Module 6 : PHYSICS OF SEMICONDUCTOR DEVICES
Lecture 35 : Diffusion
Diffusion
Diffusion is the process by which particles move from a region of higher concentration to a region of lower concentration. If the process is left undisturbed, it would result in uniform density of particles in the medium. The following points are to be noted about diffusion :
Diffusive motion takes place because of random thermal motion.
Diffusion takes place irrespective of whether the particles are charged or not.
Diffusion of particles takes place along the concentration gradient, i.e. from a region of higher concentration to
  that of lower concentration.
  If the particles of the medium are charged carriers, like electrons and holes in a semiconductor, the diffusion along the concentration gradient results in a current, known as diffusion current. Unlike the drift current , the diffusion current depends on gradient of concentration rather than on the concentration itself. If the carriers are electrons, the diffusion current is proportional to $ \nabla n$, where $ n$ is the electron density. Likewise, the hole diffusion current is proportional to $ \nabla p$.
  Consider the diffusive motion of holes in one dimension. If $ p(x)$ is the concentration at $ x$, and $ dp/dx>0$, i.e., if the concentration is increasing where $ E_F^i$ is the intrinsic Fermi level and $ E_F$ is the Fermi level in the presence of acceptor impurities (we have dropped the redundant superscript $ p$). Thus
 
$\displaystyle \nabla p$ $\displaystyle =$ $\displaystyle \frac{p_i}{kT}e^{(E_F^i-E_F)/kT}(\nabla E_F^i-\nabla E_F)$
$\displaystyle =$ $\displaystyle \frac{p}{kT}(\nabla E_F^i-\nabla E_F)$
 
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