Optoelectronics EE/OPE 451, OPT 444 Fall 2009 Section 1: T/Th 9:30-10:55 PM

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1 Optolctronics EE/OPE 451, OPT 444 Fall 2009 Sction 1: T/Th 9:30-10:55 PM John D. illiams, Ph.D. Dpartmnt of Elctrical and Computr Enginring 406 Optics Building - UAHuntsvill, Huntsvill, AL Ph. (256) mail: williams@ng.uah.du Offic Hours: Tus/Thurs 2-3PM JD, ECE Fall 2009

2 PHOTODETECTORS 5.1 Principl of th pn Junction Photodiod 5.2 Ramo's Thorm and Extrnal Photocurrnt 5.3 Absorption Cofficint and Photodiod Matrials 5.4 Quantum Efficincy and Rsponsivity 5.5 Th pin Photodiod 5.6 Avalanch Photodiod 5.7 Htrojunction Photodiods A. Sparat Absorption and Multiplication (SAM) APD B. Suprlattic APDs 5.8 Phototransistors 5.9 Photoconductiv Dtctors and Photoconductiv Gain 5.10 Nois In Photodtctors A. Th pn Junction and th pin Photodiods B. Avalanch Nois in th APD Prntic-Hall Inc S.O. Kasap ISBN:

3 pn Junction Diod Photoconductors convrt light signal into an lctrical signal such as voltag or currnt Typical pn otodiod has a p + n typ junction Th Accptor concntration (N a ) in th p sid is much gratr than th donor concntration (N d ) on th d sid Th illuminatd sid has an annular (ring shapd) lctrod opn in th cntr for light absorption A Si 3 N 4 antirflctiv coating is prsnt on Silicon otodiods to incras transmission of light into th diod. (similar antirflctiv coatings ar also grown on SiG and InGaAs diods) Th p sid is vry thin ( < 1 m) and is usually formd by a diffusion or ion implantation procss prformd on th n typ crystal layr Not this mans that th p typ structur has many dfcts and is not a prfct crystallin structur

4 pn Junction Diod pn otodiods ar rvrsd biasd A strong ngativ bias is gnratd ovr a vry small latral dimnsion in th p+ sid Th dpltion rgion xtnds dp into th thicknss of th n sid of th dvic Th total bias in th dvic V= V o +V r whr V o is th built in voltag inhrnt in th junction hn a oton of nrgy gratr than th bandgap is incidnt, it bcoms absorbd and is said to otognrat a fr lctron hol pair (EHP) Usually th nrgy of th oton is such that th otgnraotion taks plac in th dpltion layr Th lctric fild prsnt in th dpltion layr pulls th EHP apart until thy rach th nutral rgions of th dvic Motion of th lctrons otgnratd in th dvic by th lctric fild producs a otocurrnt, I in th dvic Ar w sur that currnt is not du to lctrons AND hols? YES, b/c if on intgrats th currnt to dtrmin how much charg flowd, thn w gt a total numbr of otognratd lctrons N, and not 2N from th ntir EHP systm. (a) Elctrod h> E g Antirflction coating (b) (c) N d N a SiO 2 p + nt E max E(x) h+ E V r n I R Elctrod Dpltion rgion (a) A schmatic diagram of a rvrs biasd pn junction otodiod. (b) Nt spac charg across th diod in th dpltion rgion. N d and N a ar th donor and accptor concntrations in th p and n sids. (c). Th fild in th dpltion rgion S.O. Kasap, Optolctronics (Prntic Hall) x x V out

