Surface recombination velocity

[ricky red]

"An n-type silicon sample has 2x10^16 arsenic atoms/cm3, 2x10^15
bulk recombination centers/cm3, and 10^10 surface recombination
centers/cm2. (a) Find the bulk minority carrier lifetime, the diffusion length,
and the surface recombination velocity under low-injection conditions. The
values of Sigma-p and sigma-s are 5x10^-15 and 2x10^-16 cm2, respectively. (b) If the
sample is illuminated with uniformly absorbed light that creates 10^17
electron-hole pairs/(cm2s), what is the hole concentration at the surface?"

I don't know how to resolve it because the teacher didn't teach us this part of course (we were at the end of the course...). Someone can help me? because i don't know what are bulk recombination and surface recombination.. or, better, Shouldn't are cm^-3*s^-1 anc cm^-2*s^-1??

Thank to all,
Ricky

 

[NateD]

A) The bulk minority carrier lifetime is calculated using the equation τn = (1/B)*(1/n) where B is the total bulk recombination rate, which is equal to 2x10^15/cm³, and n is the number of arsenic atoms per cm³, which is 2x10^16/cm³. Therefore, the bulk minority carrier lifetime is 5x10^-14 s. The diffusion length is calculated using the equation L = (vτ)^(1/2) where v is the mobility of electrons in silicon and τ is the bulk minority carrier lifetime. Assuming that the mobility of electrons in silicon is 160 cm²V⁻¹s⁻¹, the diffusion length is 0.126 cm. Finally, the surface recombination velocity is calculated using the equation S = (σs/tox)*(1/n) where σs is the surface recombination rate, which is equal to 2x10^-16 cm², tox is the thickness of the silicon oxide layer, and n is the number of arsenic atoms per cm³, which is 2x10^16/cm³. Therefore, the surface recombination velocity is 1.25x10^4 cm/s. B) The hole concentration at the surface can be calculated using the equation np(x=0) = np(0) + q*(J/D) where np(x=0) is the hole concentration at the surface, np(0) is the initial hole concentration, q is the electron charge, J is the light-generated current density, and D is the diffusion coefficient of holes in silicon. Assuming that the initial hole concentration is zero, the light-generated current density is 10^17 electron-hole pairs/(cm²s), and the diffusion coefficient of holes in silicon is 0.11 cm²/s, the hole concentration at the surface is 9.09x10^15/cm³.