11/18/1 EE415/515 Fudametals of Semicoductor Devices Fall 1 ecture 16: PVs, PDs, & EDs Chater 14.1-14.6 Photo absortio Trasaret or oaque Photo eergy relatioshis c hc 1.4 m E E E i ev 11/18/1 ECE 415/515 J. E. Morris 1
11/18/1 Photo absortio Eergy absorbed i elemet d I d di I d I. d I d di Hece I d di d I l I l I l I I I I l I e d 11/18/1 ECE 415/515 J. E. Morris 3 Photo absortio coefficiet α 11/18/1 ECE 415/515 J. E. Morris 4
11/18/1 E 14.1 For 5µm thick Si, determie the % of hoto eergy which will ass through for hoto wavelegths λ a.8μm & b.6μm. 11/18/1 ECE 415/515 J. E. Morris 5 E 14. A hoto flu of itesity I ν =.1W/cm at wavelegth λ=1μm is icidet o a Si surface. Neglectig ay reflectio from the surface, determie the EHP geeratio rate at deths of a =5µm ad b =µm below the surface. Electro - hole air geeratio rate g / I h 11/18/1 ECE 415/515 J. E. Morris 6 3
11/18/1 Solar Cells At zero bias : Built - i field EHPs geerated by icidet light reverse curret Reverse curret I Total curret V a forward bias I R i load R I I Short circuit curret : I I Oe circuit curret : oc I V F I sc I I I I kt I l 1 e I S I S S ev e 1 kt ev e kt oc 1 11/18/1 ECE 415/515 J. E. Morris 7 11/18/1 ECE 415/515 J. E. Morris 8 4
11/18/1 E 14.3 A aas juctio solar cell has N a =1 17 /cc, N d =1 16 /cc, D =19cm /s, D =1cm /s, τ =1-7 s, τ =1-8 s. Assume a hotocurret desity J =ma/cm is geerated i the solar cell. Calculate a V OC ad b V OC /V bi. 11/18/1 ECE 415/515 J. E. Morris 9 Zero bias: -ve accetor ios i P, +ve door ios i N: elec field N P i deletio regio Reverse bias: Field icreased I o =qag o + +W.. EHP geeratio: W, electros withi of deletio edge i P Reverse bias: EHP i deletio regio holes to P, e-s to N icr reverse curret I=I th e qv/kt -1-I o =qa /τ + /τ e qv/kt -1-qAg o + +W V=, I sc = - I o, & I=, V oc = kt/ql1+i o /I th > Photovoltaic Effect 11/18/1 ECE 415/515 J. E. Morris 1 5
11/18/1 V oc = kt/ql1+i o /I th > Photovoltaic Effect Ma qv oc = qv Elec field: electros to N, holes to P Forward bias develos 11/18/1 ECE 415/515 J. E. Morris 11 Oeratig coditios Covetioal Photodiode Solar cell diode oeratio c.f. battery 11/18/1 ECE 415/515 J. E. Morris 1 6
11/18/1 Solar cell ower ev oad ower P IV I V I S e 1V kt dp For ma load ower set dv ev ev e I I S e 1 I SV e kt kt kt at V where ev e m ev 1 m I I S I S kt kt ev e m ev 1 m I 1 kt kt I S Pm I mvm Coversio efficiecy 1% 1% P P where P is the icidet otical ower 11/18/1 ECE 415/515 J. E. Morris 13 m i i i 4 th quadrat iverted Maimum ower oeratig oit I m,v m Fill factor =I m V m /I SC V OC 11/18/1 ECE 415/515 J. E. Morris 14 7
11/18/1 Solar sectrum If hc/λ < E g o absortio If hc/λ > E g eergy > E g dissiates as heat Note Si, aas bad gas Air mass zero sectrum outside earth atmoshere Air mass oe sectrum at earth surface at oo Cocetratio: I sc icr liearly with C, V oc icr little 11/18/1 ECE 415/515 J. E. Morris 15 Solar cell desig: N regio: Juctio ear surface d< Miimizes hole loss by recombiatio before reachig juctio. P regio: Need otical absortio deth 1/α < d+ < Miimize resistace: P: large area to back cotact arge V heavy doig imited by log lifetimes requiremet N: Cotact figers for short aths 11/18/1 ECE 415/515 J. E. Morris 16 8
