A semiconductor having both donors (concentration N_d) and acceptors (concentration N_a) in the same region is called compensated semiconductor. An n-type compensated semiconductor has
N_d > N_a , and a p-type has N_a > N_d. The semiconductor is completely compensated if N_a = N_d. Compensated semiconductors occur naturally during device fabrication.

In thermal equilibrium, a semiconductor is electrically neutral, so that

where n_e is the concentration of electron and n_p is the concentration of holes, n_d is the concentration of unionized donors and p_a is the concentration of unionized acceptors.

If there is complete ionization, then  and are both zero, and the above takes the form