Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 34 : Fermi Energy
  where $ n_i$ is the intrinsic electron density. In a similar way one can show that for $ p$ type impurities, the concentration of holes is given by
  where $ p_i\ (=n_i)$ is intrinsic hole density. Thus
 
$\displaystyle \boxed{np = n_ip_i= n_i^2}$
  This relationship is known as the Law of Mass Action .
  Taking the logarithm of the equations for $ n$ and $ p$, the shift in the Fermi energies due to doping for n- type and p-type semiconductors are given by
 
$\displaystyle E_F^n-E_F^i$ $\displaystyle =$ $\displaystyle kT\ln\frac{n}{n_i}$
$\displaystyle E_F^i-E_F^p$ $\displaystyle =$ $\displaystyle kT\ln\frac{p}{p_i}$
   
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