5 Ramo s Thorm and Extrnal Photocurrnt Considr a matrial with ngligibl dark otoconductivity Such lctrods do not auto-injct carrirs du to thir slf bias, but allow xcss carrirs in th sampl to lav and bcom collctd by th battry Undr such conditions, th lctric fild throughout th sampl is uniform and can b dfind as E=V/L Suppos that a singl oton is absorbd to crat an EHP at x = l Th rspctiv drift vlocitis ar v = E v h = h E Th transit tims associatd with th carrirs and hols ar t L l v t h l v h (a) (b) t h v h t h + V Smiconductor E v l L l 0 l L h+ t t i (t) x (a) An EHP is otognratd at x = l. Th lctron and th hol drift in opposit dirctions with drift vlocitis v h and v. (b) Th lctron arrivs at tim t = (L l)/v and th hol arrivs at tim t h = l/v h. (c) As th lctron and hol drift, ach gnrats an xtrnal otocurrnt shown as i (t) and i h (t). (d) Th total otocurrnt is th sum of hol and lctron otocurrnts ach lasting a duration t h and t rspctivly S.O. Kasap, Optolctronics (Prntic Hall) t t h t t h 0 t 0 t v h /L Charg = v h /L v /L i h (t) v h /L + v /L i (t) i (t) (d) i(t) (c)

6 Ramo s Thorm (Cont.) Considr first, only th drifting lctron Th work don by th battry is whr E V / L v i i h yilding Thus, Edx Vi dx / dt ( t) ( t) v L v L h ; t t ; t t ( t) dt h Th total charg gnratd by th otocurrnt is a singl lctron. Thus th total currnt du to optical activity within th dvic can b dfind as i( t) Nv L ( t) d ; t t transit Q collctd t i ( t) dt 0 0 t h i h ( t) dt

7 Absorption Cofficint and Photodiod Uppr cut-off wavlngth (or thrshold wavlngth) of th dvic is g hc E g 1.24( V m) E ( V ) Silicon, E g = 1.12 V and g = 1.11 m G, E g = 0.66 V and g = 1.87 m Can Silicon b usd for th optical communication band ( m)? Photons at wavlngths abov th cutt-off transmit through th matrial Photons at wavlngths shortr than th cutt-off ar absorbd xponntially in in spac as thy travl through th dvic Th intnsity of light at a distanc x into th otodiod is I( x) I o whr I o is th incidnc intnsity, and is th absorption cofficint g ( / x) Matrials

8 Dirct vs. Indirct Bandgap Indirct bandgap matrials (Si, G) rquir hv =E g +h whr is th frquncy of th onons gnratd in th lattic. Thus indirct bandgap smiconductor otodiods actually hav a cutt-off nrgy just a bit abov Eg (approximatly Eg +0.1V) to compnsat for th momntum loss du to lattic vibrations

9 Quantum Efficincy and Rsponsivity Quantum fficincy is th fficincy of th convrsion procss btwn rcivd otons and EHP gnration Numbr _ of _ fr _ EHP _ gnratd _ and _ collctd Numbr _ of _ incidnt _ otons I / P / hv P optical _ powr o o Rsponsivity charactrizs th prformanc of a otodiod in trms of otocurrnt gnratd pr unit of optical powr Photocurrnt I R Incidnt _ Optical _ Powr P R hv hc Not: th valu dpnds on wavlngth. Thus R is oftn trmd spctral rsponsivity or radiat snsitivity whn plottd ovr a rang of wavlngths. Idaly (and not ralistic) th quantum fficincy of a dvic is 100%, thn th dvic is not wavlngth dpndnt and =1. o Rsponsivity (A/) Idal Photodiod QE = 100% ( = 1) Si Photodiod avlngth (nm) Rsponsivity (R) vs. wavlngth ( ) for an idal otodiod with QE = 100% ( = 1) and for a typical commrcial Si otodiod. g 1999 S.O. Kasap, Optolctronics (Prntic Hall)

10 Th pin otodiod pin (p + -intrinsic-n + ) otodiod Photon absorption occurs within th intrinsic silicon (i-si) layr Assum th i-si rgion to b truly intrinsic with a significantly smallr dopant concntration than th p or n sid Th uniformity of th built in E fild gnrats a zro potntial within th intrinsic rgion and prvnts carrir diffusion in th i-si rgion Charging both nds gnrats a dpltion layr capacitanc in th pin diod which dos not dpnd on th applid voltag as it would in a pn junction o r A Cdp pf R 50 RCdp 50 ps Any rvrs bias applid across th junction drops almost ntirly across th width of th i-si rgion Vr Vr E Eo ; V r V o SiO 2 Elctrod p + (a) (b) (c) N d N a h> E g (d) nt E(x) E o i-si n + E h + Th schmatic structur of an idalizd pin otodiod (b) Th nt spac charg dnsity across th otodiod. (c) Th built-in fild across th diod. (d) Th pin otodiod in otodtction is rvrs biasd. V r I 1999 S.O. Kasap, Optolctronics (Prntic Hall) Elctrod R x x V out

