Analysis of Mathematical Models of Semiconductor Devices

accuracy applied approximation assume assumption base contact basis elements bias voltages bipolar transistor boundary conditions bounded carrier densities carrier mobilities ch² Chapter charge-neutral circuit computed constant continuity equations convergence current components current densities current flow denote depending determined device models electron and hole electron current electrostatic potential equilibrium error example exists expect finite-element fixed point follows given H₁ hole density inner product integral iteration lemma line integral mapping maximum principle mesh points monotone condition nonnegative norms numerical ohmic contacts p-n junction Poisson equation Poisson residual procedure Proof of lemma rate of convergence readily obtain recombination expression recombination term regions satisfy shown in Figure simply smooth function solving space dimension stationary problem stream functions sufficiently small taking the inner transistor model uniformly uniqueness updated variables Xi+1 zero ΘΩ ΧΕΩ ни