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Employing first-principles combined with hybrid functional calculations, the electronic and optical properties of GaAs alloyed with isovalent impurities Bi and N are investigated. As GaAsBiN alloy is a quaternary alloy, the band gap and the lattice constant of the alloy can be individually tuned. Both impurities are important to the valence band and conduction band of the alloy, with the band gap of the alloy being dramatically reduced by Bi 6p states and N localized 2s states. Interestingly, the calculated optical properties of the quaternary alloy are similar to those of undoped GaAs except that the absorption edge has a redshift toward lower energy. These results suggest potential interest in the long-wavelength applications of GaAsBiN alloy.
© 2014 Optical Society of America
1. Introduction
Semiconductor III–V material is widely used in the fields of lasers, photovoltaic cells, optical fiber communication, and nonlinear-wavelength applications. Compared with other materials, gallium arsenide has the advantage of high operating frequency, low power consumption, and high crystal quality [1–3]. This has led to the widespread application of the 850-nm GaAs laser. Recently, a great deal of effort has been devoted to exploring other IIIer alloys by incorporating atoms, specifically isoelectronic impurity atoms, into traditional binary GaAs. These alloys provide an effectual method for tailoring electronic properties of materials required for practical optoelectronic devices [4–7]. The properties of GaAs material can thus be modulated to extend the application of the material in near-infrared to infrared regions.
Since the discovery of isovalent defect levels for semiconductors in the 1960s [4], many studies have investigated the formation mechanism and calculated the position of isovalent-bound states. In the past few decades, the mixing of isovalent compounds AC and BC to form semiconductor alloys ABC has been an effective way for band structure engineering to enhance the properties of materials, such as in the cases of GaNxAs1-x, GaPxAs1-x, GaSbxAs1-x, and GaAsxBi1-x [5–7]. GaAsN ternary alloy initially attracted much attention from both experimentalists and theoreticians because of its successful growth by metal organic chemical vapor deposition, and the modulation of the band gap over a wide range with a little incorporation of nitrogen. Owing to the large size mismatch between N and As, the growth of high-quality GaAsN alloy on GaAs substrates is a challenge. In recent years, the ternary alloy GaAsBi has also attracted much attention, and GaAs1-xBix with a high Bi concentration (22%) has been grown by molecular beam epitaxy [8]. Taking these factors into account, dual mixed alloy GaAsBiN is expected to have excellent performance in electronic and optoelectronic applications, and the matching of its lattice constant with that of GaAs will benefit its growth on GaAs substrates. There has however been a lack of study on the quaternary alloy GaAs1-x-yBixNy. In this work, we carry out a first-principles density functional theoretical study to investigate the electronic and optical properties of this alloy.
The Heyd–Scuseria–Ernzerhof (HSE) functional has been confirmed to effectively correct the well-known band gap error introduced by the local density approximation and the Perdew–Burke–Ernzerhof (PBE) functional to a certain extent [9, 10]. Thus, the results presented in this work were obtained using the projector augmented-wave method [11] as implemented in the code of the Vienna ab initio simulation package (VASP) [12] with an HSE hybrid exchange-correlation functional. Detailed electronic and optical calculations suggest that the quaternary alloy GaAs1-x-yBixNy will have excellent performance in semiconductor applications in the near infrared to infrared.
2. Computational details
The binary compounds GaN, GaAs, and GaBi in the zinc-blende phase and the quaternary alloy were studied in turn. All calculations were performed with the semilocal PBE [13] exchange-correlation functional and the HSE06 hybrid functional as implemented in VASP code. A supercell of 64 atoms was used to model the alloying systems. The outermost s-, p- and d-electrons of Ga and Bi atoms, and the outermost s- and p-electrons of As and N atom were treated as the valence electrons. The cutoff energy on a plane-wave basis was taken as 300 eV, and a 2 × 2 × 2 Γ-centered K-mesh was used for Brillouin-zone sampling. The Gaussian smearing method was employed with a smearing width of 0.05 eV. All of the atoms were fully free to relax to reach the minimization total energy of system, the tolerance for ionic relaxation was that the forces acting on all of atoms are smaller than 0.02 eV/Å. The global break condition for the electronic SC-loop was set to 10−4 eV.
