The electronic and optical properties of quaternary GaAs1-x-yN x Bi y alloy lattice-matched to GaAs: a first-principles study
© Ma et al.; licensee Springer. 2014
Received: 2 September 2014
Accepted: 11 October 2014
Published: 18 October 2014
First-principles calculations based on density functional theory have been performed for the quaternary GaAs1-x-yN x Bi y alloy lattice-matched to GaAs. Using the state-of-the-art computational method with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, electronic, and optical properties were obtained, including band structures, density of states (DOSs), dielectric function, absorption coefficient, refractive index, energy loss function, and reflectivity. It is found that the lattice constant of GaAs1-x-yN x Bi y alloy with y/x =1.718 can match to GaAs. With the incorporation of N and Bi into GaAs, the band gap of GaAs1-x-yN x Bi y becomes small and remains direct. The calculated optical properties indicate that GaAs1-x-yN x Bi y has higher optical efficiency as it has less energy loss than GaAs. In addition, it is also found that the electronic and optical properties of GaAs1-x-yN x Bi y alloy can be further controlled by tuning the N and Bi compositions in this alloy. These results suggest promising applications of GaAs1-x-yN x Bi y quaternary alloys in optoelectronic devices.
KeywordsGaAs1-x-yN x Bi y First-principles Hybrid functional Electronic structures Optical properties
In recent years, the synthesis of semiconductor alloys with specific structures, particularly electronic, and optical properties is widely demanded in the application of photoelectric devices, and a great deal of effort has been devoted to explore some nonconventional alloys, especially for III-V compound semiconductors. For example, InGaAsP, BInGaAs, and BGaAsSb have been investigated adequately from the aspects of structure, electronic, and optical properties for their potential applications in lasers, detectors, solar cells, etc.[1–5]. A GaAs alloy containing a few percents of N has significant effects on both lowering the lattice constant and narrowing the band gap. However, due to the large atomic size mismatch between As and N, it is difficult to grow high-quality GaAs1-xN x alloy on GaAs substrates. In order to overcome the problem, the coalloying approach is proposed. By substituting large-atom X, the new alloy XGaAsN can be made lattice-matched to GaAs. Most of the previous research works put emphasis on In y Ga1-yAs1-xN x grown on a GaAs substrate. However, the alloy quality deteriorates very fast when the N concentration increases, suggesting as very low photoluminescence efficiency and very short diffusion length. These impede the use of In x Ga1-xAs1-yN y in device applications[6, 7]. Considering that coalloying Bi with N in GaAs can significantly lower the N concentration, which is required to reduce the band gap of alloy XGaAsN, and the strain compensation between the small-sized N and the large-sized Bi atoms also can reduce formation energies of the alloy, GaAs1-x-yN x Bi y is proposed as a new potential III-V compound semiconductors in optoelectronic devices such as 1.06-μm solid-state lasers, high-efficiency multijunction solar cells, and so on. Therefore, it is essential to have more comprehensive investigations on the fundamental physical properties of GaAsNBi, such as structural, electronic, and optical properties (dielectric function, absorption coefficient, refractive index, energy loss function, and reflectivity).
It is well known that density functional theory (DFT) using the local density approximation (LDA) or the generalized gradient approximation (GGA) often severely underestimates the band gap, so it is much better to apply a hybrid functional to correct the band gap underestimation in the first-principles calculations[8–10]. In this paper, by first-principles calculations based on DFT as implemented in the Vienna ab initio simulation package (VASP) code with a modified Heyd-Scuseria-Ernzerhof (HSE) hybrid exchange-correlation functional, band structures and density of states were calculated. Besides, we also have calculated the optical parameters (absorption, refractive index, energy loss function, and reflectivity) of GaAs and GaAs1-x-yN x Bi y quaternary alloys. In addition, the influence of doping concentration on electronic and optical properties of the compound semiconductor has also been obtained.
All calculations were performed by using VASP with projector-augmented wave (PAW) for the interaction between electrons and ions and Perdew-Burke-Ernzerhof (PBE)-based HSE functional for the exchange-correlation functionals. The cutoff energy for the plane-wave expansion was set to 400 eV. The first Brillouin zone was sampled by a Г-centered 2 × 2 × 2 mesh for the supercells. A small Gaussian broadening σ =0.05 eV was applied so that the peaks of the defect cannot merge with the band continuum for the calculations of density of states (DOS). In the calculations of band structure and optical properties, k-point meshes were replaced by high symmetry point which was set manually according to the Brillouin zone path. All the results were obtained on the basis of the convergences. The supercell of GaAs with 64 atoms was adopted in all calculations, in which partial As atoms were replaced by the doped atoms of N or Bi. It has been validated that the dopant positions have insignificant influence on the lattice parameters by our calculated results. A crystal structure of cubic face-centered type with the space group symmetry F-43 M was adopted. And the whole system was electronic neutrality. In addition, all structures were fully optimized until the force on each atom is smaller than 0.01 eV/Å.
