QUANTUM EFFICIENCY OF A p-υ-n Si PHOTODETECTOR

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1 Vol. 19, No. 06, Novmbr 015 ISSN QUANTUM EFFICIENCY OF A -υ- Si PHOTODETECTOR Dr.Mur Aboud Hashm, Mohammad Shihab Ahmmd 1) Assist. Prof., Elctrical Eg. Dartmt, Al-Mustasiryah Uivrsity, Baghdad, Iraq. ) M. Sc., i Elctroic ad Commuicatio, Elctrical Eg. Dartmt, Al-Mustasiryah Uivrsity, Baghdad, Iraq. (Rcivd: 13/10/014; Acctd: 19/4/015) Abstract: Th quatum fficicy of a silico -υ- hotodtctor is rst. Th aalysis to obtai th quatum fficicy taks a uiform doig coctratio i ach layr ito cosidratio. Th thortical tratmt aims to ivstigat th ffct of dvic aramtrs o th fficicy. Thr diffrt cass of th icidt light wavlgths hav b cosidrd; short wavlgths, mdium wavlgths, ad log wavlgths. Thr is o wavlgth rag btw thm, but wh th most of th icidt light (about 63 % or mor) absorbd ar th surfac, it is calld short wavlgth, ad wh most of th light absorbd i υ-layr, it is calld mdium wavlgth ls calld log wavlgth.a high quatum fficicy at th wavlgth of itrst, combi with its low oratig voltag ad caability, mak this dtctor a romisig for us i commuicatio systms ad comutr itrcoctios.high sd silico -υ- hotodtctor orats at 700 m wavlgth is rortd. By usig a rvrs bias voltag to cotrol υ-layr width, a high quatum fficicy of 80 % is attaid corrsodig to υ-layr width of 5.36 m ad biasig voltag of.18 V.Th rsults showd that th quatum fficicy is dirctly roortioal to th width of th υ-layr ad biasig voltag. Th rsults ar achivd with th aid of MATLAB rogrammig tool vrsio R013a. Kywords: quatum fficicy, hotodtctor, -υ- hotodiod. الكفاءة الكمية للكاشف الضوئي -υ- سليكون الخالصة: تم تقديم الكفاءة الكمية للكاشف الضوئي المصنوع من السليكون ذو التركيب. -υ- أن تحليل كفاءة الكم المذكورة تعتبر تركيز الشوائب منتظم في كل طبقة. تهدف المعالجة النظرية لدراسة تأثير باراميترات الجهاز على الكفاءة. وقد تم اعتبار ثالث حاالت مختلفة من الطول الموجي للضوء الساقط اطوال موجية قصيرة اطوال موجية متوسطة واطوال موجية طويلة. اليوجد مدى محدد بين تلك االطوال الموجية ولكن عندما معظم الضوء الساقط )حوالي 63% او اكثر( يمتص بالقرب من السطح يسمى طول موجي قصير وعندما معظم الضوء الساقط يمتص بطبقة υ يسمى الطول الموجي المتوسط واال فيسمى الطول الموجي الطويل.ان الكفاءة الكمية العالية عند طول موجي معين باالرتباط مع الفولتية المطبقة وقابلية تشغيلها المنخفضة يجعل هذاالكاشف واعد لالستخدام في نظم االتصاالت ووصالت الكومبيوتر.الكاشف الضوئي -υ- سليكون ذو السرعة العالية عند الطول الموجي 700 نانومتر قد تم ذكره. باستخدام التحيز العكسي للسيطرة على عرض طبقة υ تم الوصول الى كفاءة كم عالية بحدود 80% عندما كان عرض طبقة υ هو 5.36 مايكرومتر وفولتية االنحياز.18 فولت.اظهرت النتائج ان كفاءة الكم تتناسب طرديا عرض طبقة υ وفولتية االنحياز. ان النتائج تم انجازها باالستعانة باداة البرمجة MATLAB النسخة *Corrsodig Author muraboud@yahoo.com 130

