Theory

Self-consistent calculation

In self-consistent calculation the eigenvalue problem and Poisson equation are solved simultaneously:

(45)

where Vb is band edge potential, Vs is self-consisting potential from the Poisson equation, F is eight component envelope wave function, n(z) is free electron density profile, p(z) is free hole density profile:

(46)

where f_e and f_h are the Fermi-Dirac distribution for electrons and holes, E_fe and E_fh are chemical potentials for electrons and holes, T is temperature and e is absolute electron charge.
Practically, the system of equations (45) is solved iteratively. At first, the eigenvalue problem is solved, than after getting the charge distribution the Poisson equation is solved and so on. The convergence is good and typically several iterations is enough.