Bell Integrated Circuit Engineering Process Simulator (BICEPS) is a comprehensive VLSI process-simulation program developed at Bell Laboratories. BICEPS incorporates the most up-to-date physical models and efficient numerical algorithms to make it a highly robust and general-purpose program. BICEPS can calculate doping profiles resulting from ion implantation, predeposition, oxidation, and epitaxy in one or two spatial dimensions as well as etching and deposition of oxide, nitride, and photoresist. In this paper, the physics of IC process simulation will be reviewed with an emphasis on the various physical models implemented in BICEPS. Calculation of the impurity profiles in VLSI devices involves the solution of a coupled set of nonlinear time-dependent partial differential equations, with moving boundaries and in more than one spatial dimension. The numerical techniques in obtaining a solution to this problem, namely, spatial discretization, time discretization, and the treatment of moving boundaries are also described in this paper. The capabilities of BICEPS are illustrated by the results of simulation of the fabrication of a typical NMOS transistor.