Band structure and carrier concentration of Gallium Antimonide (GaSb)

Band structure and carrier concentration

Basic Parameters
Temperature Dependences
Dependence of the Energy Gap on Hydrostatic Pressure
Energy Gap Narrowing at High Doping Levels
Effective Masses
Donors and Acceptors

Basic Parameters

Energy gap	0.726 eV
Energy separation (E_ΓL) between Γ and L valleys	0.084 eV
Energy separation (E_ΓX) between Γ and X valleys	0.31 eV
Energy spin-orbital splitting	0.80 eV
Intrinsic carrier concentration	1.5·10¹² cm^-3
Intrinsic resistivity	10³ Ω·cm
Effective conduction band density of states	2.1·10¹⁷ cm^-3
Effective valence band density of states	1.8·10¹⁹ cm^-3

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

Temperature Dependences

Temperature dependence of the energy gap
(Wu and Chen [1992])

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

Temperature dependence of energy E_L

E_L = 0.902 - 3.97·10^-4·T²/(T+94) (eV)

Temperature dependence of energy E_X
(Lee and Woolley [1981])

E_X = 1.142 - 4.75·10^-4·T²/(T+94) (eV)

Effective density of states in the conduction band

N_c = 4.0·10¹³·T^3/2 (cm^-3)

Effective density of states in the conduction band

N_c = 4.0·10¹³·T^3/2 (cm^-3)

Effective density of states in the valence band

N_v = 3.5·10¹⁵·T^3/2 (cm^-3)

The temperature dependences of the intrinsic carrier concentration.

Dependences on Hydrostatic Pressure

       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.

Energy Gap Narrowing at High Doping Levels

Energy gap narrowing versus acceptor acceptor doping density.
Curve is calculated for p-GaSb according to Jain et al. [1990].
Points show experimental results (Titkov et al. [1981]).

For n-type GaSb
(Jain et al. [1990]):

E_g = 13.6·10^-9·N_d^1/3 + 1.66·10^-7·N_d^1/4 + 119·10^-12·N_d^1/2 (eV)

For p-type GaSb
(Jain et al. [1990]):

E_g = 8.07·10^-9·N_a^1/3 + 2.80·10^-7·N_a^1/4+ 4.12·10^-12·N_a^1/2 (eV)

Effective Masses

Electrons:

For Γ-valley	m_Γ = 0.041m_o
In the L- valley the surfaces of equal energy are ellipsoids
	m_l= 0.95m_o
	m_t= 0.11m_o
Effective mass of density of states
	m_L= 16(m_lm_t²)^1/3= 0.57m_o
In the X- valley the surfaces of equal energy are ellipsoids
	m_l= 1.51m_o
	m_t= 0.22m_o
Effective mass of density of states
	m_X= 9(m_lm_t²)^1/3= 0.87m_o

Holes:

Heavy	m_h = 0.4m_o
Light	m_lp = 0.05m_o
Split-off band	m_so = 0.14m_o
Effective mass of density of states	m_v = 0.8m_o
Effective mass of density of conductivity (Heller and Hamerly [1985])	m_vc = 0.3m_o

Donors and Acceptors

The diagram of IV group donor states
(Vul' et al. [1970]).

Ionization energies of shallow donors (eV)

Te(L)	Te(X)	Se(L)	Se(X)	S(L)	S(X)
~0.02	≤0.08	~0.05	~0.23	~0.15	~0.30

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

Ionization energies of shallow acceptors (eV):

The dominant acceptor of undoped GaSb seems to be a native defect.
This acceptor is doubly ionizable

E_a1	E_a2	Si	Ge	Zn
0.03	0.1	~0.01	~0.009	~0.037