Question

For a semiconductor material, the number of free electrons per unit volume in the conduction band is given by the expression: and the number of holes per unit volume in the valence band is given by: exp kT where m and mp are the effective masses of the electrons and holes.

Use the equations for n and p on page 3 to obtain an expression for the intrinsic carrier concentration ni .   HINT: Use the mass action law: np=n²_i.

Answer 1

Using $n_i^2=np$

$n_i^2=np=2\left ( \frac{2\pi m_n^* KT}{h^2} \right )^{3/2}exp\left [ \frac{E_F-E_C}{KT} \right ]*2\left ( \frac{2\pi m_p^* KT}{h^2} \right )^{3/2}exp\left [ \frac{E_V-E_F}{KT} \right ]$

$n_i^2=4\left ( \frac{2\pi KT}{h^2} \right )^{3}(m_n^*m_p^*)^{3/2}exp\left [ \frac{-(E_C-E_V)}{KT} \right ]$

$n_i^2=4\left ( \frac{2\pi KT}{h^2} \right )^{3}(m_n^*m_p^*)^{3/2}exp\left [ \frac{-(E_g)}{KT} \right ]$

Intrinsic carrier concentration is $n_i=2\left ( \frac{2\pi KT}{h^2} \right )^{3/2}(m_n^*m_p^*)^{3/4}exp\left [ \frac{-(E_g)}{2KT} \right ]$