Abstract
A first-principles study has been performed to investigate the structural and electronic properties of the system. The simulations are based upon the generalized gradient approximation (GGA) within the framework of density functional theory (DFT). Calculations are performed to different Bi concentrations. The lattice constant of increases with Bi concentration while the alloy remains in the zinc-blende structure. The band gap of clearly shrinks with the Bi concentration. The optical transition of Bi dopant in GaAs exhibits a red shift. Besides, other important optical constants, such as the dielectric function, reflectivity, refractive index, and loss function also change significantly.
1. Introduction
As an important III–V direct-band-gap semiconductor, GaAs has attracted a great deal of interest. It has been characterized with high electron mobility, small dielectric constant, high temperature resistance, and antiradiation and is now widely used in the ultrafast, ultrahigh frequency, low-power devices and circuits. Technically, the electronic structure and optical properties of GaAs can be changed by doping, which provides an effective way to tailor its electronic properties for practical electronic devices. Bismuth in group-V is the heaviest nonradioactive element, but its compounds of bismuthide have been the least studied. Thus, the electronic structure of bismuthide is not well understood yet. In addition, alloy will decrease the energy gap, extending the application to long-wave emission devices and photovoltaic industry with increasing of the Bi concentrations [1].
Recently, the alloy has already been fabricated successfully by MOVPE [2], MBE [3–5], and LPE [6, 7]. Theoretically, the Bi-doped GaAs has been focused on the influence of doping with Bi on electronic properties [8–10]. Mbarki and Rebey focused on the optical properties of alloys [9]. Reshak et al. mainly discussed the linear and nonlinear optical susceptibilities of alloys [11]. Tixier et al. place extra emphasis on the structural and electronic properties of zinc blend solid solutions [12]. Ciatto et al. addressed the issue of bismuth heteroantisite defects (BiGa) in /GaAs epilayers by coupling X-ray absorption spectroscopy at the bismuth edge with density functional theory calculations of the defect structure [13]. However, consistent conclusions have not been reached yet. In order to pursue a further guidance of the impact of various concentrations of Bi on the GaAs system, theoretical research is still essential.
In this paper, the electronic structure of GaAs and is investigated in different concentrations in order to solve the inconsistence of those theoretical investigations. The optical properties are presented in order to draw a general conclusion about variation of the electronic structure. The paper is organized as follows. In Section 2, the details of the theoretical model and the computational details are presented. The simulation results and discussions are given in Section 3. Finally, we make our conclusions in Section 4.
2. Theoretical Model and Computational Method
The plane wave projector augmented-wave (PAW) method was employed as implemented in the VASP [18] based on the density functional theory (DFT). The generalized gradient approximation (GGA) in the scheme of Perdew-Wang 91 (PW91) is used to treat the exchange-correlation function. The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional is also applied to describe the defect physics accurately in wide band-gap semiconductors. The valence configurations of Ga, As, and Bi are Ga(3d104s24p1), As(3d104s24p3), and Bi(4f145d106s26p3), respectively.
The primitive GaAs unit cell is the typical tetrahedron zinc-blende (ZB) structure. The lattice constants of the ZB structure are a = b = c = 5.653 Å. In our calculation, the 2 × 2 × 2 GaAs supercell consisting of 64 atoms is used with a changing composition. The supercell is kept at constant volume and the substitutional method has been taken into account. For x = 0.0625, only two As atoms are substituted by Bi, while for x = 0.25 eight As atoms are substituted. The cut-off energy has been assumed to be 480 eV, which was determined after a series of tests. The k-point set with parameters of 7 × 7 × 4 and 4 × 4 × 2 for pure GaAs and the alloy is used for the first Brillouin zone sampling mesh. Self-consistency is considered to be achieved when the charge density difference between succeeding iterations is less than 2 × 10−5 eV/atom. In addition, the scissor operation has been used to adjust the optical absorption spectra of GaAs and its alloys.
3. Results and Discussions
3.1. The Structure Optimization
In this section, the structural optimization is presented. The lattice constants of pure zinc-blende GaAs after relaxation are a = b = 5.7232 Å and c = 5.7229 Å, respectively. In Table 1, we summarize the calculated lattice constants of GaAs and alloys together with available theoretical and experimental data from the literature. The theoretical values were presented in the framework of different functions. It is noteworthy that our calculation shows a good agreement with theoretical and experimental results [14, 19–21].
