Elsevier

Physica B: Condensed Matter

Volume 484, 1 March 2016, Pages 27-30
Physica B: Condensed Matter

Estimation of Bi induced changes in the direct E0 band gap of III–V-Bi alloys and comparison with experimental data

https://doi.org/10.1016/j.physb.2015.12.046Get rights and content

Abstract

Quantum dielectric Theory (QDT) is used to explain the band gap bowing effect observed in III–V-Bismides such as InSb1−xBix, InAs1−xBix, InP1−xBix, GaSb1−xBix, GaAs1−xBix and GaP1−xBix. The dependence of the direct E0 band gap for these alloys on Bi mole fraction is calculated using QDT which requires the evaluation of the bowing parameter c. The bowing parameter gives the deviation of the direct E0 band gap from the linear relationship of E0 with Bi mole fraction. The band gap reduction values obtained using QDT are compared with those calculated using Virtual Crystal approximation (VCA) and Valence Band Anticrossing (VBAC) model as well as with the reported experimental data and the results of the comparison shows excellent agreement.

Introduction

The effect of Bi incorporation on the band structure of III–V-Bismides has generated a lot of interest among the researchers for the last few decades. The recent work on the investigation of the various properties of these materials have been reviewed in a Springer series book [1]. The introduction of dilute concentrations of bismuth into the III–V binaries causes significant reduction in the band gap and enhancement of the spin–orbit splitting energy [1], [2], [3], [4], [5]. For example, incorporation of only 1 at% of Bi in GaAs reduces the band gap of the material by 88 meV [4]. Similar effects have been found in other semiconductors like, InSbBi, InGaAsBi, InGaSbBi and InAsSbBi and GaSbBi. Bismides are, in a way, similar to the well-studied family of group III–V-N dilute nitrides [6]. However, in dilute nitrides, the band gap reduction occurs due to the interaction of a nitrogen resonant state with the conduction band. In dilute bismides, in contrast, Bi interacts with the valence band resulting in an apparent upward shift of the band edge which is well-explained by the valence band anticrossing model [2], [5]. The large band gap bowing effect occurring in III–V Nitrides is well explained using the Band Anticrossing (BAC) model [7]. Quantum dielectric theory (QDT) is used to predict the direct E0 band gap of III–V ternary and quaternary semiconductors containing InBi and GaBi and the observed band gap bowing effect has been previously explained using tight binding method [8], k.p method [2] and density functional theory (DFT) [9]. InBi and GaBi are considered to be semi-metals which crystallizes to form tetragonal structure. Addition of small amounts of InBi to III–V semiconductors such as InSb, InAs and InP and GaBi to GaAs, GaSb and GaP results in the formation of alloys with zinc-blende structure along with the decrease in E0 as well as increase in alloy lattice constants [10]. In tetrahedrally coordinated crystals, the band gap Eg represents the energy difference between bonding and antibonding hybridized orbitals [11]. Eg can be written as,Eg=(Eh2+C2)1/2where Eh and C represent the contributions of the symmetric and non-symmetric part of the potential within a unit cell, respectively. While Eh is a function of the nearest neighbour distance and is constant for all diamond, zinc blende, and wurtzite crystals formed of elements from a given pair of rows of the Periodic Table, C depends on the valence difference of the elements forming the binary compounds like InBi or GaBi to include the effects of row or ion core differences [11]. In other words, Eh and C gives a measure of the average band gap energy due to covalent (nearest neighbour distance) and ionic (valence difference) effects, respectively [12]. However, the direct E0 transitions are affected by the presence of a filled d band which introduces a term Dav in the expression for Eg due to the interaction of the d band with the valence band states. While D gives the square of the ratio of the effective plasma frequency to the free-electron value calculated assuming four electrons per atom, Dav denotes the valence weighted average of the D value of the crystals containing the constituent atoms and the corresponding atom from the same row of the Periodic Table [11].

In this paper, we have calculated the direct E0 band gap of InBi and GaBi containing III–V alloys using quantum dielectric theory (QDT) [11], [12], [13]. The calculated values of band gap for GaBi [14] and InBi [10] using QDT are used to find out the direct E0 band gap dependence of III–V-Bi alloys on Bi mole fraction. QDT calculations are compared with the band gap reduction values obtained using Valence Band Anticrossing (VBAC) model and Virtual Crystal Approximation (VCA). The results of our calculations show excellent agreement with experimental results. The band gap bowing effect occurring in III–V Bi alloys due to the anticrossing interactions of the host III–V semiconductors with the Bi related impurity states is successfully explained using calculated results based on QDT.

Section snippets

Theory and mathematical modelling

The direct E0 band gap of a binary semiconductor is defined as the difference between the Γ valley minimum of the conduction band Γ15c and the Γ valley maximum of the valence bandΓ1v. The dependence of the direct E0 energy band gap on the mole fraction of a III–V-Bi semiconductor alloy AB1−xCx can be written as [3],E0=a+bx+cx2where a, b and c are constants. a and b are determined from the E0 values of the endpoint compounds AB and AC for AB1−xCx. c is the bowing parameter which gives the

Results and discussions

Table 1 shows the calculated values of the intrinsic and extrinsic bowing parameters along with the total bowing parameter c for Bi containing III–V alloys using QDT. The values of the bowing parameters along with the constants a and b of Eq. (2) are used for calculating the direct E0 values of different III–V-Bi alloys, the final form of which is given in the last column of Table 1. It can be observed from the table that the bowing parameter c increases in a sequence from III-Sb–Bi to III-P–Bi

Conclusions

Large band gap bowing effect, observed in III–V-Bismides, has been explained using calculations based on quantum dielectric theory (QDT). The calculated values of the direct E0 band gap reduction for InSb1−xBix, InAs1−xBix, InP1−xBix, GaSb1−xBix, GaAs1−xBix and GaP1−xBix using QDT are compared with that those obtained through calculations based on valence band anticrossing (VBAC) and virtual crystal approximation (VCA) models. Comparison of the calculated results with experimental data showed

References (40)

  • S.C. Das et al.

    Infra. Phys. Technol.

    (2012)
  • J.J. Lee et al.

    Optoelectron. Rev.

    (1998)
  • S.K. Das et al.

    Infrared Phys. Technol.

    (2012)
  • D.P. Samajdar et al.

    Mater. Sci. Semicond. Process.

    (2015)
  • D.P. Samajdar et al.

    Comp. Mater. Sci.

    (2016)
  • K. Alberi et al.

    Phys. Rev. B

    (2007)
  • J. Yoshida et al.

    Jpn. J. Appl. Phys.

    (2003)
  • S. Francoeur et al.

    Appl. Phys. Lett.

    (2003)
  • K. Alberi et al.

    Appl. Phys. Lett.

    (2007)
  • W. Shan

    Phys. Rev. Lett.

    (1999)
  • M. Usman et al.

    Phys. Rev. B

    (2011)
  • M.P. Polak

    J. Phys. D.: Appl. Phys.

    (2014)
  • S.A. Barnett

    J. Vac. Sci. Technol. A

    (1987)
  • J.A. Van Vechten

    Phys. Rev.

    (1969)
  • J.A. Van Vechten

    Phys. Rev.

    (1969)
  • J.A. Van Vechten et al.

    Phys. Rev. B

    (1970)
  • D.P. Samajdar et al.

    Calculation of Direct E0 Energy Gaps for III–V–Bi Alloys Using Quantum Dielectric Theory

  • M.P. Polak et al.

    Semicond. Sci. Technol.

    (2015)
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