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Band-gap reduction and band alignments of dilute bismide III--V alloys

Abdul Saboor, Shoaib Khalid, Anderson Janotti

TL;DR

This work uses hybrid-DFT with the HSE06 functional to quantify how dilute Bi incorporation in III–V semiconductors ($x$ = 3.125% and 6.25%) shifts both the valence-band maximum and the conduction-band minimum, thereby producing large band-gap reductions and enhanced spin-orbit splitting $\\Delta_{\\rm SO}$. It shows that Bi raises the VBM and, counterintuitively, lowers the CBM due to volume expansion, with arsenide-based alloys experiencing stronger effects than antimonides; band alignments relative to the parent compounds reveal substantial band-edge shifts not captured by simpler VBAC models. The results predict band inversion in InAs$_{1-x}$Bi$_x$ around $x\\sim0.10$ and $\\Delta_{\\rm SO}$ exceeding $E_g$ in several Sb- and In-based alloys, suggesting routes to topological phases and suppressed Auger recombination for infrared devices. These quantitative parameters—edge shifts, band gaps, $\\Delta_{\\rm SO}$, and formation enthalpies—provide practical guidance for designing dilute bismide III–V materials for optoelectronics and potential topological applications.

Abstract

Adding a few atomic percent of Bi to III--V semiconductors leads to significant changes in their electronic structure and optical properties. Bismuth substitution on the pnictogen site leads to a large increase in spin-orbit splitting $Δ_{\rm SO}$ at the top of the valence band ($Γ_{8v}-Γ_{7v}$) and a large reduction in the band gap, creating unique opportunities in semiconductor device applications. Quantifying these changes is key to the design and simulation of electronic and optoelectronic devices. Using hybrid functional calculations, we predict the band gap of III--Vs (III=Al, Ga, In and V=As, Sb) with low concentrations of Bi (3.125\% and 6.25\%), the effects of adding Bi on the valence- and conduction-band edges, and the band offset between these dilute alloys and their III--V parent compounds. As expected, adding Bi raises the valence-band maximum (VBM). However, contrary to previous assumptions, the conduction-band minimum (CBM) is also significantly lowered, and both effects contribute to the sizable band-gap reduction. Changes in band gap and $Δ_{\rm SO}$ are notably larger in the arsenides than in the antimonides. We also predict cases of band-gap inversion ($Γ_{6c}$ below $Γ_{8v}$) and $Δ_{\rm SO}$ larger than the band gap, which are key parameters for designing topological materials and for minimizing losses due to Auger recombination in infrared lasers.

Band-gap reduction and band alignments of dilute bismide III--V alloys

TL;DR

This work uses hybrid-DFT with the HSE06 functional to quantify how dilute Bi incorporation in III–V semiconductors ( = 3.125% and 6.25%) shifts both the valence-band maximum and the conduction-band minimum, thereby producing large band-gap reductions and enhanced spin-orbit splitting . It shows that Bi raises the VBM and, counterintuitively, lowers the CBM due to volume expansion, with arsenide-based alloys experiencing stronger effects than antimonides; band alignments relative to the parent compounds reveal substantial band-edge shifts not captured by simpler VBAC models. The results predict band inversion in InAsBi around and exceeding in several Sb- and In-based alloys, suggesting routes to topological phases and suppressed Auger recombination for infrared devices. These quantitative parameters—edge shifts, band gaps, , and formation enthalpies—provide practical guidance for designing dilute bismide III–V materials for optoelectronics and potential topological applications.

Abstract

Adding a few atomic percent of Bi to III--V semiconductors leads to significant changes in their electronic structure and optical properties. Bismuth substitution on the pnictogen site leads to a large increase in spin-orbit splitting at the top of the valence band () and a large reduction in the band gap, creating unique opportunities in semiconductor device applications. Quantifying these changes is key to the design and simulation of electronic and optoelectronic devices. Using hybrid functional calculations, we predict the band gap of III--Vs (III=Al, Ga, In and V=As, Sb) with low concentrations of Bi (3.125\% and 6.25\%), the effects of adding Bi on the valence- and conduction-band edges, and the band offset between these dilute alloys and their III--V parent compounds. As expected, adding Bi raises the valence-band maximum (VBM). However, contrary to previous assumptions, the conduction-band minimum (CBM) is also significantly lowered, and both effects contribute to the sizable band-gap reduction. Changes in band gap and are notably larger in the arsenides than in the antimonides. We also predict cases of band-gap inversion ( below ) and larger than the band gap, which are key parameters for designing topological materials and for minimizing losses due to Auger recombination in infrared lasers.

Paper Structure

This paper contains 10 sections, 1 equation, 7 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Computational Methods and Details of the Calculations
  3. Results and Discussion
  4. Lattice parameters, band gap, and spin-orbit splitting of the III-V parent compounds
  5. Volume variation of dilute bismide III--V alloys with Bi concentration
  6. Band gaps and spin-orbit splittings in the dilute bismide III--V alloys
  7. Band alignments between the III-V-Bi alloys and their parent compounds
  8. Formation enthalpy of dilute III--V bismide alloys
  9. Summary
  10. Acknowledgements

Figures (7)

  • Figure 1: Calculated electronic band structures of the III--V compounds, with III=Al, Ga, In and V=As and Sb, along those of AlBi, GaBi, and InBi, all in the zinc blende phase. Spin-orbit coupling is included, and the valence-band maximum (VBM) was set to zero in each case. $\Gamma_{7v}$ is split-off band and the difference to $\Gamma_{8v}$ determines the strength of the spin-orbit coupling $\Delta_{\text{SO}}$. For the III--Bi, $\Gamma_{6c}$ is below $\Gamma_{8v}$, giving negative (inverted) band gaps. The color code represents the $s$-orbital (blue) vs $p$-orbital (red) contributions to each state, and the thickness of the lines represents the strength of the orbital contribution.
  • Figure 2: (a) Volume (per two atoms) of dilute III--V$_{1-x}$Bi$_x$ alloys as function of Bi concentration. (b) Changes in the volume (per two atoms) of the dilute III--V$_{1-x}$Bi$_x$ alloys relative to the equilibrium volume of the III--V parent compound ($\Delta V/V_{0}$) as a function of Bi concentration.
  • Figure 3: Band gap as a function of Bi concentration in dilute III--V$_{1-x}$Bi$_x$ alloys: (a) shows how $E_g$ decreases with increasing Bi percentage. The decrease is larger in the arsenides as compared to the antimonides; (b) shows the relative changes in the band gap, which are mostly linear with Bi concentration. Corresponding values in terms of band-gap reduction per % of Bi are given in Table \ref{['table3']}.
  • Figure 4: (a) Calculated spin-orbit splitting $\Delta_{\rm SO}$ in dilute III--V$_{1-x}$Bi$_x$ alloys, and (b) the rate of change of the spin-orbit splitting with Bi concentration. Except for AlAs$_{1-x}$Bi$_x$ and GaAs$_{1-x}$Bi$_x$, the changes are basically linear in this dilute regime.
  • Figure 5: Valence-band and conduction-band offsets $\Delta E_v$ and $\Delta E_c$ between the dilute III--(V,Bi) alloys and the corresponding III-V parent compounds, for 3.125% and 6.25% Bi content. The conduction band is also significantly affected. The values in this plot are also listed in Table \ref{['table4']}.
  • ...and 2 more figures