ELEC4/1-1 Assignmnt 4 1 Assignmnt #4..1 (1. %),. (.6 %),.3 (1. %),. (.4 %),.8 (1. %),.9 (.4 %),. (.6 %).1. Band gap and potodtction. a) a) Dtrmin t maximum valu of t nrgy gap (bandgap) wic a smiconductor, usd as a potodtctor, can av if it is to b snsitiv to yllow ligt (6 nm). b) A potodtctor wos ara is ² cm² is irradiatd wit yllow ligt wos intnsity is mw cm ². Assuming tat ac poton gnrats on lctron-ol pair (EHP), calculat t numbr of EHPs gnratd pr scond. c) From t known nrgy gap of t smiconductor GaAs (E g 1.4 V), calculat t primary wavlngt of potons mittd from tis crystal as a rsult of lctron-ol rcombination. s tis wavlngt in t visibl? d) Will a silicon potodtctor b snsitiv to t radiation from a GaAs lasr? Wy? Solution. E E c λ 34.66 3 9 6 8 6 19 3.313 J or.7 V b) p # of EHP gnratd pr scond # of incidnt potons pr scond wr p / is # of lctrons pr scond and P₀/ν is # potons pr scond 3 P ( ) W 14 1 Trfor, # of EHP gnratd pr scond 3. s 19 ν (3.313 ) J P ν
ELEC4/1-1 Assignmnt 4 c) c λ E 1.4.873 µ m tis is infrard ligt and it is not in visibl rgion. 1.4 d) for Si, E g 1.1 V and for GaAs, E g 1.4 V corrsponding cut-off wavlngt for Si is λ cut off c E g 1.4 1.7 µm 1.1 T cut-off wavlngt of GaAs is sortr (873 nm) tan cut-off wavlngt of Si (1.7 μm); tus, Si potodtctor will b snsitiv to t radiation from a GaAs lasr. n otr words, t bandgap of t silicon is smallr tan it is in GaAs and mittd potons from lasr (GaAs) will av igr nrgy tan silicon s nrgy bandgap. Consquntly, potons will rsult in gnration of EHP in silicon potodtctor... Absorption cofficint. a) f d is t ticknss of a potodtctor matrial, ₒ is t intnsity of t incoming radiation, sow tat t numbr of potons absorbd pr unit volum of sampl is n p [ 1 xp( αd )] dv b) Wat is t ticknss of a G and n.3 Ga.47 As crystal layr tat is ndd for absorbing 9% of t incidnt radiation at 1. μm? c) Suppos tat ac absorbd poton librats on lctron (or lctron ol pair) in a unity quantum fficincy potodtctor and tat t potognratd lctrons ar immdiatly collctd. Tus, t rat of carg collction is limitd by rat of potognration. Wat is t xtrnal potocurrnt dnsity for t potodtctors in (b) if t incidnt radiation is μw mm ²?
ELEC4/1-1 Assignmnt 4 3 1 8 4 3 1 Poton nrgy (V).9.8.7 1 7 G n.7 Ga.3 As.64 P.36 1 6 α (m -1 ) Si GaAs np n.3 Ga.47 As 1 a-si:h 1 4 1 3..4.6.8 1. 1. 1.4 1.6 1.8 Wavlngt (µm) Absorption cofficint (α) vs. wavlngt (λ) for various smiconductors (Data slctivly collctd and combind from various sourcs.) Figur.3. S. O. Kasap Optolctronics and Potonics Solution. a) lt ₀ is incoming radiation wic is rprsntd by nrgy flowing pr unit ara pr scond and ₀[1-xp(-αd)] is t absorbd intnsity. Poton flux is t numbr of potons arriving pr unit ara pr unit scond, P₀/(νAra)₀/ν. So, absorbd poton flux pr unit ara is # of potons absorbd pr volum [ 1 xp( αd )]. ν [ 1 xp( αd )] dν
ELEC4/1-1 Assignmnt 4 4 b) from Fig..3 α 6. ⁵ m ¹ is t absorption cofficint for G at 1. μm incidnt radiation ( d ) xp( αd ).1 xp( αd ).1 ln.1 d α ln.1 d 6. 3.84 µ m from Fig..3 α 7. ⁵ m ¹ is t absorption cofficint for n.3 Ga.47 As at 1. μm incidnt radiation ( d ) xp( αd ).1 xp( αd ).1 c) ln.1 d α ln.1 d 7. 3.7 µ m givn η QE 1, t rat of carg collction is limitd by rat of potognration, and ₀ μw/mm² W/m² ( 1 xp( αd )) p P / ara ν ν ν ara J J p p [ 1 xp( αd )] p.9 λ ara ν c 19 1.6.9 1. 8.663 A/m 34 8 6.66 3 or.866 A/cm T rflction of t ligt from t surfac of t potodtctor is nglctd. Assumd tat t anti-rflctiv coating as fficincy %..3. G Potodiod. Considr a commrcial G pn junction potodiod wic as t rsponsivity sown in Figur.. ts potosnsitiv ara is.8 mm². t is usd undr a