Results and discussion
Structures and electronic properties
Our calculated lattice parameters of GaAs, GaN, and GaBi are 5.653, 4.586, and 6.478, respectively, which are in good agreement with experimental values of 5.653, 4.50, and 6.234. According to our calculated results, the requirement for GaAs1-x-yN x Bi y lattice-matched to GaAs shows that ratio between the Bi and N composition y/x is 1.718, in good agreement with the published literature. As the method of virtual crystal approximation has some queries, the supercell approach with 64 atoms was adopted, in which partial As atoms were replaced by the doped atoms N or Bi atoms. However, it is too hard to reach the accurate ratio 1.718. From our calculated results, the lattice parameter of GaAs1-x-yN x Bi y is about 11.297 when x =1/32 and y =1/16, very close to the lattice parameter of GaAs supercell 11.306. Therefore, we assume that the quaternary alloy GaAs1-x-yN x Bi y (x =1/32 and y =1/16) can be made lattice-matched to GaAs approximately, and we will discuss its properties in details.
As can be seen from Figure 2, the real part of the dielectric function of GaAs is not a flat curve. It increases with the increase of photon energy in some regions, which means normal dispersion properties. Whereas in the other regions, it decreases as the photon energy increases and this is an abnormal dispersion characteristic. The same is true for the real part of GaAsN1/32Bi1/16. Considering the actual application situation, the properties of low photon energies 0 to 2 eV will be discussed in detail.
In the low photon energies 0 to 2 eV, for GaAs, the real part of dielectric function shows an increase with the increase of photon energy in 0 to 1.38 eV and 1.65 to 2 eV, acting as normal dispersion. While it decreases, the photon energy increases from 1.38 to 1.65 eV, acting as abnormal dispersion. Besides, the imaginary part of dielectric function has one major peak at 1.526 eV in the low photon energies 0 to 2 eV. For GaAsN1/32Bi1/16, the real component shows an increase with the increase of photon energy in 0 to 0.52, 0.89 to 1.4, and 1.79 to 2 eV, whereas it decreases as the photon energy increases in 0.52 to 0.89 and 1.4 to 1.79 eV. In addition, the imaginary part of dielectric function has two major peaks in the low photon energies 0 to 2 eV, consistent to the decreases of the real part. Furthermore, the red curves obviously shift towards the lower photon energy in Figure 2, meaning that both the real and imaginary parts of GaAs29/32 N1/32Bi1/16 have redshifted.
It can be observed that for GaAsN1/32Bi1/16, when the photon energy is close to 1 eV, the real and image part are both near the turning point in the rise and fall, which means that the wavelength corresponding to the energy about 1 eV is far away from the resonance absorption area, avoiding great resonance absorption at this wavelength.
The refractive index shows an appreciable value in low-energy region and a considerable reduction in high-energy region. Besides, the static refractive index value of GaAs is 3.56, which is in good agreement with the experimental data 3.30. The static refractive index value of GaAs1-x-yN x Bi y which is 5.46, lager than the value of GaAs, represents more rays that can be accessed into GaAs1-x-yN x Bi y than GaAs.
The properties of GaAs1-x-yN x Bi y with different Bi (or N) composition
In order to better understand the influence of N and Bi composition, the properties of GaAs1-x-yN x Bi y with different Bi compositions or different N compositions have been calculated respectively. According to the Hume-Rothery size rule, the total concentration of N and Bi which we calculated is limited within 25%.
With the incorporation of N and Bi into GaAs, the band gap of GaAs1-x-yN x Bi y lattice-matched to GaAs has a significant reduction. It is found that N doping mainly contributes to the conduction band and Bi doping mainly contributes to the valence band.
The optical properties of GaAs1-x-yN x Bi y lattice-matched to GaAs have also been calculated. It can be seen from the dielectric function that when the photon energy is close to 1 eV, the real and image part are both near the turning point in the rise and fall. That means the wavelength corresponding to 1 eV is far away from the resonance absorption area. In addition, from the calculated results of optical properties, more rays can be accessed into GaAs1-x-yN x Bi y than GaAs and GaAs1-x-yN x Bi y has less energy loss.
The effects of different Bi and N compositions on the electronic and optical properties have also been systematically studied, including the band structure, absorption coefficient, reflectivity, refractive index, and energy loss function. The calculated results indicate the significant change induced by the incorporation of Bi and N.
It is believed that our calculated results will be useful for the device applications of GaAs1-x-yN x Bi y quaternary alloys especially in optoelectronic devices such as solid-state lasers, high-efficiency multijunction solar cells, and so on.
This work is partially supported by the National Science Foundation of China (21173134, 61078031) and the open project of Infrared Imaging Materials and Devices Laboratory of Chinese Academy of Sciences (IIMDKFJJ-12-07).
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