, 6, 222-231.

[9] Fletcher, R. (1970) A New Approach to Variable Metric Algorithms. The Computer Journal, 13, 317-322.

http://dx.doi.org/10.1093/comjnl/13.3.317

[10] Goldfarb, D. (1970) A Family of Variable Metric Methods Derived by Variational Means. Mathematics of Computation, 24, 23-26.

http://dx.doi.org/10.1090/S0025-5718-1970-0258249-6

[11] Shanno, D.F. (1970) Conditioning of Quasinewton Methods for Function Minimization. Mathematics of Computation, 24, 647-656.

http://dx.doi.org/10.1090/S0025-5718-1970-0274029-X

[12] Segall, M.D., Lindan, P.J.D., Probert, M.J., et al. (2002) First-Principles Simulation: Ideas, Illustrations and the CASTEP Code. Journal of Physics, 14, 2717-2744.

http://dx.doi.org/10.1088/0953-8984/14/11/301

[13] Zhang, F.C., Yan, J.F. and Zhang, Z.Y. (2008) Acta Optica Sinica, 57, 3138-3146.

[14] Feng, J., Xiao, B., Chen, J.C., et al. (2009) Theoretical Study on the Stability and Electronic Property of Ag2SnO3. Solid State Sciences, 11, 259-264.

http://dx.doi.org/10.1016/j.solidstatesciences.2008.04.015

[15] Monkhorst, H.J. and Pack, J.D. (1976) Special Points for Brillouinzone Integrations. Physical Review B, 13, 5188.

http://dx.doi.org/10.1103/PhysRevB.13.5188