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

Abstract

New analytical equations are derived to approximate the effective surface recombination velocity ( S eff) on p-type silicon for three different cases: low-level injection (LLI) with surface hole concentration ( p s) much greater 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 predict the dependence of S eff on individual parameters such as injection level ( Δn), doping level ( N A), and fixed dielectric charge ( Q f). The new equations 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. Δn 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 appropriate conditions, the analytical approximations agree with the numerical solutions within a factor of 3. Guided by the analytical approximations, numerical solutions are fitted to two sets of experimental data: the injection level dependence of S eff for an oxide-passivated wafer; and the doping dependence of S eff for wafers passivated by plasma-enhanced chemical vapor deposited nitride (SiN x ), conventional furnace oxide (CFO), and the SiN x /CFO stack. The SiN x /CFO stack not only provides surface passivation that is superior to either dielectric alone; it is also less doping dependent. The analytical approximations indicate that this suppressed doping dependence could be due to a lower interface state density or a higher fixed dielectric charge ( Q f).