NSM Archive - Gallium Indium Arsenide Antimonide (GaInAsSb)

GaInAsSb - Gallium Indium Arsenide Antimonide

Band structure and carrier concentration

Basic Parameters
Band structure
Intrinsic carrier concentration
Effective Density of States in the Conduction and Valence Band
Temperature Dependences
Dependences on Hydrostatic Pressure
Band Discontinuities at Heterointerfaces
Effective Masses and Density of States
Donors and Acceptors

Basic Parameters for Ga_xIn_1-xAs_ySb1-y

Zinc Blende crystal structure

		Remarks	Referens
Energy gaps, E_g	(0.29 -0.65x+0.6x²) eV	300 K; compositions lattice-matched to GaSb.	Mikhailova M.P. (1999)
	(0.36 -0.23x+0.54x²) eV	_{300 K; compositions lattice-matched to InAs.}
Electron affinity	(4.87 -0.81x) eV	300 K; compositions lattice-matched to GaSb.
	(4.9 -0.83x) eV	_{300 K; compositions lattice-matched to InAs.}
*Conduction band*
Energy separation between X valley and top of the valence band E_X	see Energy separations	300 K; compositions lattice-matched to GaSb and _InAs.	Mikhailova M.P. (1999)
Energy separation between L valley and top of the valence band E_L	see Energy separations	300 K; compositions lattice-matched to GaSb and _InAs.
Effective conduction band density of states	2.5x10¹⁹(0.022+0.03x -0.012x²)^3/2 cm^-3	300 K; compositions lattice-matched to GaSb.
	2.5x10¹⁹(0.023+0.032x -0.012x²)^3/2 cm^-3	_{300 K; compositions lattice-matched to InAs.}
*Valence band*
Energy separation of spin-orbital splitting E_so	see Energy of spin-orbital splitting	300 K; compositions lattice-matched to GaSb.	Mikhailova M.P. (1999)
Effective valence band density of states	2.5x10¹⁹(0.41+0.16x +0.23x²) ^3/2 cm^-3	300 K; compositions lattice-matched to GaSb.
	2.5x10¹⁹(0.41+0.14x +0.23x²) ^3/2 cm^-3	_{300 K; compositions lattice-matched to InAs.}
Intrinsic carrier concentration	*** cm^-3	300 K

Band structure for Ga_xIn_1-xAs_ySb_1-y

	Ga_xIn_1-xAs_ySb_1-y (zinc blende, cubic). Band structure of alloys lattice-matched to InP. Important minima of the conduction band and maxima of the valence band.. For details see Mikhailova M.P. (1999) .
	Ga_xIn_1-xAs_ySb_1-y. Energy gap E_g of vs. lattice constant Yakovlev et al.(1988)
	Ga_xIn_1-xAs_ySb_1-y. Energy gap E_g of vs. x for lattice-matched to GaSb. Experimental points are taken from five different source. Arrows show region of miscibility gap. 1 - T= 300 K; 2 - T= 77K. Mikhailova and Titkov (1994)
	Ga_xIn_1-xAs_ySb_1-y. Energy separations between G , L and X condition band minima and top of the valence band vs. composition parameter x for lattice-matched to GaSb. Adachi (1987)
	Ga_xIn_1-xAs_ySb_1-y. Energy separations between G , L and X condition band minima and top of the valence band vs. composition parameter x for lattice-matched to InAs. Adachi (1987)
	Ga_xIn_1-xAs_ySb1-y. Energy of spin-orbital splitting Eso vs. composition parameter x for GaInAsSb lattice-matched to GaSb. Tournie (1990)
	Ga_xIn_1-xAs_y_Sb1-y. Energy gap E_g of vs. x for lattice-matched to InAs. 1 - T= 300 K; 2 - T= 77K. Voronina et al.(1991,a)

Within a whole range of the compositions the is a direct gap semiconductor.
For Ga_xIn_1-xAs_ySb1-y compositions lattice-matched to GaSb there is a miscibility gap for 0.25<x<0.75 with a critical temperature estimated to be 1467^oC
(Cherng et al.(1986))
For Ga_xIn_1-xAs_ySb1-y compositions lattice-matched to GaSb :

E_g ~= 0.725x +0.290(1-x) -0.6x(1-x) (eV)	(300K)	Karouta et al.(1987)
E_g ~= 0.801x +0.354(1-x) -0.6x(1-x) (eV)	(77K)
where T is temperature in degrees K

For Ga_xIn_1-xAs_ySb1-y compositions lattice-matched to InAs :

E_g ~= 0.36x -0.23x +0.54x² (eV)	(300K)	Karouta et al.(1987)
E_g ~= 0.41x -0.29x +0.66x² (eV)	(77K)
where T is temperature in degrees K

Brillouin zone of the face centered cubic lattice, the Bravais lattice of the diamond and zincblende structures.

Brillouin zone of the hexagonal lattice.