When As atom is substituted by Bi, the lattice constants will change in the unchanged zinc-blende structure. The covalent radius of As and Bi is 1.2 Å and 1.46 Å, respectively. This difference in the covalent radius between As and Bi atom will result in an increase of the lattice constants of . Compared with experimental data, our results are slightly overestimated by around 1.48%, which can mostly be attributed to the application of the GGA method (typically overestimate the lattice constant by 2% [22]). It is noteworthy that the lattice constants of increase gradually with an increasing Bi concentration while the zinc-blende structure remains unchanged. The average Ga–Bi bond length is slightly longer than that of Ga–As in Bi-doped GaAs system.
3.2. Electronic Properties
In our calculation, the concentration of Bi-doped GaAs is ranging from 6.25% to 100%. It can be seen in Figure 1(a) that the direct band gap of intrinsic GaAs is about 0.674 eV at the highly symmetric Γ point, which is lower than the experiment data 1.45 eV [23]. This well-known underestimate can be attributed to the limitation of GGA [24]. To examine the accuracy of our calculation, the electronic structure is also calculated using the HSE hybrid functional. The direct band gap of intrinsic GaAs is 1.293 eV which is close to the experimental results. However, the calculations using HSE are time-intensive, especially for atomic relaxations in large supercells. The tendencies of the band gap between GGA and HSE are in good agreement with each other. As a result, our calculations based on GGA are reasonable. For the model of GaAs0.9375Bi0.0625, the direct band gap is 0.395 eV at the high symmetry Γ point, which is decreased by about 280 meV compared with the intrinsic case. The band gap of GaAs0.875Bi0.125 is 0.332 eV and that of GaAs0.8125Bi0.1875 is 0.258 eV.
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Figure 2 represents the total density of states (DOS) for pure and Bi-doped GaAs as a function of Bi concentrations. The Fermi level is taken to be zero. The valence band states for intrinsic GaAs consist of two main parts: the upper part around −6.0 eV which is mainly derived from Ga 3s orbitals and the lower part around −15.0 eV which is mostly due to the Ga 3d orbitals. When the Bi contents increase, it can be noted that the sharp peak in the lowest valence band (−12.0 eV to −15.0 eV) increases. What is more is that the conduction band gradually shifts toward the upper energy levels.
To further describe the properties of the band structure in detail, the partial DOS of GaAs0.875Bi0.125 is presented in Figure 3. We provide two figures which are sorted by the atomic shells and the atoms, respectively; thus it is clear to see the effect of doping. In Figure 3(a), the total DOS of GaAs0.875Bi0.125 can be divided into five parts, which corresponds to valence band 1 (about −15 eV), valence band 2 (−12.5 to −10 eV), valence band 3 (−6.5 to −5 eV), valence band 4 (−4 to 0 eV), and conduction band (1 to 2.5 eV). It can be clearly seen that the valence bands 1, 2, 3, and 4 are contributed mainly by d, s, s, and p orbitals, respectively. When doped with Bi, the main component of the electronic states at Fermi level is the 6p state of Bi atoms. For the conduction band, in addition to the hybrid orbitals formed by the presence of As and Ga atoms 4s/4p state, there is also some contribution from Bi 6s/6p. Due to the conduction band position slightly moving to the lower level areas, the optical band gaps of Bi-doped GaAs alloys become slightly smaller, which is consistent with the experimental facts [19, 20].
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Table 2 shows the band gap of pure GaAs and alloy of various concentrations (6.25%, 12.5%, 25%, 50%, 75%, and 100%). We assume that the band gap varies linearly and observe differences with respect to the experimental and theoretical values. According to experimental data reported by many research groups [25, 26], the band gap reduction ranges from 42 to 88 meV/% Bi. However, our calculation gives a band gap reduction of about 30 meV/%Bi which is better than the previous result [15] (about 6.5 meV/%Bi). It is well known that GGA underestimates the band gaps of the compounds because it does not truly represent quasi-particle excitation energies. To verify the accuracy of our calculations based on the HSE hybrid functional, the band gap of pure GaAs and alloy is also presented in Table 2. The trends between GGA and HSE are in good agreement with each other. There are some deviations from experimental data. It is worth noting that, for GaAs0.875Bi0.125, our calculated gap is 0.332 eV and 0.684, respectively. It is better than the earlier results (about 0.041 eV) reported by Mbarki and Rebey[9]. The experimental value reported by Lu et al. [17] is about 0.797 eV. The most important result is that the band gaps of alloy shrink with increasing Bi content.