3. Results and discussion
Before analyzing the electronic and structural properties of the quaternary alloy GaAs1-x-yBixNy, it is necessary to first investigate the lattice constant and band gap of the binary compounds. Table 1 presents the lattice constant a and band gap Eg for GaAs, GaN, and GaBi calculated using the PBE functional and the HSE06 hybrid functional. Experimental values are also presented for comparison [14–16]. On account of the inexistence of the GaBi compound, we refer to theoretical data [17] for contrast. To distinguish the reversal conduction band, only the outermost s- and p-electrons of the Bi are treated as valence electrons. The lattice mismatch of GaN and GaBi with GaAs were found to be −20.9% and 11.2%, respectively, suggesting that both GaAsN and GaAsBi alloys are highly strained and there is a strong possibility that phase separation will be induced at high concentrations. The large size and chemical mismatch naturally lead to uncommon and abrupt changes of material properties in the alloys.
Table 1. Calculated lattice constants a and band gap Eg for the zinc-blende phase GaAs, GaN, GaBi, both by PBE and HSE.
The band gaps of GaAs, GaN, and GaBi are respectively calculated as 1.40, 3.10, and −1.49 eV, which are in good agreement with the respective reference values of 1.52, 3.30, and −1.45 eV [14–17]. This indicates that the HSE06 functional reasonably predicts the properties of the abovementioned materials.
The lattice constant of the quaternary alloy GaAs1-x-yBixNy structure can be determined from the linear relation,
which is called Vegard’s law [18]. According to the calculation results given in Table 1, the quaternary alloy is lattice-matched with GaAs when the content ratio of N and Bi is described by the relation
Next, we investigated the electronic properties of the GaAsN ternary alloy and the GaAsBiN quaternary alloy, and finally, the optical properties of the quaternary alloy comparing with GaAs are presented. Precisely in line with the results of Eq. (2), we need a huge supercell in order to get a alloy lattice-match GaAs which would lead to a huge calculation amount. To calculation convenience, we choose a 64 atom GaAs supercell contained one nitrogen and two bismuch atoms substitute the As atoms, and mimic the Ga32As29Bi2N1 alloy lattice-matched with GaAs. According to our test, the difference between the accurate constant of the alloy and GaAs is less than 0.2%.
The band structure and total density of states (DOS) of perfect GaAs have been given in [19] with a direct band gap of 1.5 eV at the Γ point.
Our results are in line with those in [19]. We next investigated the straight substitution of one N atom for an As atom. Figure 1(a) shows the calculated band structure and total DOS of GaAs1-xNx for x = 3.125%. It is seen there is a direct band gap of 0.83 eV at the Γ point, which is well in line with the previous results [20]. We further investigated the composition of the conduction-band-edge state (C1). We found that the C1 state is mainly contributed by the 2s state of the N atom. Although the well-known band anticrossing (BAC) model has predicted that nitrogen induces a localized resonant state above the conduction band edge of the host material [21,22], it seems that the C1 defect state is likely pulled out of the conduction band and has a tendency to lie in the band gap, as for the cases of GaP:Bi and InP:Bi [23]. This could be explained by the band broadening proposed by Deng et al [24]. With an increase in the N concentration, the distance between impurity atoms becomes smaller, resulting in the broadening of the impurity level into a band through the strong interaction and hybridization between the impurity atoms. The broadening of the defect level will move the lower limit below the condution band minimum (CBM) of the host GaAs. Under the interaction of the host and defect, the conduct band of GaAs1-xNx broadens and the CBM moves down towards the Fermi level, resulting in a reduction of the band gap of this alloy. The actual mechanism for the N-N interactions that causes the broadening of the nitrogen-induced states has been thoroughly investigated by Virkkala et al with a developed TB model [25].