2 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) 1. Itroductio A high quatum fficicy (Q.E) valu mas a high amout of icidt light hav b absorbd. Th idal quatum fficicy is uity. Th lssig is du to th currt loss by rcombiatio, icomlt absortio, rflctio, tc. Th icidt hoto with a rgy hf (whr h is Plak s costat ad f is th frqucy of icidt light) Eg (whr E g is rgy of badga, rlatd with badga wavlgth g ) xcits a lctro from th valc bad to th coductio bad ad so cratig a lctro-hol air (EHP) [1]. Wh th hotodiod rvrs biasd, it orats as a hotodtctor. Th hotodtctor ca ot dtct all light wavlgths, so th dtctio of th light at crtai wavlgth rquirs a crtai dsig. Th ability of th hotodtctor to dtct th light is calld rsosivity. Th -υ- hotodiod structur is show i Fig. 1, which cosists of a larg thickss of lightly gativ dod υ-layr sadwich btw a - ad -layrs. A ositiv charg is cratd i υ- layr as ioizd doors. I 1999, Schaub, J.D. t al., dsigatd a rsoat cavity hacmt Si hotodiod grow by mrgd itaxial latral ovrgrowth (MELO), who carrid out a badwidth of 34 GHzad a ak quatum fficicy of 4 % at a wavlgth of 704 m[]. I 011, Habiboor, A., utilizd a o dimsioal (1-D) simulatio rogram basd o th drift-diffusio modl ad Discrt Fourir Trasform (DFT) is dvlod. Th rogram umrically solvs th tim-ddt cotiuity quatios for lctros ad hols i a smicoductor dvic. Th modl simulats carrir coctratios ad th imuls rsos of a gallium arsid mtal-smicoductor-mtal hotodtctor at a costat bias voltag. Th simulatio showd that for a smallr valu of carrir liftim, th rsos fall tim dcrass without sigificatly rducig th quatum fficicy of th dvic [3]. As show from Fig. 1 -sid, w is th width of υ-layr, dltio width, ad w rrsts bulk -sid width, x is th dltio width rovidd by w is bulk -sid width. x is th dltio width rovidd by -sid, w is th Figur 1. -υ- hotodiod structur. Th wavlgth of icidt light is giv by [4], c f (1) 131

3 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) whr c is light vlocity. Th gratio rat of EHPs G x is giv by [5], G x x d x x o. () whr is icidt light dsity, x 0 of icidt light wavlgth.. -υ- Photodtctor Udr Biasig o, is absortio cofficit ad it is a fuctio Th rvrs biasig voltag dtrmis th quatio of th dltio layr width w. If a larg ough rvrs bias voltag alid to th dtctor ad fully dlt th bulk of charg carrirs i th υ-layr, thr will b a o-zro lctric fild xtdig all th way across it du to th ioizd door atoms. Th voltag at which this has is rfrrd to as th uch-through voltag V PT. Wh alid rvrs bias voltag quals to uch-through voltag V, i this cas x x 0, th w w. Th uch-through voltag is giv by [6]. r V PT qnd VPT w (3) whr q is articl charg costat, 13 cm ), ad is rmittivity. N d is door doig coctratio i υ-layr (about 3. Carrir Dsity Distributio Th flow of lctros i th -sid is govrd by [7], t x, t x, t D x G x, t x, t o (4a) whr x t diffusio cofficit, x t, is lctros coctratio udr illumiatio i th -sid, D is a lctros G, is a lctros gratio rat, o is a lctros coctratio udr quilibrium, ad is lctros liftim. Th flow of hols i th -sid is govrd by [8]. 13