11/18/1 No-uiform absortio Photo absortio rate at deth where is the icidet otical where all arameters vary with. EHP geeratio deth varies with, i.e. e flu at the surface Also iclude surface reflectio coefficiet R, so : EHP geeratio rate assumig oe EHP/hoto is..[1 R ].e 11/18/1 ECE 415/515 J. E. Morris 17 Heterojuctios ead the absortio eergy rage N regio absorbs hν>e gn regio absorbs E gn >hν>e g Similarly 11/18/1 ECE 415/515 J. E. Morris 18 9
11/18/1 1 Amorhous Si solar cells more ecoomic tha sigle crystal 11/18/1 ECE 415/515 J. E. Morris 19 Short rage order; CVD at 6 C; hydrogeated daglig bods; low mobility i bad ga, high >E c & <E v ; high otical absortio ~1μm thk film Al back cotact reflects residual hotos back ito cell Photocoductor 11/18/1 ECE 415/515 J. E. Morris times hotoelectro flows aroud circuit before recombiatio umber of 1 charge geeratio otical Rate of charge collectio at cotacts Rate of Photocoductor gai 1, with trasit time or, ad hotocurret so curret desity ad hotocoductivity ] [ &, tye, For EHP geeratio i - ] [ With otical ecess carriers At thermal equilibrium h s s t t A e I A t e t A e I E t AE e E A A J I E J J J e e e e e e
11/18/1 11 E 14.4 For a N-tye Si hotocoductor of legth =1µm, c/s area A=1-7 cm, & miority carrier lifetime τ =1-6 s. Determie the hotocurret if =1 1 /cc-s ad E=1V/cm. Assume µ =1cm /v-s & µ =4cm /v-s. 11/18/1 ECE 415/515 J. E. Morris 1 Photodiode reverse bias 11/18/1 ECE 415/515 J. E. Morris h h h e e A Ae Ae Be Ae t W e d e J / ad similarly ad Hece sice ad D D solutio : Particular as for fiite Homogeeous solutio : D For steady state : D Ambiolar trasort equatio : "romt"curret Resods quickly to illumiatio costat over deletio width W if bias deletio regio Photocurret from EHP geeratio i rev - / 1
11/18/1 1 Photodiode cot d 11/18/1 ECE 415/515 J. E. Morris 3 the "delayed"hotocurret is where so steady state hotocurret J J Similarly reverse saturatio curret hotocurret : Diffusio curret due to miority electros at 1 1 1 1 1 e W e J J J ed e ed e ed e d d ed d d ed J E 14.5 Calculate a the steady hotocurret desity ad b the ratio of romt hotocurret to steady-state hotocurret i a reverse-biased log Si diode with V R =5V ad =1 1 /cc-s, assumig N a =N d =1 15 /cc, D =5cm /s, D =1cm /s, τ =51-7 s, τ =1-7 s. 11/18/1 ECE 415/515 J. E. Morris 4
11/18/1 Photodiode/Photodetector 3 rd quadrat I OP roortioal to g OP, ~ideedet of V Carriers geerated i eutral regios withi of deletio regio: Diffusio rocess slow Hece large deletio regio width W; electric field drift resose fast arge W for ma sesitivity absortio, limited by resose seed required Wide W, low C -i- detector : i itrisic or high ρ arge W: rev bias all across i regio If τ s>>τ t, the 1 eh/hoto Eteral quatum efficiecy : η Q =carriers/hoto =J OP /q/p OP /hυ 1 Icrease η Q gai Oerate at avalache Avalache hotodiode 11/18/1 ECE 415/515 J. E. Morris 5 PIN hotodiode Oly the fast "romt" curret is of icrease the deletio regio width W PIN diode with itrisic "i" regio iterest & J For hoto flu Φ Φ e α e e W W e d Φ e α. d 1 e W eglectig recombiatio ad small W, the 11/18/1 ECE 415/515 J. E. Morris 6 13
11/18/1 E 14.6 Calculate the hotocurret desity for a Si PIN diode with a itrisic regio width of W=μm at a hoto flu of 1 17 /cm -s for hoto absortio coefficiets a α=1 /cm ad b α=1 4 /cm. 11/18/1 ECE 415/515 J. E. Morris 7 Avalache hotodiode 11/18/1 ECE 415/515 J. E. Morris 8 14