11 Drift Diffusion in a pin Photodiod Drift vlocity (m s -1 ) 10 5 Elctron 10 4 Hol Elctric fild (V m -1 ) Drift vlocity vs. lctric fild for hols and lctrons in Si S.O. Kasap, Optolctronics (Prntic Hall) Rspons tim is dtrmind by th transit tims of carrirs across th width of th i-si layr t drift v v d tnds to saturat at 10 5 m/s at filds gratr than E=10 6 V/m For i-si of width 10 m, t drift = 0.1 ns which is longr than typical RC dp tim constants Thus th rspons tims in pin otodiods ar limitd by th transit tim of otognratd carrirs But wait. How dos a truly i-si dpltion rgion with NO voltag bias gnrat a dirctional drift vlocity for otoabsorbd lctrons? In actuality: pin otodiods ar actually slightly n-dopd. In ssnc, th intrinsic Si layr bcoms th dpltion rgion with a small concntration of positiv donors so that th fild is not ntirly uniform across th otodiod d

12 Si pin otodiod Rsponsivity(A/) 0.6 Photognratd lctron concntration xp(x) at tim t = 0 v d A B x A B h> E g E h avlngth(nm) i R V r Th rsponsivity of two commrcial Si pin otodiods 1999 S.O. Kasap, Optolctronics (Prntic Hall) An infinitsimally short light puls is absorbd throughout th dpltion layr and crats an EHP concntration that dcays xponntially 1999 S.O. Kasap, Optolctronics (Prntic Hall)

13 Exampl: Si pin otodiod A Si pin otodiod has an i-si layr width of 20 m. Th p+ layr on th illumination sid is vry thin (0.1 m). Th pin is rvrs biasd by a voltag of 100 V and thn illuminatd with a vry short optical puls of wavlngth 900 nm. hat is th duration of th otocurrnt if absorption occurs ovr th ntir i-si layr? From th tabl on absorption cofficints, w find that Si at 900 nm has = 30000/m. Thus th absorption dpths is approximatly 33 m. Assum that absorption occurs ovr th ntir width of th i-si layr. Vr E v v v t h h v drift 710 h 100V m 5 10 m / s 4 m / s m m / s V / m This is th rspons of tim of th pin as dtrmind by th transit tim of th slowst carrirs, hols, across th i-si layr. To improv th rspons tim, th width of th i-si layr has to b narrowd but this dcrass th quantity of absorbd otons and hnc th rsponsivity of th systm 10 s

14 Exampl: Photocarrir Diffusion in a pin Photodiod A rvrsd bias pin otodiod is illuminatd with a short wavlngth oton that is absorbd vry nar th surfac. In this cas, th otognratd lctron has to diffus to th dpltion rgion whr it is swpt into th i-si layr and driftd across. hat is th spd of th otodiod if th i-si layr is 20 m and th p+ layr is 1 m and th applid voltag is 100 V? Assum th diffusion cofficint of lctrons in havily dopd p+ Si is 3x10-4 m2/s In this cas, thr is no lctric fild outsid th dpltion rgion. Thus th lctron must drift diffusion across th p+ rgion Onc th lctron rgions th dpltion rgion, it is driftd across by its saturation vlocity. Vr E v v t l t diff drift 2 l 2D 2D t drift 100V m 5 10 m / s v m m / s m 2 m 2 / s V / m s 9 s h> E g p + Diffusion h + i-si E Drift A rvrs biasd pin otodiod is illuminatd with a short wavlngth oton that is absorbd vry nar th surfac. Th otognratd lctron has to diffus to th dpltion rgion whr it is swpt into th i-layr and driftd across. V r 1999 S.O. Kasap, Optolctronics (Prntic Hall) Th total rspons tim is tdiff tdrift 1.67ns 0.2ns 1. 87ns

