Consider ntype gallium arsenide at room temperature T 300 K

Consider n-type gallium arsenide at room temperature (T = 300 K), with fully ionized donors (N_D = 10^14 cm^-3, N_A = 0): a. Using the conduction and valence band effective densities of state, calculate the intrinsic level energy E_i. b. Calculate the Fermi level position with respect to the intrinsic level, defined as E_F - E_i. Please pay attention to the sign. c. Calculate the Fermi level position with respect to the top of the valence band, defined as E_F - E_v. Please pay attention to the sign.

Solution

Solution:-
a Given temperature, T = 300 K, and intrinsic GaAs.
From Table 5.1 (in the textbook), ni = 1.8 × 106 cm-3, µe 8500 cm2 V-1 s-1 and µh 400 cm2V-1s-1.
Thus,
= eni(µe + µh)
= (1.602 × 10-19C) (1.8 × 106 cm-3)(8500 cm2 V-1 s-1 + 400 cm2 V-1 s-1)
= 2.57 × 10-9 -1 cm-1
= 1/ = 3.89 × 108 cm.
b Donors are now introduced. At room temperature, n = Nd = 1015 cm-3 >> ni >> p.
n = eNdµe (1.602 × 10-19 C)(1015 cm-3)(8500 cm2 V-1 s-1) = 1.36 -1 cm-1
n = 1/n = 0.735 cm

In the intrinsic sample, EF = EFi,

ni = Ncexp[(Ec EFi)/kT]----------- (1)
In the doped sample, n = Nd, EF = EFn,
n = Nd = Ncexp[(Ec EFn)/kT] ---------(2)
Eqn. (2) divided by Eqn. (1) gives,
Nd/ni
= exp(EFn EFi)/kT-------(3)
EF = EFn EFi = kT ln(Nd/ni)---------(4)

Substituting we find,
EF = (8.617 × 10-5 eV/K)(300 K)ln[(1015 cm-3)/(1.8 × 106 cm-3)]

EF = 0.521 eV above EFi (intrinsic Fermi level)