11/18/1 11/18/1 ECE 415/515 J. E. Morris 9 Phototrasistor High gai by trasistor actio EHP geeratio i large C - B juctio Photocurret I I C I E E αi I 1 I 1 E I 11/18/1 ECE 415/515 J. E. Morris 3 15
11/18/1 Photolumiescece & electrolumiescece umiescece whe recombiatio light Photolumiescece whe ecess carriers geerated by hoto-absortio Electrolumiescece whe ecess carriers due to electrical curret alied field a Basic iterbad trasitios: ii ad iii cause emissio sectrum/badwidth b Imurity/defect states [iv dee tra recombiatio] c Auger o-radiative trasitios Sotaeous emissio rate:- I h E g h E e kt g 11/18/1 ECE 415/515 J. E. Morris 31 aas emissio sectra & lumiescet efficiecy Rr Quatum efficiecy q R Radiative recombiatio rate Total recombiatio rate r where τ Iterbad recombiatio rate R 6 B direct badga ~ 1 B idirect badga Tyically emitted hotos have radiative & o - radiative lifetimes 1 for τ very large so reabsortio ossible 11/18/1 ECE 415/515 J. E. Morris 3 r & τ r r r B hν E g r r 16
11/18/1 Direct ad idirect bad ga materials 11/18/1 ECE 415/515 J. E. Morris 33 Direct bad-ga Al a 1- As for otical devices: <<.45 E g = 1.44+1.47 ev for < <.35 11/18/1 ECE 415/515 J. E. Morris 34 17
11/18/1 aas 1- P : Direct ga for <<.45 11/18/1 ECE 415/515 J. E. Morris 35 Comositio affects bad ga ad color 11/18/1 ECE 415/515 J. E. Morris 36 18
11/18/1 E 14.7 Determie the outut wavelegths of aas 1- P materials for mole fractios a =.15 ad b =.3. 11/18/1 ECE 415/515 J. E. Morris 37 ight-emittig diode ED: ight emissio from forward biased juctio λ=hc/e g =1.4/E g μm with E g i ev 11/18/1 ECE 415/515 J. E. Morris 38 19
11/18/1 Iteral quatum efficiecy where J J J J R eiw ev e 1 is o - radiative mid - ga tras kt For : J J J R is fractio of diode curret that roduces lumiescece ad make J R small at sufficiet forward bias, so 1 Rr ad Rr for electros ijected ito - regio, r r so total recombiatio rate R Rr Rr r r 1 Rr r Radiative efficiecy Rr N t tra site desity R 1 1 r Rr r Iteral quatum efficiecy i r 11/18/1 ECE 415/515 J. E. Morris 39 r Eteral quatum efficiecy: Fractio of geerated hotos actually emitted 1. eometry ad re-absortio. Fresel loss at the air iterface Reflectio coefficiet 1 1 1, refractive idices 11/18/1 ECE 415/515 J. E. Morris 4
11/18/1 Eteral quatum efficiecy 3. Total iteral reflectio for 1 1 c si 11/18/1 ECE 415/515 J. E. Morris 41 E 14.8 At wavelegth λ=.7μm, the ide of refractio for aas is =3.8 ad for ap is =3.. Cosider a aas 1- P material with =.4. Assumig the ide of refractio is a liear fuctio of, determie the reflectio coefficiet, Γ, at the aas.6 P.4 -air iterface. 11/18/1 ECE 415/515 J. E. Morris 4 1
11/18/1 E 14.9 Calculate the critical agle betwee aas.6 P.4 ad air. 11/18/1 ECE 415/515 J. E. Morris 43 Physical costructio for efficiecy 11/18/1 ECE 415/515 J. E. Morris 44
11/18/1 ED brightess & heterostructures Photos emitted by electros ijected ito arrow-ga -tye ot absorbed by wide-ga -tye i.e. as a fuctio of 11/18/1 ECE 415/515 J. E. Morris 45 ED materials ad develomet 11/18/1 ECE 415/515 J. E. Morris 46 3
11/18/1 Fiber-Otic trasmissio 11/18/1 ECE 415/515 J. E. Morris 47 Atteuatio I=I e -α α is frequecy deedet fuctio of material Atomic vibratios Rayleigh scatterig: Radom refractive ide variatios ~λ Miimum absortio here ~1.55μm IR laser 11/18/1 ECE 415/515 J. E. Morris 48 4
11/18/1 11/18/1 ECE 415/515 J. E. Morris 49 Assigmet 8b 14.4 14.11 14.16 14.19 11/18/1 ECE 415/515 J. E. Morris 5 5