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Distinct electron and hole quasi-Fermi potentials, øf,n and øf,p, are included into a one-dimensional SOI MOSFET model that accounts for finite inversion and depletion layer thicknesses. The inclusion of øf,n, øf,p in the nonlinear analytical model is demonstrated to describe phenomena like kink effect and the multistable-charge-controlled-memory effect (MCCM) in SOI MOSFETs. The calculation of øf,p(t) depends on the device history and generation/recombination rates.