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Abstract
The effects of Bi in InP1-xBix ternary semiconductor alloys are studied based on first-principles. The mBJLDA potential is used to obtain accurate band structures. The band gap is modified mainly by the large Bi atom-induced strain at high concentration. The incorporation of Bi mainly perturbs the valence bands due to the interaction of Bi impurity states with heavy/light hole bands and spin-orbit split off bands. Several different Bi complexes including [100] chain, [111] chain, clustered and SQS in a 128-atom supercell are considered. For random Bi distribution at high concentration, the resulting band structures can be understood together as a work of all Bi complexes arrangements. Measuring band gap narrowing mechanism dependent on configurations as a function of Bi composition can potentially help to distinguish the types of Bi arrangement distributions in samples as well as to promote the applications in mid-infrared regime.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Extensive experimental and theoretical investigations have been focused on III-V semiconductors due to their promising applications in optoelectronic electronic devices [1–5]. Isoelectronic impurities in host III-V materials can modify the electronic or optical properties to meet various optoelectronics requirements. Such as Bi or N doping, the interaction between defect energy levels and host levels results in a band gap bowing with impurity concentration increasing. For dilute nitride GaAs1-xNx alloys, the band gap bowing is contributed by hybridization of N-s orbitals with host conduction band, and the well-distinguishable localized defect states corresponding to the experimentally detected conduction band tail [6,7]. In the case of GaAs1-xBix alloys, the Bi mainly perturbs the host valence band edge rather than conduction band, which does not affect the electron mobility [8], and the Bi-induced effect on electronic structures is clearly smaller than that induced by N [9]. An anomalously large spin-orbit splitting in GaAs1-xBix has been detected [10], which means the possibility of tuning spin-orbit splitting energy for semiconductor spintronic applications by altering Bi concentration. Moreover, Bannow et al. found that, the band gap of GaAs1-xBix is modified mainly by a Bi-Bi p orbital interaction and by the large Bi atom-induced strain at high concentrations [11].
The incorporation of Bi into InP can further extend transition wavelengths as well as suppress Auger recombination and inter-valence band absorption (IVBA) processes [12]. InPBi is assessed as the most robust infrared optoelectronic material, and the most difficult to synthesize among In-V-Bi (V = P, As and Sb) [13]. InPBi was firstly grown by gas source molecular beam epitaxy (MBE) by Wang et al. in 2014 [14]. Bi concentration in InPBi alloys is at a low level, which making such a material very promising for InP based optoelectronics devices [15]. The Bi incorporated into InP with a doping level always functions as isoelectronic impurity energy level and is experimentally detected rich spectroscopic information near the band gap of InP (1.3 to 1.4 eV) at low temperature [16,17]. Although some experimental [12,14,18–20] and theoretical [21–23] investigations have been implemented to study electronic and optical characterization of InP1-xBix alloys, there are few detail explanations of dilute Bi induced band gap bowing, especially under the different Bi complexes arrangement conditions.
The impurity tends to concentrate as clusters or other complexes configurations in high Bi concentration, which is contributed by the Bi-Bi interaction. X-ray absorption spectroscopy analysis of GaBixAs1-x [24] reveals that Bi atoms tend to form pairs and clusters in the alloys when x ≥1.9%. Such pairs and clusters also have been observed in InP with dilute Bi concentration [14]. Therefore, it is necessary to explore the impact of different arrangements of Bi, for instance, pairs, clusters, chain, and random distribution, on the electronic structures of InP1-xBix. Measuring the band gap reduction with increasing Bi concentration also can potentially help identifying the types of Bi arrangement distributions during samples development.
In this work, different sizes of supercells with a single Bi atom are used to investigate the band bowing effect, which are band anti-crossing and lattice deformation respectively. Band structures and spin-orbit split energies of isolated Bi alloys are calculated. The band gap bowings of several Bi complexes arrangements including chain-100, chain-111, clustered, and SQS in 128-atom supercells are analyzed in detail.
2. Theoretical methods
Our theoretical calculations are performed based on density functional theory (DFT) [25] as implemented in Vienna ab initio simulation package (VASP) [26,27]. The projector augmented wave (PAW) [28,29] method is utilized to describe the core electrons and the exchange–correlation interaction is described with the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) [30]. The valence-electron configurations for In, P and Bi atoms are employed as 5s25p1, 3s23p3, and 6s26p3, respectively. A cutoff energy of 350 eV is used for the plane-wave basis set providing the convergence of the total energy. The structural optimization is allowed to relax until the maximum force on each atom becomes less than 0.01 eV/Å and maximum energy change between two steps is smaller than 10−5 eV. The further electronic structures are calculated by employing the modified form of Becke–Johnson exchange potential in combination with local density approximation correlation (mBJLDA) [30,31], which yields an accuracy band gap similar to hybrid functional or GW methods. Spin-orbit coupling (SOC) is considered in all calculations. Special Quasi-random Structures (SQS) approach [32,33] to model random distribution of Bi atoms on the P sites, as implemented in the Alloy Theoretic Automated Toolkit (ATAT) [34,35].
