The Junction at Equilibrium Zero Bias

The profile of the electrostatic potential V in an MS junction can be calculated by solving Poisson s equation 

is the dielectric permittivity of the semiconductor. The charge density is given by 

Although Eqs. (14.2) and (14.4) can be solved analytically (as will be shown in the next section), here it is sufficient to use the renowned depletion, or Schottky approximation, in which it is assumed that the effective density of charge is constant and equal to qN in the depletion region, and zero outside this region. In this case, a double integration of Eq. (14.2) directly gives 

Finally, the total charge per irnit area due to the uncompensated donors in the depletion region is given by 

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