3.3. Optical Properties
The imaginary part of the dielectric function (ω) is calculatedin order to understand the optical properties of the alloy. The interaction of a photon with the electrons can be described in terms of time-dependent perturbations in the ground electronic states. Optical transitions between occupied and unoccupied states are induced by the electric field of the photon. The spectra from the excited states can be exactly described by the joint density of states between the valence and conduction bands. The imaginary part (ω) of the dielectric function can be calculated using the momentum matrix elements. The corresponding eigenfunctions of each of the occupied and unoccupied states contribute to these matrix elements. The real part (ω) of dielectric function can be derived from imaginary part (ω) by the Kramer-Kronig relationship. With (ω) and (ω), we can straightforwardly calculate other optical parameters such as absorption coefficient α(ω), energy loss spectrum L(ω), and reflectivity R(ω). The corresponding expressions of these principal parameters can be expressed as follows: To present the optical properties of the Bi-doped GaAs system well, four kinds of doping concentrations (6.25%, 12.5%, 18.75%, and 25%) are chosen from which the main conclusions are shown in Figure 4. As a primary parameter for the analysis of optical properties, the imaginary part of the dielectric functions (ω) and its dependence on the photon energy are shown in Figure 4(a) for pure GaAs and the alloy. Two sharp peaks can be seen around the photon energy between 2.0 eV and 4.0 eV, respectively, and our result agrees well with [9]. With the increasing Bi concentrations, (ω) shows a clear red shift in Figure 4(a), which is consistent with the previous result [11]. Besides, it is the optical transition from Ga-p, As-p, Bi-p states to Ga-s/p, As-p, and Bi-s/p/d states that cause the first peak, while the second peak corresponds to transition of the Ga-s/p and Bi-p to Ga-p/d and Bi-s/p/d states 8. The width of the first peak in (ω) is essentially determined by the width of the highest occupied valence band [11]. The shift of the optical transition indicates that the direct band gap decreases. Besides, the optical transition is gradually enhanced with increasing Bi concentrations, which induces the enhancement of band edge emission of the alloy.
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(c)
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Figure 4(b) shows the optical absorption spectra of pure GaAs and alloy using the scissor operation in the range of 0 eV~6 eV. The energy scissor approximation is employed to adjust the absorption edge to fit the experimental data [24]. From Figure 4(b), we can immediately notice that the introduction of Bi introduces the red shift of the optical absorption edge to GaAs. Moreover, the absorption coefficient of these alloys is zero below the fundamental energy band gap and increases rapidly to form the first absorption peak at around 5.0 eV.
Figure 4(c) shows the calculated reflectivity R(ω) of pure GaAs and alloy. The reflectivity of Bi-doped GaAs enhances in the low energy range in comparison to those of the pure GaAs, which indicates that the band gap of Bi-doped GaAs decreases. It is not difficult to find that there is an abrupt reduction in the reflectivity spectrum around 11.0 eV which verifies the occurrence of a collective plasmon resonance. The depth of the plasmon minimum is determined by the imaginary part of the dielectric function at the plasma resonance and is representative of the degree of overlap between the interband absorption regions [11].
In Figure 4(d), we can investigate the peaks in the energy range of 10.6 eV~10.8 eV in the energy loss spectra, which is also an important factor describing the energy loss of a fast electron traversing in a material. The peaks in the L(ω) spectra represent the characteristics associated with the plasma resonance and their corresponding frequency is the so-called plasma frequency, above which the material exhibits the dielectric behavior [(ω) > 0], whereas below the frequency the material has a metallic property [(ω) < 0]. It means that the positions of peaks in L(ω) spectra indicate the transition from the metallic to the dielectric property for a material. What is more is that the peaks of L(ω) also correspond to the trailing edges in the reflection spectra; for instance, the peak of L(ω) for alloy is at around 10.65 eV corresponding to the abrupt reduction of R(ω).
4. Conclusion
In conclusion, a first-principles study has been performed to investigate the structural and electronic properties of the alloy. The lattice constants of increase with the Bi concentration while the alloy remains in the zinc-blende structure all along. The band gap of clearly shrinks with the Bi concentration. shows metallic properties. When doped with Bi, there is a little change in the crystal structure of the alloy, while the electronic structure varies a lot which is contributed by the Bi 6p states at the uppermost valence band and the Bi 6s/6p states at the lowest conduction band. In addition, the optical transition of Bi doped GaAs exhibits a clear red shift with increasing Bi concentrations.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work is supported by Natural Science Foundation of Zhejiang Province (LY13F020045, LY13F020047), Natural Science Foundation of China (Grants no. 61202094 and 61300211), and National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2012BAH24B04).