ELEC4/1-1 Assignmnt 4 rvrs bias of V wn t dark currnt is.3 μa and t junction capacitanc is 4 pf. T ris tim of t potodiod is. ns. a) Calculat its quantum fficincy at 8, 13 and 1 nm. b) Wat is t intnsity of ligt at 1. μm tat givs a potocurrnt qual to t dark currnt? c) Wat would b t ffct of lowring t tmpratur on t rsponsivity curv? d) Givn tat t dark currnt is in t rang of microamprs, wat would b t advantag in rducing t tmpratur? ) Suppos tat t potodiod is usd wit a Ω rsistanc to sampl t potocurrnt. Wat limits t spd of rspons? Rsponsivity(A/W).8.7.6..4.3..1. 1 1. Wavlngt(µm) T rsponsivity of a commrcial G pn junction potodiod 1999 S.O. Kasap, Optolctronics (Prntic Hall) Figur.. S. O. Kasap Optolctronics and Potonics
ELEC4/1-1 Assignmnt 4 6 Solution. a) ara.8 mm² 8. ⁹ m² η QE P R P p p / / ν η Rν EQ cr λ Wavlngt, nm 8 13 1 Rsponsivity, A/W.6.8.7 η QE, % 38..43 7.71 b) p d.3 μa c) P p / R.3 /.7.4 W or.4 µ P.4 ara 8. 9. W/m or. mw/cm T nrgy band gap is incrasing wit t dcrasing of t tmpratur; consquntly, t cut-off wavlngt is dcrasing as tmpratur is dcrasing. So, t igr poton nrgy is ndd to initiat poton absorption. For instanc, t curvs rprsnting t rlationsip btwn absorption cofficint and wavlngt dmonstratd in Figur.3 will b siftd to t lft, wn tmpratur is dcrasd. Hnc, t sam absorption cofficint for a givn smiconductor will b at lowr wavlngt and at igr poton nrgy wn tmpratur is dcrasd. T cang in t absorption cofficint attributabl to t variations in tmpratur mans tat t optical powr absorbd in t dpltion rgion and t quantum fficincy vary wit tmpratur. T pak of t rsponsivity in Figur. will mov to t lft, to t lowr valus of t wavlngt, wit dcrasing W
ELEC4/1-1 Assignmnt 4 7 tmpratur, sinc t amount of t optical powr absorbd in dpltion rgion incrass wit t dcrasing in tmpratur valu. d) Dark currnt is proportional to xp(-e g /k B T), trfor, it will rducd if t tmpratur will b dcrasd. T advantag is t improvmnt of SNR. ) tim constant limitation RC Ω 4 pf.4 ns T RC constant is comparabl to t ris tim,. ns. Trfor, t spd of t rspons dpnds on bot t ris tim and RC constant.. ngaas pin Potodiods. Considr a commrcial ngaas pin potodiod wos rsponsivity is sown in Figur.. ts dark currnt is na. a) Wat optical powr at a wavlngt of 1. μm would giv a potocurrnt tat is twic t dark currnt? Wat is t QE of t potodtctor at 1. μm? b) Wat would b t potocurrnt if t incidnt powr in (a) was at 1.3 μm? Wat is t QE at 1.3 μm opration?
ELEC4/1-1 Assignmnt 4 8 Figur.. S. O. Kasap Optolctronics and Potonics a) Rsponsivity(A/W) 1.8.6.4. 8 1 14 16 18 Wavlngt(nm) T rsponsivity of an ngaas pin potodiod 1999 S.O. Kasap, Optolctronics (Prntic Hall) Solution. η QE R P P p p R.87 from Figur. R cr 6.66 λ 1.6 dark 34.87 9 8 3.87 9 1 19 11.49 nw.6973or 7. % From t dimnsional idntitis: [ p ] AC/s, [P₀] W J/s, [R] A/W C/J So, rsponsivity is t carg collctd pr unit incidnt nrgy b) for λ 1.3 μm R.8 A/W from Figur.
