III-V binaries

Lattice parameters and bandgap

System		Si	GaP	GaAs	GaSb	InP	InAs	InSb
Lattice parameters(Å)	Calculation	5.421	5.474	5.689	6.134	5.939	6.138	6.556
	Experiment at 0K	5.430	5.442	5.642	6.082	5.861	6.050	6.469
	Deviation	-0.009	0.032	0.047	0.052	0.078	0.088	0.087
Bandgap (eV)	Calculation	1.19	2.36	1.47	0.64	1.43	0.36	0.03
	Experiment at 0K	1.17	2.34	1.52	0.81	1.42	0.41	0.24
	Deviation	0.02	0.02	-0.05	-0.17	0.01	-0.05	-0.21

Transitions in bandgap nature in different III-V binary semiconductors

As valence band maxima in all cases remains at the Γ-point, the location of conduction band minimum (CBM) solely determines the nature of bandgap and hence, the different transitions.

System	Transition**			CBM transition path		References
System	Type*	Isotropic strain (%)	Biaxial strain (%)	Isotropic strain	Biaxial strain	References
Si	IDT	10.31 (t)	×	Δ_m→ L → Γ (t)	Δ_m → K → L (c)	1
GaP	IDT	2.63 (t)	×	Δ_m → L → Γ (t)	Δ_m → L (c)	2,3,4
GaAs	DIT	1.56 (c)	3.52 (t)	Γ → L → Δ_m → X (c)	Γ → Δ_m (t)	5,6,7,8,9,10,11,12
GaSb	DIT	1.00 (c)	3.71 (t)	Γ → L → Δ_m (c)	Γ → Δ_m (t)	13
InP	DIT	4.40 (c)	7.66 (t)	Γ → X (c)	Γ → Δ_m (t)	13
InAs	DIT	7.41 (c)	×	Γ → X (c)	×	13
InSb	DIT	5.18 (c)	×	Γ → L → Δ_m (c)	×	14

* The DIT and IDT correspond to the direct to indirect and indirect to direct transition respectively.
** The 't' and 'c' in brackets correspond to tensile and compressive strain, respectively.
× No transitions within ±10% of strain.
Δ_m = [0.0000, 0.4231, 0.4231] in reciprocal space.
CBM : conduction band minimum.

Direct to Indirect Transitions (DIT) in different III-V binary semiconductors under hydrostatic pressure

System	Transition			CBM transition path
	Strain(%)		Pressure (GPa)	CBM transition path
	Theory	Experiment	Theory	Experiment	Theory
GaAs	1.56	2.75	3.94	G→L	G→X
GaSb	1.00	1.54	1.85	G→L	G→L
InP	4.40	5.16	13.36	G→X	G→X
InAs	7.41	8.17	24.22	G→X	G→X
InSb	5.18	4.23	11.20	G→L	G→X

For the strain-pressure conversion the third order Birch-Murnaghan eqation of state is used. \[ P(V) = {3\over 2}B_0 \left[\left({V_0 \over V}\right)^{7\over 3} - \left({V_0 \over V}\right)^{5\over 3}\right] \times \left\{1+{3\over4}(B_0'-4)\left[\left({V_0 \over V}\right)^{2\over 3} -1\right] \right\} \]
The bulk modulus data that are used in the above conversions [ref.]: \(B_0\)(GPa)={Si: 98, GaP: 88.7, GaAs: 74.8, GaSb: 57, InP: 71, InAs: 60, InSb: 47.4}
The 1st derivative of bulk modulus data that are used in the above conversions [ref.]: \( B_0'\)={Si: 4.16, GaP: 4.77, GaAs: 4.67, GaSb: 4.80, InP: 4.90, InAs: 4.80, InSb: 4.90}

Biaxial strain summary data in different III-V binary semiconductors

System/Substrate	Si			GaP			GaAs			GaSb			InP			InAs			InSb
System/Substrate	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature	Strain (%)	E_g (eV)	Nature
Si	0.00	1.19	I	0.98 (t)	1.24	I	4.94 (t)	1.41	I	13.15 (t)	0.46	D	9.55 (t)	1.30	I	13.23 (t)	0.43	D	20.94 (t)	--	--
GaP	0.97 (c)	2.31	I	0.00	2.36	I	3.93 (t)	1.98	D	12.06 (t)	0.17	D	8.50 (t)	0.92	D	12.13 (t)	0.16	D	19.77 (t)	--	--
GaAs	4.71 (c)	1.78	I	3.78 (c)	1.84	I	0.00	1.47	D	7.82 (t)	0.00	--	4.39 (t)	0.45	D	7.89 (t)	0.00	--	15.24 (t)	0.00	--
GaSb	11.62 (c)	0.25	I	10.76 (c)	0.34	I	7.25 (c)	0.70	I	0.00	0.64	D	3.18 (t)	0.00	--	0.07 (t)	0.62	D	6.88 (t)	0.00	--
InP	8.72 (c)	1.92	I	7.83 (c)	2.00	I	4.21 (c)	2.21	D	3.28 (c)	2.03	D	0.00	1.43	D	3.35 (t)	0.82	D	10.39 (t)	0.00	--
InAs	11.68 (c)	1.33	I	10.82 (c)	1.41	I	7.32 (c)	1.66	D	0.07 (c)	0.37	D	3.24 (c)	0.93	D	0.00	0.36	D	6.81 (t)	0.00	--
InSb	17.31 (c)	--	--	16.50 (c)	--	--	13.22 (c)	0.54	I	6.44 (c)	1.13	I	9.41 (c)	0.91	I	6.38 (c)	1.13	I	0.00	0.03	D

Linear interpolation/extrapolation is used to determine the exact bandgap magnitudes in between DFT data and close to the >10% of strain where no DFT data are available.
The 't' and 'c' in brackets correspond to tensile and compressive strain, respectively.

Semiconductor to metal (SMT) and Semiconductor to semi-metal transitions (SsMT) in different III-V binary semiconductors

System		Si	GaP	GaAs	GaSb	InP	InAs	InSb
ΔE_Γ (eV)		3.14	2.99	1.47	0.64	1.43	0.36	0.03
SMT*	Isotropic strain (%)	~15.00 (t)	~13.00 (t)	6.67 (t)	2.85 (t)	8.20 (t)	2.10 (t)	0.34 (t)
SMT*	Biaxial strain (%)	×	×	7.86 (c)	5.00 (c)	9.90 (c)	4.74 (t), 4.36 (c)	0.34 (t), 0.34(c)
SsMT*	Isotropic strain (%)	×	×	×	×	×	×	×
SsMT*	Biaxial strain (%)	3.70 (t), 6.50 (c)	8.45 (t), 9.83 (c)	8.00 (t)	5.07 (t)	10.38 (t)	×	×

ΔE_Γ = Energy difference between conduction band and valence band at the Γ-point.
* The 't' and 'c' in brackets correspond to tensile and compressive strain, respectively.
× No transitions within ±10% of strain.

Note: These transitions depend on the closing of the CBM and VBM gaps. As the VBM always remains at the Γ point, therefore these transition points depend on ΔE_Γ. As the ΔE_Γ increased, so did the S(s)MTs.