The binary compounds of InP and InBi with zinc-blende (ZB) are computed in 8-atom supercell. The applied k-mesh for the structure optimization is 5 × 5 × 5 [36]. Lattice constants of zinc-blend InP and InBi are 6.00 and 6.85 Å respectively, which are consistent with previous calculations of 5.87 and 6.69 Å [12]. The 14% lattice mismatch between InP and InBi is as a result of the large covalent radii difference between P and Bi (1.07 and 1.48 Å) [37], which implies incorporated Bi atoms in host InP will induced large strains. The energy gaps of InP and InBi binary compounds are 1.32 and −1.49 eV, respectively. Our results are very close to the experimental (1.42 eV in InP) and theoretical reports (−1.62 eV in InBi [18]). For the isolated Bi model, a stable primitive cell is used to construct supercells of 2 × 2 × 2, 3 × 3 × 3, and 4 × 4 × 4 with one P atom replaced by one Bi atom. The corresponding Monkhorst-Pack sets are 4 × 4 × 4, 3 × 3 × 3 and 2 × 2 × 2 k-points, respectively. For the Bi complexes model, [111] chain, [100] chain, clustered and SQS in a 128-atom supercell are constructed, and three concentrations for x = 3.13, 4.69, 6.25% are under consideration.
3. Results and discussion
3.1 Strain and chemical effects on band gap bowing
Band structures that are generated by overlaps between primitive cells can be perturbed by lattice strain, described as band deformation potentials [38]. The 14% lattice mismatch between InP and InBi binary compounds means that Bi atoms in host InP will impose a large lattice distortion in host lattices, which is defined as the strain effect. Another perturbation is due to the higher energy of the Bi-p valence orbitals than the P-p orbitals that called the chemical effect.
In order to distinguish the strain and chemical effects of Bi on the band gap bowing (ΔEg), three kinds models are taken into account: (i) relaxed Bi (total effect), the atoms positions of different size supercells are optimized by minimizing the forces arising to Bi incorporation. (ii) strain effect, replaces Bi back by P with fixing the supercell lattice and size which gets from i. (iii) chemical effect, with atomic positions frozen as the host lattice, disregards the local lattice distortions due to Bi. For the Bi concentration in InPBi alloys is about 2.4% under experimental conditions, InPBi alloys with 12.5% of Bi concentration is sufficient for the calculations. Therefore, InPBi alloys with the composition of Bi varying from 0 to 12.5% is under consideration. The 2 × 2 × 2, 3 × 3 × 3, and 4 × 4 × 4 supercells with one P atom replaced by one Bi atom is constructed, corresponding to the Bi concentration of 12.5%, 3.70%, and 1.56%, respectively. The corresponding Monkhorst-Pack sets are 4 × 4 × 4, 3 × 3 × 3 and 2 × 2 × 2 k-points, respectively.
The band gap bowings that originate from stain effect, chemical effect, and total-effect (namely relaxed Bi) as a function of Bi composition are shown in Fig. 1. Three kinds of effects increase with the increase of Bi. We find that the chemical effect on band bowing is a little stronger than the strain effect at low Bi concentration. While the stain effect from lattice distortion becomes stronger than chemical effect with the increase of Bi content. This phenomenon means that band gap is modified mainly by the large Bi atom-induced strain at high concentration, and the summation of strain effect and chemical effect is less than the bang gap bowing observed in the relaxed Bi.
Fig. 1 Variation of the band gap as a function of Bi composition, which originate from stain effect, chemical effect, and total-effect (namely relaxed Bi) respectively. .
3.2 Isolated Bi effects on electronic structures
Due to heavy atom Bi, SOC effect plays a key role in electronic properties of InP1-xBix alloys. Calculated band structures and partial density of states (PDOS) of bulk In64P63Bi, In27P26Bi, and In8P7Bi with SOC are displayed in Fig. 2. The red lines in band structures represent the contribution of Bi, the deeper the red, the more contribution of Bi. At the top of valence band, we find the heavy and light hole bands spitting from the SO bands at the Γ point. It clearly shows that the band gaps of InPBi narrow with the concentration of Bi, while the spin-orbit split energies inversely increase. The narrowing of band gaps is contributed from both the downward shift of the conductor band minimum(CBM) and upward shift of the valence band maximum(VBM). While the enhancement of spin-orbit splitting energies is caused mainly by a strong shift of heavy/light hole (HH/LH) bands from VBM towards CBM. The shift of spin-orbit split off bands is very weak. Figure 3 shows the band gap Eg, spin-orbit splitting energy Δso, and Eg + Δso transition energies of InP1-xBix alloys as a function of Bi concentration. The fundamental band gap Eg transition shifts significantly to longer wavelengths (−62 meV/%Bi), while Eg + Δso transition shifts weakly (−14meV/%Bi) with increasing Bi concentration. The results are consistent with the experiment phenomenon by J. Kopaczek [39]. It indicates that the decreasing band gaps and the increasing spin-orbit splitting energies will lead to a crossover at about 10% Bi composition. Moreover, considering increase Bi composition can engineer band structures to be candidates for mid-infrared applications.