4 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) x, t x, t whr x t cofficit, x t x, t o D G x, t (4b) t x, is hols coctratio udr illumiatio i th -sid, D is hols diffusio is hols liftim. G, is hols gratio rat, o is hols coctratio udr quilibrium, ad Carrirs diffusio cofficits ar giv by, D L (5a) D L (5b) whr L is lctro diffusio lgth, ad L is hol diffusio lgth, 4. Currt of Vrtical Illumiatd -υ- Photodtctor Th currt gratd isid υ-layr is calld drift currt ad th currt gratd outsid υ- layr is calld diffusio currt. Th o-dimsioal diffusio currt dsity, for lctros, J diff,, ad for hols, J diff,, ar [9]: x d Jdiff, x qd -sid (6a) ad J diff x d, x qd -sid (6b) 4.1. Diffusio Currt i) -sid Diffusio Currt Th flow of miority carrir dsity (lctros) i th bulk -sid is dtrmid by (4a). At x, t x, ad G x, t G x. Usig (4a) with () givs, stady stat, 133

5 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) x x x o L x o D Th gral solutio to (7) is a sum of homogous solutio Pa x. (7) h x ad articular solutio x x x h a (8) Th homogous solutio is, h x x L x L C D (9) ad th articular solutio is, a x x A B (10) ' x From (10), x B x, '' x B, substitutig x ' Pa, x ito (7) yilds, A o ad Pa Pa ol 1 L B. D Substitutig A ad B ito (10) givs, Pa ad '' Pa x a x o ol D 1 L x ad substitutig (9) ad (10) ito (8), th miority carrir distributio is giv by, x L x x L ol x C D o D 1 L (11) (1) ad usig th first boudary coditio ( x 0), 0 C D C 1 (13a) o whr C 1 ol 1 L. D Usig th scod boudary coditio ( x w ) 0,, 134

6 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) w L w L w 0 C D o C1 (13b) From (13a) ad (13b), C C w L w 1 o sih w L ad D C w L w 1 o sih w L Substitutig C ad D ito (1) givs, d x w x L C1 sih x w L C sihx L sihw L w o sih 1 o C1 (14a) w C x w 1 1 cosh w L C L sihw L w o cosh w L (14b) L sih w L 1 Substitutig (14b) ito (6a), J diff, w w C 1 cosh w L w 1 o qd C1 coth w L (15a) L sih w L L Th trm i (15a) that cotais o rrst diffusio hotocurrt i th -sid J diff, h, so, J diff, h, w ii) -sid Diffusio Currt w 1 cosh w L w qdc1 (15b) L sihw L Th flow of miority carrir dsity (hols) i th bulk -sid is dtrmid by (4b). At x, t x, ad G x, t G x. Usig (4b) with () givs, stady stat, 135

7 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) x x o L x x o D (16) Th rocdur usd to fid x o ad x w w 0 x is th sam to fid x. Th hols distributio i th -sid utral rgio is, x whr w w x x w w L o o C C1 From (17a), ol C1. D 1 L but th boudary coditios ar, 1 (17a) d x 1 w w x x w w L o C 1 C1 L (17b) Substitutig (17b) ito (6b) yilds, qod q0l w w w w Jdiff, (18a) L 1L Th trm i (18a) that cotais o rrst diffusio hotocurrt i th -sid so, J diff, h, Jdiff q0l w w h, 1L, (18b) 4.. Drift Currt Th drift currt dsity du to absorbd light isid υ-layr is, w w w w w x q Jdrift, h, w q G o 1 (19) 136

8 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) 5. Quatum Efficicy Aalysis Thr ar sstially thr tys of th hotogratio rocss that ca articiat to th absorbd hotocurrt I h, du to th wavlgth of th icidt light Short Wavlgths I this cas th absortio dth 1 is lss tha th width w. Th hotogratio taks lac maily withi w. Th total gratio hotocurrt quals to th lctros hotocurrt i th -sid as show i Fig., so th quatum fficicy is giv by, w J diff h q 1 cosh w L,, L w (0) o 1 L L sihw L 5.. Mdium Wavlgths Figur. Absortio du to short wavlgths. Th absortio dth i this cas is comarabl with w w. Sigificat hotogratio ow taks lac withi υ-layr. Th total gratio hotocurrt quals to th lctro hotocurrt i th -sid lus drift hotocurrt i th υ-layr as show i Fig. 3, so th quatum fficicy is giv by, w J diff h J drift h w q 1 cosh w L,,,, w w w w o L sih w L 1 (1) by surig L 1, w 1 () 137

