Band structure and carrier concentration of Gallium Phosphide (GaP)

Band structure and carrier concentration

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

Basic Parameters

Energy gap	2.26 eV
Energy separation E_o (Γ_1c - Γ_15ν)	2.78 eV
Energy spin-orbital splitting	0.08 eV
Intrinsic carrier concentration	2 cm^-3
Effective conduction band density of states	1.8·10¹⁹ cm^-3
Effective valence band density of states	1.9·10¹⁹ cm^-3

Band structure and carrier concentration of GaP.
Important minima of the conduction band and maxima of the valence band. 300 K E_g = 2.26 eV
E_L = 2.6 eV
E_o = 2.78 eV
E_so = 0.08 eV

Temperature Dependences

Temperature dependence of the direct energy gap.

E_g=2.34-6.10^-4·[T²/(T+460)] (eV),
where T is temperature in degrees K (0 < T < 1200),
(Panish and Casey [1969]).

Temperature dependence of the direct band gap E_o

E_o=2.866-0.108·[coth(164/T)-1] (eV),
where T is temperature in degrees K (0 < T < 300),
(Takizawa [1983]).

Effective density of states in the conduction band

N_c≈3.4·10¹⁵·T^3/2 (cm^-3)

Effective density of states in the valence band

N_n≈3.6·10¹⁵·T^3/2 (cm^-3)

	The temperature dependence of the intrinsic carrier concentration.
	Fermi level versus temperature for different concentrations of shallow donors and acceptors.

Dependences on Hydrostatic Pressure

,
where P is pressure in kbar;
(Ves et al. [1985]).

Energy Gap Narrowing at High Doping Levels

Energy gap narrowing versus donor (curve 1) and acceptor (curve 2) doping density, T= 300 K,
(calculated according Jain et al. [1990]).

For n-type GaP

ΔE_g = 10.7·10^-9·N_d^1/3 + 3.45·10^-7·N_d^1/4 + 9.97·10^-12·N_d^1/2 (eV)
(Jain et al. [1990]).

For p-type GaP:

ΔE_g = 12.7·10^-9·N_a^1/3 + 5.85·10^-7·N_a^1/4 +3.90·10^-12·N_a^1/2 (eV)
(Jain et al. [1990]).

Effective Masses

Electrons:
The surfaces of equal energy are ellipsoids (X-valley)
	m_l = 1.12m_o
	m_t = 0.22m_o
Effective mass of density of states
m_c=(9m_lm_t²)^1/3	m_c=0.79m_o
Effective mass of conductivity	m_cc=0.35m_o
For Γ-valley	m_Γ = 0.09m_o
For L-valley	m_l = 1.2m_o
	m_t = 0.15m_o
Holes:
Heavy	m_h = 0.79m_o
Light	m_lp = 0.14m_o
Effective mass of density of states	m_v = 0.83m_o

Donors and Acceptors

Ionization energies of shallow donors (eV)

S_p	Se_p	Te_p	Li_p	Ge_Ga	Si_Ga	Sn_Ga	Li_Ga
0.107	0.105	0.093	0.091	0.204	0.085	0.072	0.061

(Dean [1973), Kopilov and Pikhtin [1978]).

Ionization energies of shallow acceptors (eV)

Ge_p	C_p	Si_p	Be_Ga	Cd_Ga	Mg_Ga	Zn_Ga
0.265	0.0543	0.210	0.0566	0.1022	0.0599	0.0697

(Dean [1973]).

Most important deep levels

Impurity	Position in the forbidden gap
O_p(donor)	E_c - 0.89 (eV)
Cr (acceptor)	E_c - 1.2 (eV)
	E_c - 0.5 (eV)
Radiative centers(Baegh and Dean[1976])
N	Ev + 0.008 (eV)
Zn_Ga - O_p	E_c - 0.3 (eV)
Capture cross section for electrons to neutral Zn-O complex (at 300 K)	σ_n~(1.5÷4.5)·10^-16 (cm²)
Capture cross section for holes to negative Zn-O complex (at 77 K):	σ_p ~ 5·10^-17 (cm²
Cd_Ga - O_p	E_c - 0.40 (eV)
Mg - O	E_c - 0.14 (eV)

(Dean and Henry [1968], Clerjaud et al. [1981]).