Fig. 1 (a)The band structures and the total DOS of GaAs1-xNx (x = 3.125%). (b) The band decomposed charge density of defect band, isosurfaces correspond to 0.0002 e/Å3.
The partial band-decomposed charge density calculations for the defect bands of the GaAsN alloy are presented. Figure 1(b) describes the C1 states at the Γ point in Fig. 1(a). We observed that the charge density is clearly localized at the impurity N atom and has an ideal spherical shape. These isosurfaces for the charge density affirm that the C1 state originates from the N 2s orbit.
We doped both N and Bi atoms in the super cell and calculated the quaternary alloy GaAs1-x-yBixNy. Figure 2(a) shows the band structure and total DOS of this alloy. As we known, Bi can induce a significant spin-orbit (SO) splitting which would be interesting and important for this material, but this feature is beyond our scope of this work. From this figure, we find that the band gap of 0.52 eV is less than that of previous GaAsN results. The impurity states related to the doped N atom are highlighted; they are similar to the above results for GaAsN. It is seen that the three levels of the valence band maximum (VBM) at the Γ point appeared separation, which is different from the case for GaAsN in Fig. 1(a). This indicates that the influence of the Bi defect state is near the valence band edge. The three defect bands (V1, V2, and V3) derived from 4p electrons of Bi are located in the valence band [26] (highlighted in color in Fig. 2), which raises the VBM. This phenomenon can be explained by the 2s state of N being lower than the 4s state of As, and N thus generating a potential trap for the electron either in the N-impurity state or CBM state. Likewise, the 6p state of Bi is notably higher than the 4p state of As, and Bi is likely to generate a potential trap for the hole either in the Bi-impurity state or the VBM state [27]. Virkkala’s investigation also demonstrated that due to the Bi substitution the mixed Bi-bulk states near the VBM leading to a broadening of these states near the Γ point causing the band-gap reduction [28].Another important factor that cannot be neglected is lattice distortion from the large mismatch of the host and two kinds of anions. According to our calculation, the alloy GaAs1-x-yBixNy without relaxation has a band gap of 1.02 eV. The volume of the Ga tetrahedron surrounding the nitrogen atom is greatly reduced by the lattice mismatch, which assists the N in generating a trap for the electron, and likewise, the Bi atoms in generating a trap for the hole. The interaction of the host and defect states notably reduces the band gap.
Fig. 2 (a)The band structures and the total DOS of GaAs1-x-yBixNy (x = 6.25%, y = 3.125%). (b) The band decomposed charge density of defect band, isosurfaces correspond to 0.007 e/Å3
To further understand the mechanism of formation of the defect bands, partial band-decomposed charge density calculations are made for the defect bands. Figure 2(b) presents the charge distribution at the Γ point of the alloy GaAsBiN, from the V3 defect state to V1 in Fig. 3. The charge density is mostly located at the Bi. The intensity maximizes at the Bi site, but it is also present at all As sites, which renders a perturbed charge distribution of the GaAs VBM. The charge transfer Bi, N and surrounding Ga atoms produce the defects states, leading to the reduction of the GaAs band gap, and enhancing the photon absorption of the material. From the configuration of the electronic state, we can also visualize that the defect band originates from the hybridization of Bi 6p and its nearest As 4p orbitals.
Figure 3 describes the partial DOS of the four elements of GaAs1-x-yBixNy. Bi has a very high peak at about −1.0 eV under the VBM, which corresponds with the band structure in Fig. 2. The VBM is mainly constituted by the hybridization of the 4p state of As and the 6p state of Bi. This new peak could have a strong effect on the optical absorption, leading to a redshift of the absorption edge of the alloy. The 2s state of N forms an extremely strong peak at about 0.7 eV near the CBM, which correlates with the C1 defect state in Fig. 2. Compared with the defect state of Bi, this state would have a weaker effect on the optical property because of its strong localization, which can be seen clearly in Fig. 1(b).
