Variational formulation of Poisson's equation in semiconductor at quasi-equilibrium and its applications

Variational formulation of Poisson's equation with Boltzmann carrier statistics at quasi-equilibrium is used to find analytical solutions of the potential distribution in multidimensional semiconductor devices with reasonably good accuracy. To demonstrate this approach, short-channel effects in the threshold voltage of fully-depleted SOI MOSFETs are analyzed. The usefulness of our idea is extended further to determine the quasi-Fermi potential of the floating gate of an EEPROM device, which has been determined to be very difficult to find by conventional methods.