Away from equilibrium the ionization of donors and acceptors is still given by Equation 3-41 and Equation 3-42, except that the relevant quasi-Fermi level should be used in the equation system:

It is often more convenient to express Equation 3-86 in terms of the carrier concentrations rather than the relevant quasi-Fermi levels. From Equation 3-49:

Substituting Equation 3-86 into Equation 3-87 gives:

where ΔEd=Ec-Ed and ΔEa=Ea-Ev. Equation 3-88 is used in COMSOL Multiphysics when incomplete ionization with the standard ionization model is chosen in the Dopant Ionization section of the Semiconductor Material Model node. It is also possible to select a user defined ionization model, in which case the ionization ratios are specified directly by user-defined expressions. If complete ionization is chosen (the default) then Nd+=Nd and Na–=Na.