Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 35 : Diffusion
Fermi level in a material remains uniform inside a material, i.e. $ \nabla E_F =0$ Thus
$\displaystyle \nabla p = \frac{p}{kT}\nabla E_F^i\eqno (B)$
  Thus diffusion takes place when there exists an intrinsic Fermi level gradient. In order to evaluate the gradient of $ E_F^i$, consider the valence band. The kinetic energy of the holes is the difference between the energy of the top of the valence band and the total energy of the holes. Thus the energy at the top of the valence band is the potential energy of the holes. Similarly, the energy at the bottom of the conduction band is the potential energy of the electrons. As the intrinsic Fermi energy depends on these two energy levels, temperature and other constants, the change in the electron or hole energy is also given by the difference between the intrinsic Fermi energy $ E_F^i$ and the (uniform) Fermi energy $ E_F$,
 
$\displaystyle q\phi = (E_F-E_F^i)$
  The electric field, $ E(x)$ is then given by
 
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