Abstract The drift-diffusion formulation, modelling semiconductor materials in terms of carrier densities and electric potential, is considered together with an alternative formulation in terms of dimensionless logarithmic quantities. Stability of both formulations in presence of sharp variations with a Galerkin Finite Element discretisation is assessed in two realistic problems: a p-n junction and an n-MOSFET device. The robustness with respect to the initial guess and the computational efficiency of the Newton-Raphson and Gummel non-linear solvers are also compared.