ELEC4/1-1 Assignmnt 4 9 p P 11.49 nw R from part (a) p 9 P R 11.49.8 9.4 na η QE cr 6.66 λ 1.6 19 34 8 3.8.784 or 78.4 % 6 1.3.8. Transint potocurrnts in a pin potodiod. Considr a rvrs biasd Si pin potodiod as sown in Figur.3. t is appropriatly rvrs biasd so tat t fild in t dpltion rgion (i-si layr) EV r /W is t saturation fild. Tus, potognratd lctrons and ols in tis layr drift at saturation vlocitis v d and v d. Assum tat t fild E is uniform and tat t ticknss of t p+ is ngligibl. A vry sort ligt puls (infinitsimally sort) potognrats EHPs in t dpltion layr as sown in Figur.3 wic rsults in an xponntially dcaying EHP concntrations across W. Figur.3 sows t potognratd lctron concntration at tim t and also at a latr tim t wn t lctrons av driftd a distanc x v d t. Tos tat rac t back lctrod B bcom collctd. T lctron distribution sifts at a constant vlocity until t initial lctrons at A rac B wic rprsnts t longst transit tim τ W/v d. Similar argumnt apply to ols but ty drift in t opposit dirction and tir transit tim τ W/v d wr v d is tir saturation vlocity. T potocurrnt dnsity at any instant is p ( t) + j( t) Nvd Nvd j j + wr N and N ar t ovrall lctron and ol concntration in t sampl at tim t. Assum for convninc tat t cross sctional ara A 1 (drivations blow ar not affctd as w ar intrstd in t potocurrnt dnsitis). a) Sktc t ol distribution at a tim t wr τ > t > and τ ol drift tim W/v d. b) T lctron concntration distribution n(x) at tim t corrsponds to tat at t siftd by v d t. Tus t total lctrons in W is proportional to intgrating tis distribution n(x) from A at x v d t to B at x W.
ELEC4/1-1 Assignmnt 4 Givn n(x) n₀xp(-αx) at t, wr n₀ is t lctron concntration at x at t w av W Total numbr of lctrons at tim t n xp[ α( x v t) ] dx and Total numbr lctronsat tim t N Volum Tn N W ( t) n xp[ ( x v t) ] W n t α d dx 1 xp αw 1 W τ 1 vdt v wr N () is t initial ovrall lctron concntration at tim t, tat is, 1 W n N( ) n ( x) dx [ ( W )] W xp α 1 xp α Wα W not tat n₀ dpnds on t intnsity of t ligt puls so tat n₀. Sow tat for ols, n ( ) ( ) xp αw t N xp 1 t αw 1 Wα τ c) Givn W 4 μm, α ⁴ m ¹, v d ⁵ m/s, v d.8 ⁵ m/s, n₀ ¹³ cm ³, calculat t lctron and ol transit tims, sktc t potocurrnt dnsitis j (t) and j (t) and nc j p (t) as a function of tim, and calculat t initial potocurrnt. Wat is your conclusion? d t d
ELEC4/1-1 Assignmnt 4 11 Potognratd lctron concntration xp( αx) at tim t v d A W B x υ > E g E + i p R Figur.3. S. O. Kasap Optolctronics and Potonics V r An infinitsimally sort ligt puls is absorbd trougout t dpltion layr and crats an EHP concntration tat dcays xponntially 1999 S.O. Kasap, Optolctronics (Prntic Hall) a) Solution. T ol distribution is rsmbl to t lctron distribution as it is sown in Figur.3. An infinitsimally sort ligt puls is absorbd trougout t dpltion layr and crats an EHP concntration tat dcays xponntially.
ELEC4/1-1 Assignmnt 4 1 b) N N W ( ) vdt t n xp[ α( x + v t) ] dx [ xp( αv t) xp( αw )] ( t) 1 W n xp Wα ( αw ) n d Wα t xp αw 1 1 τ d c) τ W / v τ W / v d d 4 4.8 6 6 4 ps ps At tim t, N () N (), n₀ ¹³ cm ³ ⁷ m ³ N N n Wα ( ) [ 1 xp( αw )] 19 4 ( ) [ 1 xp( 4 )] 4 T initial currnts ar 4 4.33 18 m -3 or 4.3 1 cm -3 j ( ) N ( ) v d 1.6 19 4.3 18 6.9 4 A/m or 6.9 A/cm or 69 ma/mm 19 18 4 j( ) N( ) vd 1.6 4.3.8. A/m t total initial potocurrnt is j ()+j () 69+ 14 ma/mm² T individual transint potocurrnts ar givn by j n v Wα t τ or. A/cm ( ) ( ) d t N 1 xp α 1 t vd W for t < τ or ma/mm j ( t) N ( t) v d n v d xp Wα ( αw ) t xp αw 1 1 τ for t < τ T rspons is dtrmind by t slowst transint tim. Tr is a kink in t potocurrnt wavform wn all t lctrons av bn swpt out at τ 4 ns.