15 Rsponsivity in a pin Photodiod A Si pin otodiod has an activ light rciving ara of diamtr 0.4 mm. hn radiation of wavlngth 700 nm and intnsity 0.1 m/cm 2 is incidnt it gnrats a otocurrnt of 56.6 na. hat is th rsponsivity and quantum fficincy of th otodiod at 700 nm. Rsponsivity(A/) 0.6 Incidnt powr on th pin otodiod is Po AI (0.02cm) Th rsponsivity is R I / P ( Th quantum fficincy is hc R 0.45A/ o / cm A) V nm 700nm % A/ avlngth(nm) A B Th rsponsivity of two commrcial Si pin otodiods 1999 S.O. Kasap, Optolctronics (Prntic Hall)

16 Othr pin Diod Rsponsivitis Rsponsivity(A/) avlngth(nm) Th rsponsivity of an InGaAs pin otodiod 1999 S.O. Kasap, Optolctronics (Prntic Hall) Rsponsivity(A/) avlngth(µm) Th rsponsivity of a commrcial G pn junction otodiod 1999 S.O. Kasap, Optolctronics (Prntic Hall)

17 Avalanch Photodiods Avalanch otodiods (APDs) ar usd widly in optical communications du to thir high spd and intrnal gain Th n+ sid is vry thin and illuminatd dirctly by light incidnt upon it Thr p typ layrs ar burid within th thicknss of th substrat. A thin p- layr is diffusd or implantd undr th n+ rgion Th middl layr is narly intrinsic yilding only a slight potntial across th thicknss of th dvic p+ rgion is locatd at th countr lctrod Th diod is rvrsd biasd to incras filds within th dpltion rgion whr absorption occurs. Elctrod h > E g nt SiO 2 n + E(x) p Avalanch rgion E I h + š p + Absorption rgion R Elctrod x x (a) (b) (c) (a) A schmatic illustration of th structur of an avalanch otodiod (APD) biasd for avalanch gain. (b) Th nt spac charg dnsity across th otodiod. (c) Th fild across th diod and th idntification of absorption and multiplication rgions S.O. Kasap, Optolctronics (Prntic Hall)

18 Avalanch Photodiods hn drifting lctrons gnratd within th nar intrinsic rgion drift diffus into th p- rgion thn thy xprinc larg E filds that provid sufficint kintic nrgy (gratr than E g ) to impact-ioniz som of th Si covalnt bonds and rlas mor EHPs. Th scondary EHPs ar also acclratd by th sam high filds, ioniz and gnrat vn mor EHPs This ffct lads to an avalanch of impact ionization procsss and th otodiod can b said to possss and intrnal gain mchanism that amplifis th ffct of a singl EHP absorption in th intrinsic rgion Th otocurrnt gnratd in th APD in th prsnc of avalanch multiplication thus corrsponds to a quantum fficincy gratr than 1 n + E p Avalanch rgion (a) h + š (a) A pictorial viw of impact ionization procsss rlasing EHPs and th rsulting avalanch multiplication. (b) Impact of an nrgtic conduction lctron with crystal vibrations transfrs th lctron's kintic nrgy to a valnc lctron and thrby xcits it to th conduction band S.O. Kasap, Optolctronics (Prntic Hall) Th avalanch multiplication factor applid to fficincy and rsponsivity calculations is Multiplid _ otocurrnt I M Primary _ unmultiplid _ otocurrnt I 1 M Vr 1 V br 2 Vbr is th avalanch brakdown voltag, Vr is th rvrs bias, and n is a charactristic indx that is usd to bst fit th xprimntal data E (b) h + E c E v o

