stem/Semiconductors/Doping.md

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}