At the metallurgical junction, x = 0, the electric field is continuous, which requires
that the following condition has to be fulfilled
Outside the space-charge region the material is electrically neutral and therefore the
electric field is zero there.
The profile of the electrostatic potential is calculated by integrating the electric field
throughout the space-charge region and applying the boundary conditions,
We define the zero electrostatic potential level at the outside edge of the p-type
semiconductor. Since we assume no potential drop across the quasi-neutral region the
electrostatic potential at the boundary of the space-charge region in the p-type material is
also zero,
Using Eqs. (8.7) for describing the electric field in the n- and p-doped regions of the
spacecharge region, and taking into account that at the metallurgical junction the
electrostatic potential is continuous, we can write the solution for the electrostatic
potential as
Under equilibrium a difference in electrostatic potential, V bi , develops across the
spacecharge region. The electrostatic potential difference across the p-n junction is an
important characteristic of the junction and is denoted as the built-in voltage or diffusion
potential of the p-n junction. We can calculate V bi as the difference between the
electrostatic potential at the edges of the space-charge region,
Using Eq. (8.11a) we obtain for the built-in voltage
The built-in potential V bi can also be determined with using the energy-band diagram
presented in Fig. 8.3 b).