EE 232 Lightwave Devices Lecture 3: Basic Semiconductor Physics and Optical Processes. Optical Properties of Semiconductors

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1 3 Lightwav Dvics Lctur 3: Basic Smicoductor Physics ad Optical Procsss Istructor: Mig C. Wu Uivrsity of Califoria, Brly lctrical girig ad Computr Scics Dpt. 3 Lctur 3- Optical Proprtis of Smicoductors Itrabad Trasitio (Fr-Carrir Absorptio) Absorptio missio Itrbad Trasitio Impurity-to-Bad Trasitio A V Optical trasitios Absorptio: xcitig a lctro to a highr rgy lvl by absorbig a photo missio: lctro rlaxig to a lowr rgy stat by mittig a photo 3 Lctur 3-

2 Bad-to-Bad Trasitio Sic most lctros ad hols ar ar th baddgs, th photo rgy of bad-to-bad (or itrbad) trasitio is approximatly qual to th badgap rgy: hv = g Th optical wavlgth of bad-to-bad trasitio ca b approximatd by λ = c ν = hc g.4 g λ : wavlgth i µm g : rgy badgap i V 3 Lctur 3-3 rgy Bad Diagram i Ral Spac ad -Spac = + m v * C = - m v * h V h V x Momtum: = m * v ffctiv Mass Approximatio = + m * h = V m h * Ral Spac K-Spac 3 Lctur 3-4

3 Bad-to-Bad Trasitio Absorptio Spotaous missio Stimulatd missio Photodtctors;; Solar Clls LD Optical Amplifirs;; Smicoductor Lasrs 3 Lctur 3-5 Cosrvatio of rgy ad Momtum 3 Lctur 3-6 Optical trasitios ar vrtical lis Coditios for optical absorptio ad missio: Cosrvatio of rgy Lattic Costat = hν Cosrvatio of momtum - = p, ~ a p h ~ l ( a ~ 0.5 m) << ( l ~ µ m) Þ = 3

4 Dirct vs Idirct Badgaps Phoo X Dirct badgap matrials miimum ad maximum occur at th sam 3 Lctur 3-7 xampls GaAs, IP, IGaAsP (Al x Ga -x )As, x < 0.45 Idirct badgap matrials miimum ad maximum occur at diffrt xampl Si, G (Al x Ga -x )As, x > 0.45 Not optically activ Absorptio Cofficit Light itsity dcays xpotially i smicoductor: I( x) - a x = I 0 Dirct badgap smicoductor has a sharp absorptio dg Si absorbs photos with hv > g =. V, but th absorptio cofficit is small Sufficit for CCD At highr rgy (~ 3 V), absorptio cofficit of Si bcoms larg agai, du to dirct badgap trasitio to highr 3 Lctur 3-8 4

5 Rviw of Smicoductor Physics lctro ad hol coctratios: = f ( ) r ( ) d C V p = f ( ) r ( ) d p Frmi-Dirac distributios: h f( ) = æ - F ö + xpç è T B ø fp ( ) = æ Fp - ö + xpç è T B ø F : lctro quasi-frmi lvl F p ò ò - : hol quasi-frmi lvl 3 Lctur 3-9 lctro/hol Dsity of Stats () L z L x z x 3 Lctur 3-0 L y +D y Spi Up ad Dow lctro wav with wavvctor i r Priodic boudary coditios " i r = i ( r+l x x) i r+l y y = A lctro stat is dfid by ( ) i r+l z z = ( ) ( x, y, z ) = m π, π,l π & $ L x L y L ( z ' Numbr of lctro stats btw ad + D i -spac pr uit volum 4p = = V p p p p L L L d ( ) d r d x y z 5

6 lctro/hol Dsity of Stats () Numbr of lctro stats btw ad + D pr uit volum = + m d = * m d * Liwis, hol dsity of stats ρ h () = 3/ * m $ h π " & V 3 Lctur 3- ( ) π d = m * m * π ρ () = π * m $ " & 3/ d = ρ ()d lctro ad Hol Coctratios = f ()ρ ()d = F = N C F / " B T N C = πm * B T $ " π & 3/ p=n V F V F p / " B T N V = πm * h B T $ " π & 3/ $ & $ & * m $ + xp F $ π & " & " B T ( h ) d Frmi-Dirac Itgral F j x = G ( j + ) ò + Gamma Fuctio 3 p G ( ) = 0 j x- h dx 3 Lctur 3-6

7 F j ( η) = Γ( j +) Approximatio of lctro/hol Coctratio 0 x j dx + x η,. -. /. η wh η << 4 & η 3 ) ( + 3' π * / wh η >> Wh F << (Boltzma approximatio) N C F B T Wh F >> (Dgrat) & 4 F ) C ( + ' N C B T * 3 π 3/ N C Boltzma Approx Quasi-Frmi Lvl Cross Bad dg Dgrat 3 Lctur 3-3 F B T 7