19 APD Dsign Spd of th APD diod dpnds on thr factors: lctron diffusion tim in th intrinsic rgion, th tim rquird to build up th avalanch procss, and th tim it taks for th last hol gnratd by th avalanch procss to transit through to th intrinsic rgion On practical drawback to APD dsign is that th priry of th dvic rachs avalanch brakdown bfor th illuminatd rgion This is corrctd by th stablishmnt of an n typ guard ring around th cntral illuminatd rgion that prvnts priral brakdown Antirflction coating Elctrod SiO 2 n + p Guard ring n n + p n (a) š p + Avalanch brakdown (b) š p + Substrat Elctrod Substrat Elctrod (a) A Si APD structur without a guard ring. (b) A schmatic illustration of th structur of a mor practical Si APD 1999 S.O. Kasap, Optolctronics (Prntic Hall)

20 Exampl: InGaAs APD Rsponsivity An InGaAs APD has a quantum fficincy of 60% at 1.55 m in th absnc of multipl amplification. It is biasd to oprat with a multiplication of 12. Calculat th otocurrnt if th incidnt optical powr is 20 n. hat is th rsponsivity whn th multiplication factor is 12. Rsponsivity(A/) For M = 1, th quantum th rsponsivity is 1500nm R A/ hc 1240V nm If I o is th primary otocurrnt and Po is th incidnt optical powr, thn by dfinition, R= I o /P o. I o RP o (0.75A/ ) A Th otodiod currnt I in th APD is avlngth(nm) I MI o (12) A1.810 A Th rsponsivity at M = 12 is R M A/ 9A/ hc Th rsponsivity of an InGaAs pin otodiod 1999 S.O. Kasap, Optolctronics (Prntic Hall)

21 Exampl: Silicon APD A silicon APD has a QE of 70% at 830 nm in th absnc of multiplication. Th APD is biasd to oprat with a multiplication of 100. If th incidnt optical powr is 10 n, thn what is th otocurrnt? Th unmultiplid rsponsivity is 830nm R 0.7 hc 1240V nm 0.47A/ Th unmultiplid primary otocurrnt from th dfinition of R is I o RP Th multiplid otocurrnt is o (0.47A/ ) nA I MI o nA 0.47A

22 Htrojunction Photodiods Sparat Absorption and Multiplication (SAM) APD Htrojunction of two diffrnt matrials within th sam otodiod p typ surfac with thr n typ layrs of yilding diffrnt lctric filds throughout th dvic Absorption occurs in th lightly dopd n typ rgion and th multiplication rgion is st by th dopd N typ rgion Bandgap diffrncs btwn InGaAs and InP trap driv th diffrnt rgims and hlp to mov lctrons across th dvic Hols in th dvic tnd to b trappd by th changs in valanc band nrgy. This lads to slowr rspons tims. Evn if th multiplir for such dvics is many tims highr than homojunction diods. Elctrod h E(x) InP EE I P + N n n + Avalanch rgion InP V r h + InGaAs x R Absorption rgion Simplifid schmatic diagram of a sparat absorption and multiplication (SAM) APD using a htrostructur basd on InGaAs-InP. P and N rfr to p and n -typ widr-bandgap smiconductor S.O. Kasap, Optolctronics (Prntic Hall) V out

23 Simplifid schmatic diagram of a mor practical msa-tchd SAGM layrd APD. Sparation Absorption Grading and Multiplication (SAGM) APDs Th sharp intrfac from btwn n layrs in th SAM diod tnds to trap hols and dgrad drift diffusion fficincy Th addition of grading layrs and multipl short acclration rgions to improv avalanch fficincy at th p sid of th dvic Rducs hol trapping by lowring th nrgy diffrnc btwn n typ barrirs (a) (b) E c E v InP InP E v E v E h + E c InGaAs E v InGaAsP grading layr InGaAs h + E v (a) Enrgy band diagram for a SAM htrojunction APD whr thr is a valnc band stp E v from InGaAs to InP that slows hol ntry into th InP layr. (b) An intrposing grading layr (InGaAsP) with an intrmdiat bandgap braks E v and maks it asir for th hol to pass to th InP layr Photon 1999 S.O. Kasap, Optolctronics (Prntic Hall) Elctrod Elctrod n In 0.53 Ga 0.47 As (5-10m) Absorption lay Gradd n InGaAsP (<1 m) N InP (2-3 m) Multiplication layr. P + InP (2-3 m) Buffr pitaxial layr P + InP Substrat

