Band structure and carrier concentration of Gallium Arsenide Antimonide (GaAsSb)

Band structure and carrier concentration

Basic Parameters
Temperature Dependences
Dependence of the Energy Gap on Hydrostatic Pressure
Effective Masses
Donors and Acceptors

Basic Parameters

Energy gap	1.42-1.9x+1.2x² (for 0<x<0.3)
Effective conduction band density of states	2.5·10¹⁹·(0.063-0.0495x+0.0258x²)^3/2 cm^-3

	Band structure and carrier concentration of GaAs. 300 K E_g = 1.42 eV E_L = 1.71 eV E_X= 1.90 eV E_so = 0.34 eV
	Band structure and carrier concentration of GaSb. 300 K E_g= 0.726 eV E_L = 0.81 eV E_X = 1.03 eV E_so = 0.8 eV
	Variation of energy gap E_g with composition x for GaAs_1-xSb_x (Biryulin et al. (1979,a)).

For 0 < x < 0.3 at 300K:

Eg =1.42 - 1.9x + 1.2x²

Energy separation between L- valley of conduction band and top of the valence band
(curve 1; Rosenbaum and Woolley (1975))
and energy gap
(Curves 2-4; Taylor and Fortin (1970)) versus composition x.
2 - T=100 K, 3 - T=210 K, 1,4 -T=300 K.

Temperature Dependences

Temperature dependence of energy gap Eg for GaAs_1-xSb_x.
1 - x = 0.026,
2 - x = 0.05.
( Biryulin et al. (1979,b)).

For GaAs (x=0)

E_g=1.519-5.405·10^-4·T²/(T+204) (eV),

For GaSb (x=1)

E_g = 0.813 - 3.78·10^-4·T²(T+94) (eV),
where T is temperature in degrees K (0 < T < 300).

The temperature dependences of the intrinsic carrier concentration.
1 - x=0 (GaAs),
2 - x=0.3,
3 - x=0.8,
4 - x=1 (GaSb) .

Dependences on Hydrostatic Pressure

For GaAs (x=0)

       E_g = E_g(0) + 0.0126·P - 3.77·10^-5P² (eV)
       E_L = E_L(0) + 5.5·10^-3P (eV)
       E_X = E_X(0) + 1.5·10^-3P (eV)

For GaSb (x=1)

       E_g = E_g(0) + 14.5·10^-3P (eV)
       E_L = E_L(0) + 5.0·10^-3P (eV)
       E_X = E_X(0) - 1.5·10^-3P (eV),
where P is pressure in kbar.

Effective Masses

Electrons:

m_Γ=(0.063 - 0.0495x + 0.0258x²)m_o

Dependence of electron effective mass m on composition parameter x.
The curve is calculated.
Dashed part of the curve corresponds to the miscibility gap.
Symbols are experimental data taken from Delvin et al. (1981).

Holes:

Heavy	m_h = (0.51 - 0.11x) m_o
Light	m_lp = (0.082 - 0.032x )m_o
Split-off band	m_so = 0.15 m_o

Donors and Acceptors

Ionization energies of shallow donors (meV)

	S	Se	Te
x=0 (GaAs):	6	6	30
x=1 (GaSb): L	150	50	20
x=1 (GaSb): X	300	230	<80

For typical donor concentrations N_d≥10¹⁷ cm^-3 the shallow donor states in GaSb connected with Γ - valley did not appear.

Ionization energies of shallow acceptors (meV)

	Si	Zn	Ge
x=0 (GaAs):	30 100 220	25	30
x=1 (GaSb):	10	37	9

The dominant acceptor of undoped GaSb seems to be a native defect.
This acceptor is doubly ionizable: E_a1 =30, E_a2 =100.