We considered the correlation of the band gap and size of the super cell of the quaternary alloy GaAs1-x-yBixNy, which has 32, 64, 96 and 128 atoms. All of the models have one N atom and two Bi atoms substituting for three As atoms, which are located as far as possible from each other. Figure 4 shows the variations of the band gap obtained using the PBE functional and the HSE06 hybrid functional with two kinds of atom position: the atoms being located in the perfect position as for GaAs and the atom positions being relaxed by VASP. With an increase in the defect concentration, the broadening of the impurity level reduces the band gap of the alloy. Although the traditional DFT method seriously underestimates the gap of this alloy, it still describes the same trend and hybrid functional. The results obtained with the two methods differ by around 1.0 eV. The variation in band gap is due to the lattice distortion having a maximal value for the 32-atom cell, and gradually reducing with expansion of the super cell. We also investigate the effect of the cluster, which is three defect atoms surrounding one Ga atom, and find that the gap increases by 0.1 eV in the relaxed situation. This result shows that defect clustering weakens the effect of structure distortion.
Fig. 4 The band gap of GaAs1-x-yBixNy with different size of cell, the concentrations of Bi and N are: (32) 12.5% and 6.25%; (64) 6.25% and 3.125%; (96) 4.17% and 2.08%; (128) 3.125% and 1.57%
We calculated the optical properties of GaAs and GaAs1-x-yBixNy (x = 6.25%, y = 3.125%). The interaction between photons and electrons can be described by the dielectric function ε(ω) = ε1(ω) + iε2(ω). The absorption coefficient is obtained from the relationship with the real and imaginary parts of the dielectric function:
Figure 5(a) presents the imaginary part of the dielectric function as a function of the photon energy for GaAs and GaAs1-x-yBixNy (x = 6.25%, y = 3.125%). The imaginary part, which is important to the optical properties, has two major peaks at 3.1 and 4.4 eV, matching well with the experimental data of 3.1 and 4.8 eV [29]. Figure 5(a) also shows that the quaternary alloy GaAs1-x-yBixNy grows rapidly in the lower energy region, which is consistent with previous results of a reduced band gap.
Fig. 5 (a) The imaginary part ε2 of the dielectric function and (b) absorption coefficient of GaAs and GaAs1-x-yBixNy (x = 6.25%, y = 3.125%)
Figure 5(b) compares the absorption coefficient between undoped GaAs and GaAs1-x-yBixNy. The interband transitions between the top of the valence band and the bottom of the conduction band mainly decide the absorption edge. The absorption edge of the alloy is located around 0.4 eV, revealing an obvious redshift compared with the case of an absorption edge for perfect GaAs located at 1.3 eV. The alloy shows enhanced absorption in the low energy region, which could be attributed to the doped elements, and the absorption spectrum of alloy is as broad as that of GaAs in the high energy region. This can be explained as the incorporation of Bi enhancing the electron activity to make the transitions more frequent. Hence, the dual mixed defect reduces the optical gap of GaAs, while the good saturable absorption property of GaAs is maintained.
4. Conclusion
In summary, we presented the structural, electronic and optical properties of GaAs1-x-yBixNy alloy using the first-principles method. HSE06 provides a more accurate description of the alloy. The incorporation of two elements and the subsequent lattice distortion effectively reduce the band gap of GaAs. The optical properties of the alloy were calculated, revealing the large changes induced by the defect atom, which can be used to enhance the performance of the alloy in future long-wavelength applications.
Acknowledgments
The work was supported partly by “973 project” (No. 2012CB921300) and partly by the NSF of China (Grants No. 11104254 and 11304288).
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