24 Suprlattic APDs Institution of singl carrir multiplication by th incorporation of quantum wlls through MBE dpositd multilayr dvics Th multi-quantum wll ffct is usd to crat a staircas suprlattic APD in which th bandgap is gradd in ach layr from E g1 to E g2. Elctrons drift in th conduction band and hols drift in th valanc band of ach quantum wll as it is lind up by th applid lctric fild. Multiplication of lctrons by impact ionization gnrats th ffct commonly known by th dvic nam a Solid stat otomultiplir nm h E E c E g2 E c p + E g 1 n + h + E v (a) (b) Enrgy band diagram of a staircas suprlattic APD (a) No bias. (b) ith an applid bias S.O. Kasap, Optolctronics (Prntic Hall)

25 Phototransistors A bipolar junction transistor (BJT) that oprats as a otodtctor with otocurrnt gain In an idal ototransistor, only th dpltion rgions (spac charg layr or SCL) contain and lctric fild E filds prsnt in th SCL rgion sparat EHP gnratd by absorbd otons hn th drifting lctron rachs th collctor it is nutralizd by th battry Howvr whn hols ntr th nutral rgion (bas), thy can only b nutralizd by injcting a larg numbr of lctrons from th mittr Th long EHP rcombination tim in th nutral bas rgion rquirs a significant numbr of lctrons to b injctd from th mittr for vry hol driftd into th rgion Th xcss lctrons diffus across th bas and rach th collctor, and thus amplify th ffct of th optical otocurrnt gnration procss Emittr n + I I SCL E V BE Bas p V CC I h h + E SCL V BC Collctor n I Th principl of opration of th otodiod. SCL is th spac charg layr or th dpltion rgion. Th primary otocurrnt acts as a bas currnt and givs ris to a larg otocurrnt in th mittr-collctor circuit S.O. Kasap, Optolctronics (Prntic Hall) o ( V / k T ) BE B Is th currnt gain du to xcss lctrons mittd to rcombin with hols in th Bas V BE bas mittr voltag in gnratd by th xcss lctrons rquird to rcombin hols in th bas

26 Photoconductiv Dtctors and Gain Two lctrods ar attachd to a smiconductor with a dsird absorption cofficint and quantum fficincy ovr th wavlngth of intrst Rspons of th dtctor dpnds on whthr th contacts ar ohmic or blocking du to carrir rcombination at th contact In this class, w considr ohmic contacts such as a mtallic contact pad Photoconductiv gain is achivd through th consrvation of lctric fild. know that lctrons drift much fastr than hols So as an lctron rachs th ohmic contact on th positiv sid, th hol has not yt rachd th ngativ contact Thus an lctron is jctd from th ngativ sid contact to balanc th charg This crats a gain multiplir basd on th numbr of lctrons that drift across th lngth of th otoconductor in th tim it taks for a singl hol to drift to th ngativ sid of th dvic or rcombin with an injctd lctron (whichvr coms first) Light n = n o + n p = p o + p V I oto A smiconductor slab of lngth, width w and dpth d is illuminatd with light of wavlngth S.O. Kasap, Optolctronics (Prntic Hall) h+ Ph otoco nductor (a) (b) (c) (d) () I w d I I I I A otoconductor with ohmic contacts (contacts not limiting carrir ntry) can xhibit gain. A th slow hol drifts through th otoconductors, many fas t lctrons ntr and drift through otoconductor bcaus, at any instant, th otoconductor must b nutral. Elctrons drift which mans as on lavs, anothr must ntr S.O. Kasap, Optolctronics (Prntic Hall)

27 Mathmatical Asssmnt Suppos a otoconductor is suddnly illuminatd by a stp light. If is th numbr of otons arriving pr unit ara pr unit scond, thn =I/(hv) (intnsity/nrgy of oton) Th numbr of EHP gnratd pr unit volum pr scond is g A Ad whr A is th ara I hv d I hcd At any givn scond, th xcss lctron concntration (diffrnc btwn otognratd lctrons and dark lctions) is And th rat incras of xcss lctron concntration is th rat of otognration minus th rat of rcombination of xcss lctions If is th man rcombination tim of xcss lctrons, thn on can dtrmin th rat of chang of n dn dt g In th stady stat condition (th point at which tim dpndnc gos to zro) n n no p n I n hcd I n g hcd

