Analytical approximation of effective surface recombination velocity of dielectric-passivated p-type silicon

New analytical equations are derived to approximate the effective surface r ecombination velocity (S-eff) on p-type silicon for three different cases: low-level injection (LLI) with surface hole concentration (p(s)) much great er than surface electron concentration (n(s)) and with silicon charge (Q(Si )) due primarily to ionized acceptors, LLI with n(s) >> p(s) and Q(Si) due primarily to ionized acceptors, and high-level injection with n(s) >> p(s) and Q(Si) due primarily to mobile electrons. The three new equations predic t the dependence of S-eff on individual parameters such as injection level (Deltan), doping level (N-A), and fixed dielectric charge (Q(f)). The new e quations complement a previously derived result (for LLI with n(s) >> p(s) and Q(Si) due primarily to mobile electrons) and together allow reasonable explanations to be given for all sections of all S-eff vs. Deltan and S-eff vs. N-A curves generated by a quasi-exact numerical method. The analytical approximations are compared with the full numerical solutions. Under appro priate conditions, the analytical approximations agree with the numerical s olutions within a factor of 3. Guided by the analytical approximations, num erical solutions are fitted to two sets of experimental data: the injection level dependence of S-eff for an oxide-passivated wafer; and the doping de pendence of S-eff for wafers passivated by plasma-enhanced chemical vapor d eposited nitride (SiNx), conventional furnace oxide (CFO), and the SiNx/CFO stack. The SiNx/CFO stack not only provides surface passivation that is su perior to either dielectric alone; it is also less doping dependent. The an alytical approximations indicate that this suppressed doping dependence cou ld be due to a lower interface state density or a higher fixed dielectric c harge (Q(f)). (C) 2001 Elsevier Science Ltd. All rights reserved.