This paper introduces that the nonlinear Poisson–Boltzmann equation for semiconductor devices describing potential distribution in a doublegate metal oxide semiconductor field effect transistor (DG-MOSFET) is exactly solvable. The DG-MOSFET shows one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry. Lie symmetry properties of this model is investigated in order to extract some exact solutions. The reproducing kernel Hilbert space method and group preserving scheme also have been applied to the nonlinear equation. Numerical results show that the present methods are very effective.
