The study of energetics, structural, the electronic and optical properties of Ga and As atoms substituted for doped germanane monolayers were studied by first-principles calculations based on density functional theory. Both of the two doping are thermodynamically stable. According to the band structure and partial density of the states, gallium is p-type doping. Impurity bands below the conduction band lead the absorption spectrum moves in the infrared direction. Arsenic doping has impurity level passing through the Fermi level and is n-type doping. The analy sis of optical properties confirms the value of bandgap and doping properties .
Since the successful extraction of graphene by British scientists Andre Geim and Andre Geim using mechanical stripping in 2004, it has quickly led to the research and exploration of two-dimensional materials due to its excellent properties. In order to further enhance the application value of two-dimensional materials, it is important to improve the properties of materials by doing with graphene [
The first principle calculation is implemented in CASTEP (Cambridge Serial Total Energy Package) code [
To assess the stabilities of nanostructures, we calculate the formation energy E F as follows:
E form ( X ) = E X − E germanium + μ Ge + μ H − μ Ga (1)
E form ( X ) = E X − E germanium + μ Ge − μ As (2)
The first two terms E X and E germanium are the total energies of Ga or As doped germanane and pristine germanium respectively. The μ Ge and μ H terms are the chemical potentials of the host Ge atom (obtained as the total energy per Ge atom from the unit cell of germanane monolayer) and H atom (obtained as the total energy per H atom from the hydrogen molecule), whereas the μ X term is the chemical potential of the Ga defect (obtained as the total energy per Ga atom from face centered cubic Ga structure) or As defect (obtained as the total energy per As atom from the corrugate hexagonal structure structure) respectively. The calculation results show that the formation energies of gallium and arsenic doping are −2.01 eV and −0.63 eV, respectively. This means that the two structures are thermodynamically stable.
The Ge-Ge bond length( d Ge-Ge ), the lattice parameter (a), and the buckled height ( Δ z , show in
After the doping of gallium, the structure and symmetry distort much. The length of the bond between the gallium atom and the neighboring germanane atom is 2.455Å, 2.455Å, 2.458Å respectively. The nearby Ge-Ge bond length also have changed in the range of −0.3Å to +0.3Å. Gallium defect also causes large changes in corrugate, buckled height Δ z Ge-Ge = 0. 73 0 Å change to Δ z Ga-Ge = 0.0 47 Å. The hydrogen atom corresponding to the germanium atom interacting with gallium shifts away from the gallium atom. On the other hand, the doping of arsenic does not affect the structure and symmetry of the original germanane due to the remaining of the corresponding hydrogen atoms. The arsenic defected germanane monolayer is Δ z Ge-As = 0.728 Å that is basically same as pristine germanane, and the original hexagonal structure is well maintained.
This section analyzes the mechanism of the change of the energy band width of pristine germanane and doping system. The band structure and distribution of the density are shown in
bottom of the conduction band is contributed by the Ge-4s and Ge-4p orbit, while the valence band of monolayer is derived from the contribution of H-s, Ge-4s and Ge-4p orbit, but the top of valence is mainly contribute by H-s and Ge-4p.
In order to further explore its electronic properties, we also made specific calculations and data analysis on the optical properties of germanane. The study of electronic structures helps to make materials practically used in optoelectronic devices. Optical properties can be analyzed from the peaks and the intersection of the coordinates of the dielectric function. The dynamical dielectric function of germanane at arbitrary wave vector q and frequency ω, ϵ(q, ω), is calculated in the self-consistent-field approximation. The corresponding optical constants of germanane and its doping structures can be analysis from the real and imaginary parts of the dielectric function. The absorption coefficient n, the complex refractive index and the reflectance R of pristine germanane can be obtained by the Equations (4)-(6), respectively [
ε 1 ( ω ) = 2 e 2 Ω ε 0 ∑ | 〈 ψ k c | u ⋅ r | ψ k v 〉 | δ ( E k c − E k ν − E ) (1)
ε 2 ( ω ) = 1 + 2 π P ∫ 0 ∞ ω ′ ε 2 ( ω ′ ) ω ′ 2 − ω 2 (2)
α ( ω ) = 2 [ ε 1 2 ( ω ) + ε 2 2 ( ω ) − ε 1 2 ( ω ) ] 1 / 2 (3)
n ( ω ) = 2 2 [ ε 1 2 ( ω ) + ε 2 2 ( ω ) + ε 1 2 ( ω ) ] 1 / 2 (4)
k ( ω ) = 2 2 [ ε 1 2 ( ω ) + ε 2 2 ( ω ) − ε 1 2 ( ω ) ] 1 / 2 (5)
R ( ω ) = | ε ( ω ) − 1 ε ( ω ) + 1 | 2 (6)
lines of black and grey in
Germanane monolayer was doped with gallium atom or arsenic atom. The Ga defect can be integrated within a germanane monolayer at a relative low formation energy, without major structural distortions and symmetry breaking. The As defect relaxes outward of the monolayer and breaks the symmetry. The density of states plots indicate that Ga doped germanane monolayer is p-type doping, whereas the As, which has a extra outermost electron, is n-type doping. The optical properties of Ga and As doping were also examined, the result demonstrates that As doping has static dielectric constants ε 1 ( ω ) close to12 which means a stronger polarization ability. The results of this study will be of great guiding significance for the practical application.
The authors declare no conflicts of interest regarding the publication of this paper.
Liu, L., Ji, Y.J., Liu, Y.F. and Liu, L.Q. (2019) First-Principle Studies on the Ga and As Doping of Germanane Monolayer. Journal of Applied Mathematics and Physics, 7, 46-54. https://doi.org/10.4236/jamp.2019.71005