Supplementary Information
The density functional theory (DFT) calculations were carried out with the Vienna ab
initio simulation package (VASP).[1,2] The local density approximation (LDA) exchangecorrelation functional was employed and spin-orbital coupling, which is crucial to describe
the special relativity effects in Bi, was included. The projector augmented wave method
was used together with the following potentials: Ga_GW (4s24p1, Ecut = 134.8 eV), As_GW
(4s24p3, Ecut = 208.9 eV), P_GW (3s23p3, Ecut = 255.2 eV), and Bi_d_GW (5d106s26p3, Ecut
= 242.9 eV). The plane-wave energy cutoff for the calculations was set to 400 eV. The
supercell has 216 atoms (about 16.9 Å in each direction) with P and Bi randomly distributed
on the As sites according to the special quasirandom structures approach as implemented
in the ATAT code.[3] The Monkhorst-Pack k-point grids for Brillouin zone sampling are
3 × 3 × 3. To mimic the epitaxial GaAsPBi film grown on GaAs(001), the lattices of
GaAsPBi in (001) were fixed to those of GaAs(001) and the lattice length in [001] direction
was relaxed. For the structures in Fig. S1, fully relaxations in all directions were carried
out in order to compare with the available experimental results.
The well-known underestimation of DFT band gaps were fixed by shifting up all DFT
values by 0.88 eV to give a good agreement with the experimental results of GaAs, GaAs1yP y,
and GaAs1-zBiz as shown in Fig. S1. Following the model used for the band gap of
GaAsNBi,[4] we expanded the band gap of GaAs1-y-zPyBiz in terms of the band gap of
GaAs1-yPy and GaAs1-zBiz using the following relationship.
EGaAs
1-y-z Py Biz
= EGaAs
1- y Py
+g (EGaAs
+ EGaAs
1-y Py
1-z Biz
- EGaAs
- EGaAs )(EGaAs
1-z Biz
- EGaAs )
(S1)
Wherein the EX is band gap of X and γ is a coupling factor. We calculated the band gaps of
21 GaAs1-y-zPyBiz structures and obtained the following relationships and a fitted γ value of
0.08.
EGaAs
= 1.42 + 0.811y - 0.118 y 2 - 0.059 y 3
EGaAs
= 1.42 - 6.429z + 9.293z 2 +14.224z 3
1- y Py
1-z Biz
EGaAs = 1.42
(S2)
The standard deviation of Eqn. S1 compared to the DFT values is about 40 meV. Because
1
the experimental data in Fig. S1 have y in the range 0-0.40 and z in the range 0-0.10, the
above equations and fitted  value should be considered applicable only for y and z values
close to the above-mentioned ranges. Note that GaAs1-yPy has a direct band gap for y < 0.48
and an indirect one for y ≥ 0.48. Therefore, the band gap formula for GaAs1-yPy in Eqn. S2
should only be used for y < 0.48.
Experimental band gap (eV)
2.0
1.5
0.88 eV
1.0
GaAsP
GaAs
0.5
GaAsBi
0.0
0.0
0.5
1.0
1.5
DFT gap (eV)
2.0
Figure S1. DFT band gaps versus experimental values for fully relaxed GaAs, GaAs1-yPy
(y = 0.093, 0.167, 0.250, 0.306, 0.333, and 0.398), and GaAs1-zBiz (z = 0.028, 0.046, 0.074,
and 0.102). The original DFT gaps are obviously underestimated, but a good agreement
with the experimental data is obtained after a constant upward shift of 0.88 eV. The
experimental band gaps of relaxed GaAs1-yPy and GaAs1-zBiz are from Ref. 5 and Ref. 6,
respectively.
[1] G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
[2] G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
[3] A. van de Walle, P. Tiwary, M. M. de Jong, D. L. Olmsted, M. D. Asta, A. Dick, D.
Shin, Y. Wang, L.-Q. Chen, and Z.-K. Liu, Calphad, 42:13, 2013.
[4] A. Janotti, S.-H. Wei, and S. B. Zhang, Phys. Rev. B 65, 115203 (2002).
[5] I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001).
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[6] M. Usman, C. A. Broderick, A. Lindsay, and E. P. O’Reilly, Phys. Rev. B 84, 245202
(2011).
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