Temperature Dependences

The energy gap versus temperature for Ga_xIn_1-xAs_yP_1-y

GaSb (x=1, y=0)	E_g ~= 0.813 - 3.78·10^-4xT²/(T+94) (eV)	0 < T < 300	Wu and Chen (1992)
InAs (x=0, y=1)	E_g = 0.415 - 2.76·10^-4xT²/(T+83) (eV)		Fang et al. (1990)
Ga_0.07In_0.93As_0.88Sb_0.12	E_g ~= 0.378 - 4.27·10^-4xT²/(T+288) (eV)		Gong et al. (1994)
	where T is temperature in degrees K

Lasing wavelength λ₀

Intrinsic carrier concentration:

n_i = (N_c·N_v)^1/2exp(-E_g/(2k_BT))

	Ga_xIn_1-xAs_ySb1-y. Intrinsic carrier concentration vs. temperature for Ga_xIn_1-xAs_ySb_1-yalloys lattice-matched to GaSb. 1 -- x= 0; 2 -- x= 0.2; 3 -- x= 0.8; 3 -- x= 1.0. Mikhailova M.P. (1999)
	Ga_xIn_1-xAs_ySb1-y. Intrinsic carrier concentration vs. temperature for Ga_xIn_1-xAs_ySb_1-yalloys lattice-matched to InAs. 1 -- x= 0; 2 -- x= 0.2; 3 -- x= 0.8; 3 -- x= 1.0. Mikhailova M.P. (1999)

Effective density of states in the conduction band: N_c

N_c ~= 4.82 x 10¹⁵ · (m_Γ/m₀)^3/2T^3/2 (cm^-3) ~= 4.82 x 10¹⁵ · (0.022 +0.03x -0.012x²)^3/2T^3/2 (cm^-3) :
(for GaInAsSb alloys lattice-matched to GaSb)

N_c ~= 4.82 x 10¹⁵ · (m_Γ/m₀)^3/2T^3/2 (cm^-3) ~= 4.82 x 10¹⁵ · (0.023 +0.032x -0.012x²)^3/2T^3/2 (cm^-3) :
(for GaInAsSb alloys lattice-matched to InAs)

Effective density of states in the valence band: N_v

N_v ~= 4.82 x 10¹⁵ · (m_h/m₀)^3/2T^3/2 (cm^-3)= 4.82 x 10¹⁵ · (0.41 +0.16x +0.23x²)^3/2T^3/2 (cm^-3) :
(for GaInAsSb alloys lattice-matched to GaSb)

N_v ~= 4.82 x 10¹⁵ · (m_h/m₀)^3/2T^3/2 (cm^-3)= 4.82 x 10¹⁵ · (0.41 +0.14x +0.23x²)^3/2T^3/2 (cm^-3) :
(for GaInAsSb alloys lattice-matched to InAs)

Dependence on Hydrostatic Pressure

Band Discontinuities at Heterointerfaces

at GaInAsSb/GaSb and GaInAsSb/InAs heterojunctions.

	Ga_xIn_1-xAs_ySb1-y. *Valence band discontinuity offset ΔE_v* vs. concentration x** for lattice-matched Ga_xIn_1-xAs_ySb1-y/GaSb heterostructure. Mebarki et al. (1993)
	Ga_xIn_1-xAs_ySb1-y. *Valence band discontinuity offset ΔE_v* vs. concentration x for lattice-matched Ga_xIn_1-xAs_ySb1-y/InAs** heterostructure. Nakao et al. (1984)
	Ga_xIn_1-xAs_ySb1-y. *Conduction band discontinuity offset ΔE_c* vs. concentration x** for lattice-matched Ga_xIn_1-xAs_ySb1-y/GaSb heterostructure. Mikhailova M.P. & Titkov (1994)

Effective Masses and Density of States:

Electrons

Effective Electron Masses		Remarks	Referens
Effective electron mass m_e	0.022+0.03x -0.012x² m_o	300K; for GaInAsSb lattice-matched to GaSb	Mikhailova M.P. (1999)
	0.023+0.032x -0.012x² m_o	300K; for GaInAsSb lattice-matched to InAs

Holes

		Remarks	Referens
Effective mass of density of states m_v	m_v ~= 0.41 +0.16x +0.023x² m_o	300K; for GaInAsSb lattice-matched to GaSb	Mikhailova M.P. (1999)
	m_v ~= 0.41 +0.14x +0.023x² m_o	300K; for GaInAsSb lattice-matched to InAs	Mikhailova M.P. (1999)

Donors and Acceptors

Undoped Ga_xIn_1-xAs_ySb1-y compositions ( 0 < x < 0.2 ) have the conductivity of p-type .
Three native acceptor traps have been observed for these compositions :
E_t -E_v 0.01 eV
(E_c -E_v₎ ~= 0.03--0.035 eV
(E_t -E_v₎ ~= 0.07 eV
Undoped Ga_xIn_1-xAs_ySb1-y compositions ( 0.76 <x < 1 ) have the conductivity of n-type.

Ionization energies of Shallow Donors			Remarks
Te (donor)	E_c -E_t	~ 5x10^-3 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
	E_c -E_t	0.04 -- 0.05 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
	E_c -E_t	0.09 -- 0.1 eV	Ga_xIn_1-xAs_ySb1-y (0.8 < x)	Voronina et al.(1991,a)
Ionization energies of Shallow Acceptor
Ge, Cd (acceptor)	E_t -E_v	~ 0.01 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
Ge +V_ac(acceptor)	E_t -E_v	~ 0.017 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
Cd +V_ac (acceptor)	E_t -E_v (acceptor)	~ 0.017 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
Zn (acceptor)	E_t -E_v	~ 0.1 -- 0.15 eV	Ga_xIn_1-xAs_ySb1-y (0 < x <0.2)	Baranov et al.(1990), Voronina et al.(1991,b)
Mn	E_t -E_v	~ 0.02 -- 0.25 eV	Ga_xIn_1-xAs_ySb1-y (0.8 < x)	Voronina et al.(1991,a)