9 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) Figur 3. Absortio du to mdium wavlgths Log Wavlgths I this situatio th absortio dth is logr tha w w, as show i Fig. 4. Th total gratio hotocurrt quals to th lctro hotocurrt i th -sid lus drift hotocurrt i th υ-layr lus hol hotocurrt i th -sid. Th quatum fficicy is, J diff, h, J drift, h, w J diff, h, q w o w w w w w L 1 1 L w w L 1 cosh w L sihw L (3) Figur 4. Absortio du to log wavlgths. Th flowchart i Fig. 5 shows th sts of th aalysis to obtai th quatum fficicy at diffrt wavlgths of icidt light. 6. Maximum Quatum Efficicy Th rlatio btw quatum fficicy ad wavlgth is giv by [10], m 1. 4 (4) whr is rsosivity of th dvic. 138

10 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) From (4), th maximum quatum fficicy ca b obtaid by diffrtiatio rsosivity with rsct to, th sttig th drivativ to zro, this givs a li through th origi that is a tagt to th vrsus curv. This tagtial oit is X as show i Fig. 6. At this oit, 700 m ad 0.45 A W, substitutig ad ito (4) yilds [4], 0.8 or 80 % (5) 7. Rquirmts for Maximum Q.E As dmostratd i sctio (5.) th bst quatum fficicy ca b obtaid for mdium wavlgths, sic th diffusio trms surssd, so th bst dsig is by makig th absortio dth is comarabl to w w. Substitutig () ito (5) yilds, w (6) 3 At 700 mth absortio cofficit is 3 10 cm -1, th from (6) w 5.36 m, this valu rrsts υ-layr width rquird to gt full absortio of icidt light. 1 Usig (1), wh 700 m th f Hz, ad hoto rgy is E h 1.77 V, this rgy is gratr tha th dirct badga rgy of silico, so dirct absortio is obtaid. At w 1, th quatum fficicy is, 1 1 w % (7) 8. Rsults ad Discussio Th uch-through voltag ad quatum fficicy as a fuctio of υ-layr width ar show i Fig. 7 ad Fig. 8, rsctivly. Th rortd quatum fficicy is 63 % at υ-layr width of 0.33 m, ad is 80 % at υ-layr width of 5.36 m. It ca b s that as th width of υ-layr icrass th uch-through voltag is icrasd. Th quatum fficicy icrass with icrasig i υ-layr width. Th quatum fficicy ca b imrovd by makig th width of υ- layr width as much as ossibl, sic this layr is comltly dltd of carrirs. A maximum valu of th quatum fficicy ca b rachd for th cas of mdium wavlgth of dtctio, whr th wavlgth of th icidt light is ot small for maximum absortio ar th surfac to occur that is lad to rduc th quatum fficicy as a rsult of rcombiatio. Also th wavlgth is ot high, whr th light trats mor dly as a rsult of vry small absortio. Th ractical curv btw rsosivity ad wavlgth is show i Fig. 6. From (4) th idal curvs of rsosivity vrsus wavlgth ar show i Fig. 9. This figur is ot a ractical o, sic as wavlgth icrass th absortio cofficit dcrass, ad th th icidt light trs dly ito th dtctor ad this rquirs a larg υ-latr width to gt full absortio. 139

11 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) Cotiuity Equatio -sid x x o G x x L D -layr x Cotiuity Equatio -sid x x Gx L o D Boudary Boudary Coditios 0 w 0 o w w J q drift, h, w G w x Boudary Coditios w w 0 o w w J x drift, h, w q o 1 x d x x d J w qd Jdiff, dark, Jdiff, h, d x x d J w w qd J diff, dark, J diff, h, Diffusio Photocurrt J diff, h, Diffusio Photocurrt J diff, h, For short wavlgths J diff q, h, o For log wavlgths Jdiff, h, Jdrift, h, w J diff, h, o q For mdium wavlgths J diff, h, J drift, h, w o q Figur 5. Flowchart showig sts to obtai quatum fficicy. 140

