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The electric potential is related to the density of the space-charge by Poisson equation:

(1.31)

where ψ represents the electrostatic potential, the local permittivity is given by ε, and ρ represents the density of the local space charge.

The total contribution from all charges which may be mobile or fixed, including holes, electrons and ionized impurities is expressed as local space charge density.

(1.32)

Where the elementary charge is given by q, n gives the electron concentration, p represents the concentration of holes, Na is the concentration of ionized acceptors and Nd is the concentration of ionized donor.

The electric field is obtained by the gradient of the potential as:

(1.33)