ELEC4/1-1 Assignmnt 4 13 14 x 4 Potocurrnt dnsity 1 Potocurrnt dnsity (A/m ) 8 6 4 j (t) j (t) j t (t) lctrons Total potocurrnt dnsity ols 1 3 4 6 Tim (sc) x - τ τ.9. Fibr attnuation and ngaas pin Potodiod. Considr t commrcial ngaas pin potodiod wos rsponsivity is sown in Figur.. Tis is usd in a rcivr circuit tat nds a minimum of na potocurrnt for a discrnibl output signal (accptabl signal to nois ratio for t customr). Suppos tat t ngaas pin PD is usd at 1.3 μm opration wit a singl mod fibr wos attnuation is.3 db km ¹. f t lasr diod mittr can launc at most mw of powr into t fibr, wat is t maximum distanc for t communication witout a rpatr? Solution. f p na, R.81 A/W at 1.3 μm wavlngt from Figur. 9 p 9 Powr absorbd by potodiod P 6.173 W R.81
ELEC4/1-1 Assignmnt 4 14 3 in P out 9 6.173 T attnuation loss is log ( P / ) log. db From attnuation cofficint α.3 db/km T maximum distanc for t communication witout a rpatr, L, is givn as attnuation loss. L 17.444 km α.3.. Potoconductiv dtctor. An n-typ Si potodtctor as a lngt L μm and a ol liftim of 1 μs. T applid bias to t potoconductor is V. a) a) Wat ar t transit tims, t and t, of an lctron and a ol across L? Wat is t potoconductiv gain? b) t sould b apparnt tat as lctrons ar muc fastr tan ols, a potognratd lctron lavs t potoconductor vry quickly. Tis lavs bind a drifting ol and trfor a positiv carg in t smiconductor. Scondary (i.. additional lctrons) tn flow into t potoconductor to maintain nutrality in t sampl and t currnt contributs to flow. Ts vnts will continu until t ol as disappard by rcombination, wic taks on avrag a tim τ. Tus mor cargs flow troug t contact pr unit tim tan cargs actually potognratd pr unit tim. Wat will appn if t contacts ar not omic, i.. ty ar not injcting? c) Wat can you say about t product σ and t spd of rspons wic is proportional to 1/τ. Solution. from givn lngt and applid voltag EV/L V/ μm ⁵ V/m 1 1 1 1 from t insid covr of t txtbook: µ 13 cm V s, 4 cm V s µ T transit tims of an lctron and a ol across L is givn
ELEC4/1-1 Assignmnt 4 1 t t L 4 µ E 13 L 4 µ E 4 7.41 ns. ns Anotr way to solv for transit tims of an lctron and ol across L in Si is by using Figur.7: v 1.3 ⁴ m/s at E ⁵ V/m and v 4. ³ m/s t t L v L v 1.3 4 4 4. 4 3 7.69 ns. ns Potoconductiv gain is Rat of lctron flow in xtrnal circuit τ G Rat of lctron gnration by ligt absorption 1 G ( 13 + 4) 4 18 ( µ + µ ) b) if t contacts ar not omic, scondary lctrons cannot flow into t potoconductor to maintain nutrality. So, only t potognratd cargs can flow troug t xtrnal circuit; no xcss carg can flow and w will not gt potoconductiv gain. f t contacts cannot injct carrirs, tn tr will b no potocurrnt gain, G 1. c) cang in t conductivity or potoconductivity is ηλτ σ cd ( µ + µ ) T spd of rspons is invrsly proportional to t rcombination tim of t minority carrirs, τ. For instanc, if t ligt is turnd off, it will tak τ sconds for t xcss carrirs to disappar by rcombination. Trfor, t product of σ and t spd of rspons is proportional to ηλ σ 1 τ cd ( µ + µ ) wic is constant for a givn dvic gomtry and ligt intnsity. L E