Lecture 1: Photoconductors and p-i-n Photodiodes

Transcription

1 Lcur 1: Poocoucors a p-i- Pooios Isrucor: Mig C. Wu Uivrsiy of Califoria, Brkly Elcrical Egirig a Compur Scics Dp. 1 Prof. Mig Wu

2 Poocors Covrs lig o lcric sigals Mai yps of poocors Poocoucors P-i- pooios Mal-smicoucor-mal (MSM) poocor Avalac poocors (APD) Ky prformac paramrs Rsposiviy [A/W] Wavlg rag Moulaio bawi Nois caracrisiics 2 Prof. Mig Wu

3 Opical Propris of Smicoucors Iraba Trasiio (Fr-Carrir Absorpio) E C Absorpio Emissio E A Irba Trasiio Impuriy-o-Ba Trasiio E V Opical rasiios Absorpio: xciig a lcro o a igr rgy lvl by absorbig a poo Emissio: lcro rlaxig o a lowr rgy sa by miig a poo 3 Prof. Mig Wu

4 Ba-o-Ba Trasiio Sic mos lcros a ols ar ar bags, poo rgy of ba-o-ba (or irba) rasiio is approximaly qual o bagap rgy: v = E g T opical wavlg of ba-o-ba rasiio ca b approxima by λ 1.24 E g λ : wavlg i µ m E : rgy bagap i V g 4 Prof. Mig Wu

5 Ergy Ba Diagram i Ral Spac a k-spac E 1 E = E + mv 2 * 2 C E C CB E E Effciv Mass Approximaio k = EC + 2m 2 2 * 1 E = E mv 2 * 2 V E V x Momum: k = mv * VB E k k = EV 2m 2 2 * Ral Spac K-Spac 5 Prof. Mig Wu

6 Ba-o-Ba Trasiio CB CB CB ν ν ν ν VB Absorpio VB Spoaous Emissio VB Simula Emissio Poocors; Solar Clls LED Opical Amplifirs; Smicoucor Lasrs 6 Prof. Mig Wu

7 Cosrvaio of Ergy a Momum CB VB ν E k 1 k 2 E 1 E 2 k Opical rasiios ar vrical lis Coiios for opical absorpio a missio: Cosrvaio of rgy Laic Cosa E E = ν 2 1 Cosrvaio of momum k2 k1 = k ν 2π k2, k1 ~ a 2π k ν ~ λ a ~ 0.5 m << λ ~ 1µ m ( ) ( ) k = k Prof. Mig Wu

8 Dirc vs Iirc Bagaps CB CB ν ν Poo X VB VB Dirc bagap marials CB miimum a VB maximum occur a sam k Exampls GaAs, IP, IGaAsP (Al x Ga 1-x )As, x < 0.45 Iirc bagap marials CB miimum a VB maximum occur a iffr k Exampl Si, G (Al x Ga 1-x )As, x > 0.45 No opically aciv 8 Prof. Mig Wu

9 Absorpio Coffici Lig isiy cays xpoially i smicoucor: I( x) I = 0 αx Dirc bagap smicoucor as a sarp absorpio g Mai poocor marials 1.3/1.55µm: IGaAs o IP 850m: GaAs or Si Si absorbs poos wi v > E g = 1.1 V, bu absorpio coffici is small u o iirc bagap Suffici for CCD 9 Prof. Mig Wu

10 Poocoucors ω + - x Ara = w L Equival Circui ω Dark curr: ( p) J = σ E= qµ + pqµ E Lig illumiaio gra lcro-ol pairs, icrasig couciviy: δ δ = G0 τ Say sa: / --> 0 δ= Gτ 0 ( p) J= δ q µ + µ E Poocoucor rquirs bo coacs o b Omic 10 Prof. Mig Wu

11 Poocarrir Graio Ra ω Lig Isiy α x + - x Ara = w L Pop (1 R) x (1 α ) Pop 1 1 G0 = η : poocarrir graio ra [ ] 3 ω lw cm s α η = η (1 R)(1 ) i R : rflciviy of poocoucor surfac α: absorpio coffici : absorpio lg α : fracio of lig rmais afr absorpio lg 11 Prof. Mig Wu

12 Poocouciv Gai ( 0τ )( µ µ p) I = lw J = lw G q + E Pop 1 I = lw η τ q( µ + µ p) E ω lw Pop 1 q 1 I η τ q( µ E) = ηp τ v ω ω τ = : rasi im v I q τ ηp = op ω τ op Poocurr Poocouciv Gai 12 Prof. Mig Wu

13 Aalogy o Curr Gai i Bipolar Trasisor Curr gai i bipolar rasisor: E B C I β = I C B T curr gai ca also b xprss as τ rb β = τ τ : rasi im τ rb : carrir rcombiaio lifim i bas 13 Prof. Mig Wu

