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Lecture notes from ece 440: optical absorption and direct recombination in semiconductors, taught by prof. Eric pop at the university of illinois. The notes cover topics such as thermal generation of carriers, photon absorption, absorption coefficient, excess electron-hole pairs (ehps), recombination, and direct vs. Indirect band gap semiconductors.
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Optical Absorption and Direct Recombination Today, we turn the light ON semiconductors. But before we do, recall that with the lights OFF, the number of carriers present in a sample are just given by: (1) Thermal generation: (2) Charge neutrality: [two equations with two unknowns; a little nicer when ND ≫ NA or NA ≫ ND] When we turn the light on, we can generate electron-hole pairs (EHPs), depending on the light frequency ~ energy.
Consider sample of thickness L How much of the incident light is absorbed/transmitted? Qualitatively plot I(transmitted) vs. incident photon energy
Plot the absorption coefficient vs. photon energy: Keep in mind some of the material band gaps: Semiconductors only absorb photons with energies larger than the band gap. ( ћωω > EG )
Recall, light absorption creates EHPs: What do excess EHPs do? They _____________. How long do excess EHPs “live” for before they recombine? Remember direct vs. indirect band gap semiconductors? They both emit light when they have excess EHPs (in excess of what?). Which one is more efficient as a light emitter?
Direct band gap generation vs. recombination rate: n ( t ) n^2 n ( t ) p ( t ) dt d r i What is each term due to? Excess carrier notation: δn(t) = δp(t) instantaneous excess EHPs at time tn(t) = δn(t) = δp(t) instantaneous excess EHPs at time tp(t) instantaneous excess EHPs at time t Δn = δn(t=0) initial excess EHPs at time t = 0, right aftern = δn(t) = δp(t) instantaneous excess EHPs at time tn(t=0) initial excess EHPs at time t = 0, right after initial excitation (e.g. light flash) n = n 0 + δn(t) = δp(t) instantaneous excess EHPs at time tn and p = p 0 + δn(t) = δp(t) instantaneous excess EHPs at time tp How do the excess EHPs decay? Assume n-type sample (n 0 ≫ p 0 ) so holes are in minority. Will majority carriers (electrons) be disturbed much? _____ What about minority carriers (holes)? __________________ Excess minority carriers (here, holes) will recombine with already existing electrons: p ( t ) n 0 p ( t ) dt d r Solution is a simple decaying exponential
p ( t ) pe ^ r^ n^^0 t pe t /^ p Where we’ve approximated the decay time τ ~ This is the recombination lifetime for excess EHPs. More generally τ = Typical EHP recombination lifetimes in Si are ~ For direct recombination excess δn(t) = δp(t) instantaneous excess EHPs at time tn decay at the exact same rate as excess δn(t) = δp(t) instantaneous excess EHPs at time tp. (one electron + one hole = one photon).