Fig. 2 Band structures and PDOS for bulk supercell (a) In64P63Bi, (b) In27P26Bi, and (c) In8P7Bi. The red lines represent the contribution of Bi in band structures.
Fig. 3 The band gap Eg, spin-orbit split energy Δso, and Eg + Δso in InP1-xBix as functions of Bi concentration.
Since the contributions of In-d, P-s and Bi-s/d are weak in InP1-xBix alloys, we only plot the dominant states (In-s/p, P-p, Bi-p) of the PDOSs for a sake of simplicity. According to the PDOSs, the doped Bi tends to perturb the valence bands around Fermi level, while have a weak effect on the lower conduction bands. The conduction bands are mainly comprised of P-p states and In-s/p states. The VBM is mainly constituted by the hybridization of P/In-p states and Bi-p states. With the increasing of Bi concentration, the peaks start to broaden and the valance band edge moves upwards around the Γ point. A comparison with other experimental works [40,41] indicates a similar behavior of the variation of energy gaps. Such results indicate InPBi is a promising candidate material in spintronic field.
3.3 Bi complexes effects on electronic structures
Four kinds of models have been analyzed to understand the influences of Bi complexes arrangements in InPBi alloys, especially for high concentration. [111] chain, [100] chain, clustered and SQS models in a 128-atom supercell are shown in Fig. 4. We construct three concentrations for x = 3.13, 4.69, and 6.25%, namely two, three, and four Bi atoms distributed as chain along axis [111], chain along axis [100] and clustered. The SQS approach of Zunger et al. [42], has been used to produce a random structure.
Fig. 4 Four kinds of Bi complexes models in In64P60Bi4 are shown, namely [111] chain, [100] chain, clustered and SQS structures.
Table 1 summarizes the effects of different Bi complexes configurations. Table 1 and Fig. 5 display that the Eg bowings of isolated Bi atom (62 meV/%Bi) and SQS arrangement (−68 ± 4 meV/%Bi) are close to experimental values of 60~90meV/%Bi [12,14,20,39]. The band gap bowing of [111] chain structure is smaller than the experimental values cited. It is noteworthy that [111] chain structure is the most favorable total energy configuration. The clustered configuration exhibits a larger Eg bowing, which is explained by stronger Bi-Bi interaction of concentrated Bi atoms. The Bi-Bi interaction may broaden the mixed impurity states at VBM and further narrow energy gap. The band gap bowing of [100] chain arrangement is dramatically larger than both the experimental values and the other calculated values. The difference slopes of these band gap variations shown in Fig. 5 demonstrate that impurities arrangements or doping ways significantly affect alloys electronic properties. The imparity between our calculated results and early experimental values can been explained by the cooperative contribution from above-mentioned structures. Namely, Bi atoms will distribute or concentrate with different arrangements during sample growing. Measuring band gap narrowing mechanism dependent on configurations as a function of Bi composition can potentially help to distinguish the types of Bi arrangement distributions in samples as well as promote the applications in mid-infrared regime.
Table 1. Effects of different Bi arrangements in a 128-atom supercell on the band gap Eg (eV) for two, three and four Bi atoms. ΔETOT (eV) is the total energy difference between those supercells with corresponding to the lowest total energy of [111] chain arrangement.
Fig. 5 Variation of the band gap in InP1−xBix alloys for different types of arrangements. Including isolated atom arrangement from Fig. 3 (black squares), [111] chain, [100] chain, clustered, and SQS data from Table1.
4. Conclusion
The electronic properties of InP1-xBix ternary semiconductor alloys are investigated based on first-principles using VASP code. The mBJLDA exchange potential together with SOC are used to obtain accurate band structures. The results of supercell calculations for energy gaps and band gap bowing parameters are in good agreement with experimental values. The strain effect that comes from lattice distortion becomes stronger than chemical effect with increasing Bi concentration. It means that band gap is modified mainly by the large Bi atom-induced strain at high concentration. The incorporation of Bi mainly perturbs the valence band due to the interaction between Bi impurity states with HH, LH and SO bands. The fundamental band gaps transition significantly shifts to longer wavelengths, while the Eg + Δso transition is very weak as increase Bi concentration. The band gap bowings of four types Bi complexes arrangements in a 128-atom supercell are measured. It indicates that the impurities arrangements or doping ways have a profound effect on electronic properties. And the band properties of experiments can be viewed as a together work of these different Bi atoms arrangements.
Funding
National Natural Science Foundation of China (NSFC) (61741503, 61671085); Open Program of State Key Laboratory of Functional Materials for Informatics.
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