14 N ωn1 η ω lw τ 1 Pop 1 N = η ω lw τ Small sigal rspos: N= N + N j N = ηp1 1 ω ω+ 1/ τ ( lw ) j ( ) jω P 1 N = I = J lw = N qv lw Frqucy of Poocoucors I1 ηq τ 1 = P1 ω τ jωτ + 1 = Poocouciv Rspos (B) τ / τ = 10, 000 τ / τ = 1, 000 τ / τ = 100 τ / τ = 10 τ / τ = 1 ( DC Quaum Efficicy) ( Poocouciv Gai) ( Normaliz Frqucy Rspos) Frqucy (Hz) 14 Prof. Mig Wu

15 Rvrs-bias p-i- jucio Mos of volag rop across i-rgio, mai absorpio rgio P-i- Pooio P ν i N Hig fil sparas poogra lcro a ol Larg bagap marials ar us for P a N if possibl Fas rspos 0 Ec0 i 1 q Ev0 i 2 q ν Low ois F0 q 3 No gai (quaum fficicy < 100%) Prof. Mig Wu x i

16 I-V Curv kt B Dark curr: I = I ( 1) 0 qv I ηq Poocurr: Ip = Pop ω α Quaum fficicy: η = η (1 R)(1 ) i V kt B Toal curr: I = I ( 1) + I 0 qv p I p1 I p2 Loa Li for Biasig PD 16 Prof. Mig Wu

17 Two Typs of p-i- Pooios L Surfac-Illumia p-i- α η = η (1 R)(1 ) i η : iral quaum fficicy i R : rflciviy : absorpio layr ickss Wavgui p-i- ΓαL η = η (1 R)(1 ) i η : iral quaum fficicy i R : rflciviy Γ : cofim facor L : lg of wavgui PD 17 Prof. Mig Wu

18 Ramo s Torm T curr caus i xral circui by a movig carg q movig a a volociy v ( ) i a paralll pla wi a sparaio of a a volag bias of V is qv() i () = A Proof: Work o o carg: W = Forc Displacm V = qex = q x Work provi by powr supply: W = i() V V i() V = q x q x qv() i () = = 18 Prof. Mig Wu

19 Rspos of O Poogra Elcro-Hol Pair qv / i () = i() + i() i () P N qv / i () Tim 0 x Hol Trajcory Elcro Trajcory Tim 19 Prof. Mig Wu v x 0 0 x v Toal carg gra: Q = i () + i () qv x qv x v v = + = O absorb poo o carg c q

20 Trasi Tim i () = i() + i() i () P N i () May lcro-ol pairs gra v v Tim Elcro curr s w las lcro gra ar P-si racs N-lcro: = v Hol curr s w las ol gra ar N-si racs P-lcro: = v Hol is usually slowr A cosrvaiv sima of rasi im: τ = v 20 Prof. Mig Wu

21 Toal Rspos Tim of p-i- (1) RC im: ε A τ RC = RC = R ( A: ara of p-i-) (2) Trasi im: τ = Toal rspos im: τ= τ f 3B v RC + τ 1 2πτ Absorpio layr ickss for opimum frqucy rspos: τ= τ RC Rε A τ 2 v 1 1 v f3b = f3 B,max 2πτ 4π Rε A Opimum bawi occurs w Rε A = opimum Rε A + τ = + v = Rε Av v 21 Prof. Mig Wu

22 Mor Rigorous Aalysis of p-i- Rspos Tim 20 Small-sigal aalysis: assum ipu lig is moula a frqucy ω, poocurr is proporioal o 2 ωτ si 1 2 i () jωrc ωτ 2 T firs rm is sigl-pol rspos from RC, wil sco rm is pas lay u o rasi im rspos. RC ( ( ) ) 2 20 log H1 f i Trasi Tim Toal ( ( ) ) 2 20 log H2 f i ( ( ) ) 2 20 log H3 f i f i f i Prof. Mig Wu f i

23 Exampl: τ f RC τ = 3B = 14.4 ps 20 ps Compariso of Numric Exampls 1 1 = = 4.6 GHz 2πτ + τ RC 2 ωτ si 1 2 i () = H( ω) 2 1+ jωrc ωτ 2 1 Solvig H( ω) =, f3b = 9.7 GHz 2 T iscrpacy is smallr w RC omias, a largr w rasi im omias. (Trasi im rspos as a sarp rop-off). 23 Prof. Mig Wu RC ( ( ) ) 2 20 log H1 f i Trasi Tim Toal ( ( ) ) 2 20 log H2 f i ( ( ) ) 2 20 log H3 f i f i f i f i

24 Bawi-Efficicy Prouc (1) For surfac-illumia p-i- (assum AR coaig: R=0%), i xrm of i absorbig layr a rasi-im-omia rspos: α η = η (1 ) η (1 (1 α)) = ηα i i i 1 v f3b 2π 1 v ηαv Bawi-fficicy prouc: f3b η ( ηα i ) = 2π 2π (2) O or a, fficicy of wavgui p-i- is ΓαL η = η (1 ) ηγαl i i i 1 RC-limi bawi: f3b 2π RεLw 1 Bawi-fficicy prouc: f3b η ( ηiγ αl) = 2π RεLw I gral, r is a bawi-fficicy ra-off ηiγα 2πRεw 24 Prof. Mig Wu