28 Mathmatical Asssmnt From our basic undrstanding of smiconductors, th conductivity in th dvic is givn by n p And th chang in th conductivity du to otognratd carrir activity is n p n( ) I ( h) hcd From this, on can writ th currnt dnsity as V J E l And th numbr of lctrons flowing in th circuit as I wdj h ) h wi ( h hc h E Howvr, th rat of EHP otognration is only Thus th otoconductiv gain, G, in th systm must qual volum g I wl hc ( h G l ) E

29 Mathmatical Asssmnt Also rcall that on can solv for th transit (drift) tim of lctrons or hols in a smiconductor as t l E t h l E h Substitution of transit tims for carrir mobility givs th Gain as a function of drift tim h G 1 t th t Thus th otoconductiv gain can b quit high if /t is kpt larg which rquirs a long rcombination tim and a short transit tim. As on might imagin, th transit tim can b mad shortr by applying a gratr fild, but this will also incras th dark currnt which thrby incrass th nois in th systm

30 Nois in a Photodtctor Th lowst signal that a otodtctor can dtct is dtrmind by th xtnt of random fluxuations in dark currnt within th dvic from statistical procsss in th dvic Th fluxations, or shot nois, in th dvic is du to th fact that EHP xcitations and rcombinations ar actually discrt instancs that sum to produc randomly gnratd lctrical currnt within th dvic Th root man squar (rms) valu of shot nois du to dark currnt can b drivd from th frquncy bandwidth, B, of th dtctor and th dark currnt, I d prsnt. Currnt i ndark 2 I d B I d + I Illuminatd P o I d + I + i n I d Dark n p R A V ou Tim In pn junction and pin dvics th main sourc of nois is shot nois du to th dark currnt and otocurrnt S.O. Kasap, Optolctronics (Prntic Hall) V r

31 Nois in a Photodtctor (Cont.) Bcaus shot nois is actually basd on singl lctron vnts w can also assign a quantum nois componnt to th systm i I B Such that th total rms nois in th systm is i 2 n nquantum indark inquantum 2 I And th total currnt in th systm is I I I d Th Signal to nois ratio, SNR = signal nois /nois powr. For a simpl otodtctor, th SNR is simply th ratio of I 2 / i n2. i And for a rcivr must includ th nois powr gnratd by th thrmal nois (impdanc) in th input lmnts d n I B Th nois quivalnt powr (NEP) is frquntly quotd for otodtctors. NEP is th optical signal powr rquird to gnrat a otocurrnt signal (I ) that is qual to th total nois currnt (i n ) at a givn wavlngth and within a bandwidth of 1 Hz. i. NEP is th valu SNR = 1 at a givn and B = 1Hz

32 If R is th rsponsivity and Po is th monochromatic incidnt powr, thn th gnratd otocurrnt is I RP o Th NEP rquirs that I = i n so, on can thn writ RP RP 2 From this w can find th optical powr pr squar root of bandwidth (nois quivalnt powr) as P1 1 2I d I B R Taking B = 1 Hz, thn P 1 = NEP in th units of /Hz 1/2 1 I Th dtctivity, D, of any otoconductor = 1/NEP rprsnts thn limit of dtction availabl by th dvic d I B

33 APD Nois In SPD dvics, both otognratd and thrmally gnratd carrirs ntr th avalanch zon. As such th shot nois of both of ths carrirs is multiplid Yilding an APD nois valu of i 2 n i 2 ndark i 2 nquantum 2M 2 F I do I o B whr F is calld th xcss nois factor and is a function of M and th impact ionization probabilitis (cofficints). x F M Th valu x is xprimntally dtrmind for th smiconductor. For Silicon APDs, x varis btwn 0.3 and 0.5 For G and III-V compounds such as InGaAs, x varis btwn 0.7 and 1