12 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) Figur 6. Rsosivity vrsus wavlgth Figur 7. Puch-through voltag vrsus υ-layr width Figur 8. Quatum fficicy vrsus υ-layr width 141

13 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) 9. Coclusios Figur 9. Idal curv for rsosivity vrsus wavlgth for diffrt quatum fficicy valus Th aalysis of -υ- hotodtctor was accomlishd. Th followig oits ar cocludd; i- At low frqucy of icidt light th -υ- hotodtctor ca orat with log wavlgths (lss hoto rgy). ii- At high frqucy, th absortio cofficit b high, th th light absorbd ar th surfac, th rcombiatio rat ar th surfac is vry high du to rcombiatio ctrs ar it, th th quatum fficicy b low. If th light frqucy is low, th th light trs dly ito th saml, ad if th coditio E h Eg dos ot xist, th th dtctor is as trasart layr (th light ot absorbd by th dtctor) ad th quatum fficicy is low. iii- At a υ-layr width of 5.36 m, th low biasig voltag rquird about 7.5 V, that is bcaus th υ-layr i -υ- hotodtctor is alrady dltd. iv- I th hotodtctor dsig, th choosig of υ-layr width, ddig o th absortio cofficit, which i tur fuctio of wavlgth of icidt light. v- Sic a high width of υ-layr lads to high quatum fficicy, this lads also to bttr RC tim costat accordig to low valu of juctio caacitac. This icrass th trasit tim of carrirs to ass through υ-layr, ad affct th badwidth caability of th dvic. A trad-off btw th mtiod aramtrs should b tak ito cosidratio for otimum dvic oratio. Rfrcs 1. Gr, M.A. ad Kvrs, M.J. (1995). Otical rortis of itrisic silico at K 300. Progrss i Photovoltaics, Rsarch ad Alicatios, Vol. 3, No. 3, Schaub, J.D, Li, R., Schow, C.L. ad Cambll, J.C. (1999). Rsoat-cavity-hacd highsd Si hotodiod grow by itaxial latral ovrgrowth. IEEE Photoics Tchology Lttrs, Vol.11, No.1,

14 Joural of Egirig ad Dvlomt Vol. 19, No. 06, Novmbr (ISSN ) 3. Habiboor, A. ad Mashaykhi, H.R. (011). Numrical modlig of th trasit rsos of mtal-smicoductor-mtal hotodtctor usig discrt Fourir trasform. Joural of Physics, Vol. 86, No.1, Kasa, S.O. (01). Otolctroics ad Photois. d Ed., Prtic Hall. 5. Suzuki, G., Koo, K. Navarro, D., Sadachika, N., Mizuka, Y., Matsushima, O. ad Miura-Mattausch, M. (005). Tim-domai-basd modlig of carrir trasort i latral i hotodiod,. Itratioal cofrc o IEEE, Simulatio of Smicoductor Procsss ad Dvics, Colig, J.P. ad Colig, C.A. (005). Physics of Smicoductor Dvics. Srigr, 7. Zghbrock, B.V. (001). Pricils of Smicoductor Dvics. Prtic-Hall. 8. Jou, J.J., Liu, C.K., Hsiao, C.M., Li, H.H. ad L, H.C. (00). Tim-dlay circuit modl of high-sd -i- hotodiods. IEEE Photoics Tchology Lttrs, Vol.14, No. 4, Adrso, B.L. ad Adrso, R.L. (004). Fudamtals of Smicoductor Dvics McGraw-Hill. 10. Yu, J., Sha, C.X., Qiao, Q., Xi, X.H., Wag, S.P., Zhag, Z.Z. ad Sh, D.Z. (01) Ehacd rsosivity of hotodtctors ralizd via imact ioizatio. Ssors, Vol. 1, No.,