Doping

Doping

n=N_c\cdot e^{\frac{-(E_c-E_F)}{kT}}

p=N_v\cdot e^{\frac{-(E_F-E_v)}{kT}}

$E_c$ is the position of the conduction band minimum
$E_v$ is the position of the valence band maxmimum
$k$ is Boltzmann’s constant
$N_x$ are the effective density of states

np=n_i^2

$n_i$ = Intrinsic carrier concentration

n_i=\sqrt{N_cN_v}e^{\frac{-E_g}{2kt}}

$E_g$ = Band Gap = $E_c-E_v$

Substitutional Doping

Donated electrons are delocalised
Ions are immobile

N_c \equiv 2 \left[ \frac{2\pi m_nkT}{h^2}\right]^{3/2}

N_v \equiv 2 \left[ \frac{2\pi m_pkT}{h^2}\right]^{3/2}