Question

1) Calculate the difference in energy between the intrinsic Fermi level and the midgap energy at T = 300 K for Si.

2) Determine the electron and hole concentrations in Si at 300 K for NA = 1016 cm-3 and ND = 3 x 1015 cm-3 . You must derive the equations used to determine the concentrations

Answer 1

1)

$n_i^2=N_cN_vexp[Eg/KT]$ from this We get, $n_i=1.5*10^{10}cm^{-3}.$

At temperature T = 300K the values of effective density of states function in the conduction band ($N_c$ ) and the effective density of states function in the valence band ($N_v$ ) are $2.8*10^{25}m^{-3}$ and $1.04*10^{25}m^{-3}$ respectively. Assume the value of bandgap energy ($E_g$ ) of silicon is 1.12 eV does not vary over this temperature range.

2)

The majority carrier electron concentration is

$n_o = ½((10^{16} – 3 * 10^{15} ) + (((10^{16} – 3 * 10^{15} )^2 + 4(1.5 * 10^{10})^2 )^{1/2} ) ≅ 7 * 10^{15} cm^{-3}$

The minority carrier hole concentration is

$p_0 = \frac{ni_2}{n_0} = (1.5 * 10^{10} )^2/(7 * 10^{15}) = 3.21 * 10^4 cm^{-3}$

If we assume complete ionization and $N_d - N_a >> n_i$ , the majority carrier electron concentration is a very good approximation, just the difference between the donor and acceptor concentrations.