Notes for ECE-606: Spring 013 Carrier Recombination Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA lundstro@purdue.edu /19/13 1 carrier recombination-generation N-type, equilibrium Δp( t = 0) n 0 0 17 cm -3 p 0 = n i n 0 0 3 cm -3 Δp( t = 0) >> p 0 Δn( t = 0) Δp( t = 0) << n 0 (low-level injection) expect: Δp( t) = Δp( t = 0)e t τ Δp may be either positive or negative.
how can excess carriers recombine? 1) Band-to-band recombination E = hf = B np n i t b b energy given to photon (Note that this is zero in equilibrium as it should be.) 3 excess carriers n = n 0 + Δn E F p = p 0 + Δp Δn Δp filled states n 0 0 17 cm -3 p 0 0 3 cm -3 example: Δn 0 8 cm -3 << n 0 Δp Δn 0 8 cm -3 >> p 0 low level injection 4
low level injection The term low level injection means that the excess carrier concentration is orders of magnitude smaller than the equilibrium majority carrier concentration but orders of magnitude larger that the equilibrium minority carrier concentration. 5 Low level injection in a p-type semi E = hf n = n 0 + Δn Δn p = p 0 + Δp N A = B np n i t b b BN A Δn = Δn τ bb t b b τ BN A bb np Δn N A >> n i 6
excess carrier concentration vs. time = Δn t bb τ bb Δn( t) = Δn( 0)e t/τ b b Δn( t) = Ce t/τ bb τ b-b = minority carrier lifetime Δn( 0) = C τ b b BN A 7 how can excess carriers recombine? ) Auger recombination energy given to a second electron = C n n np n i t Auger + C p p( np n i ) (Note that this is zero in equilibrium as it should be.) 8
low level injection in a p-type semi energy given to a second electron = C p p np n i t Auger n = n 0 + Δn Δn p = p 0 + Δp N A t Auger C p N A Δn = Δn τ Auger τ Auger = 1 C p N A np Δn N A >> n i 9 how can excess carriers recombine? 3) SRH recombination (defect assisted recombination) E T energy released as thermal energy donor like or acceptor like = p = n + n 1 np n i + τ n ( p + p 1 ) (steady-state) 10
SRH recombination E T = p = n + n 1 np n i + τ n ( p + p 1 ) (steady-state) ( n 1 = n i e E T E i ) k B T ( p 1 = n i e E i E T ) k B T τ n c n c p 11 SRH recombination (low injection) = p = np n i + τ n ( p + p 1 ) n + n 1 p-type Δn >> n 0 Δp << p 0 = Δn τ n τ n c n n-type Δp >> p 0 Δn << n 0 Δp = Δp c p 1
SRH recombination (high injection) = p = n + n 1 np n i + τ n ( p + p 1 ) Δn >> n 0 Δp >> p 0 Δn Δp = Δn τ n + τ n c n c p 13 SRH recombination (depla]etion) = p = n + n 1 np n i + τ n ( p + p 1 ) np << n i, n << n 1, p << p 1 = p n = + i + τ n τ n c n c p 14
low level injection (summary) band-band = Δn t b b τ b b τ b b BN A Auger t Auger = Δn 1 τ Auger = τ Auger C p N A SRH = Δn τ n τ n c n = = Δn 1 + 1 + 1 t tot t t b b Auger τ eff τ eff τ b b τ Auger τ SRH 15 low level injection (summary) = Δn 1 + 1 1 t tot τ eff τ eff τ b b τ Auger τ SRH Δn( t) = Δn( 0)e t τ eff 16
recombination-generation X = B X = C n n + C p p X = R = X ( np n i ) 1 ( n + n 1 ) + τ n ( p + p 1 ) band-to-band radiative Auger SRH ( np > n i ) net recombination ( np < n i ) net generation 17 summary 1) Band-to-band radiative recombination dominates in direct gap semiconductors makes lasers and LEDs possible ) Auger recombination dominates when the carrier densities are very high (heavily doped semiconductors or lasers) 3) SRH recombination dominates in high quality, indirect gap semiconductors and in low quality direct gap semiconductors 18
other types of generation 1) Impact ionization Inverse of Auger recombination ) Optical generation Inverse of band-to-band recombination 19 photoelectric effect E = hf > Φ M AC Φ M E F Einstein, in 1905, when he wrote the Annus Mirabilis papers 0 http://en.wikipedia.org/wiki/photoelectric_effect
how many photons can be absorbed? Example: Silicon.1 ev. Only photons with a wavelength smaller than 1.13 µm will be absorbed. solar spectrum λ < hc E (AM1.5G) G 1 wasted energy Energy is lost for photons with energy greater than the bandgap. hf > Electron is excited above the conduction band. However, extra energy is lost due to thermalization as electron relaxes back to the band edge.
absorption coefficient Incident flux: Φ 0 Flux at position, x : Φ( x) = Φ 0 e α( λ)x optical absorption coefficient: α ( λ) > 0 for E > ( λ < hc ) Generation rate at position, x : = dφ( x) G x dx α λ = Φ 0 α ( λ)e α( λ)x 3 direct vs. indirect conduction band E conduction band E E = p m need phonon p p valence band valence band Direct gap: strong absorption (high alpha) 4 Indirect gap: weaker absorption lower alpha)
light absorption vs. semiconductor thickness The direct bandgap of CIGS allows it to absorb light much faster than Silicon A layer of silicon must be 10 4 microns thick to absorb ~100% of the light, while CIGS need only be about microns thick. 5