Context. Lecture 10: P-N Diodes. Announcements. Transport summary. n p

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1 Cotext Lecture : P oes I the lst few lectures, we looke t the crrers semcouctor, how my there re, how they move (trsort) Mss cto lw, oors, Accetors rft ffuso I the ths lecture, we wll ly these cocets to P oes Aoucemets Trsort summry The Thursy lb secto wll be move hour lter strtg ths week, so tht the TA s c tte lecture other clss Reg: Strt chter 3 the text The umber of mjorty crrers eutrl semcouctor goes ccorg to the umber of oors or ccetors, the umber of morty crrers s fou from the lw of mss cto For tye mterl: For tye mterl: The totl curret s gve by the sum of rft ffuso: = rft ff = qµ E q x 1

2 Electrosttcs summry The chcke the Egg I oe meso, the electrosttcs equtos reuce to the E fel growg or mshg eeg o the et chrge: ρ( x') E( = E( x) x' ε x x Whch c lso be wrtte s fferetl equto for the otetl (voltge). φ ( ρ( = x ε We ee to f both the osto of the chrges, whch wll crete the E fel, but the E fel wll lso ush the chrges rou. Fortutely, most cses we wll be ble to brek ths u to two smle cses: Regos where the moble holes or electros re swet out by E fel, cotrbute eglgbly to the chrge Regos where eutrlty s mte, there s o E fel The regos whch the mout of chrge from moble crrers s eglgble re clle eleto regos et Chrge The P jucto The et chrge esty semcouctor s clculte from the umber of chrge crrers fxe chrges locto: ρ( = q ( ( ( ( ( ) If rego oes ot hve the rght umber of electros or holes to ccel the mout of chrge from the ots, the fxe chrge of the ots wll fluece the electrc fels. The P jucto s just semcouctor where oe rego oe wth oors s ext to other oe wth ccetors. P juctos re usully me by mltto or ffuso, or sometmes by growg semcouctor wth ots s ew lyer. P Tye Tye

3 eutrlty rft ow ooses ffuso otce tht f the electros holes were to just to sty where they were, the the whole volume woul be eutrl, there woul be o electrc fel. However, there s tremeous cocetrto gret t the jot, for both the electros the holes. Becuse of the lrge gret the cocetrto, the electros wll strt to wer to the tye mterl, the holes wll strt to wer to the tye mterl Wht stos the electros holes from sreg out to uform cocetrto? P Tye Tye The E fel whch s estblshe by the fxe chrges left bre the eleto rego stos the crrers from ffusg cross. The ffuso s exctly blce by the rft cuse by the E fel therml equlbrum. P Tye Fxe egtve chrges Fxe ostve chrges Tye Estblshmet of otetl brrer P ucto Fels Wht stos the crrers from sreg out uformly: The movemet of the crrers wll cuse et chrge to be eveloe, oosg E fel Excess crrers ( > ) wll me tht recombto wll be fster th geerto, the extr oulto wll recombe go wy. The e result wll be rego elete of electros holes, therefore left wth chrge: P Tye Fxe egtve chrges Fxe ostve chrges Tye = Hole oulto I most cses, the oultos chge by my orers of mgtue, so quckly becomes smll comre to P Tye = E E Fxe egtve chrges Fxe ostve chrges ( x ) ff rft x x ff rft Tye = = Electro oulto eleto Rego: moble crrer esty << fxe chrge u to er the eges 3

4 et Chrge eleto Rego To solve for the electrc fels, we ee to wrte ow the chrge esty the trsto rego: ρ ( = q( ) I the se of the jucto, there re very few electros, some holes, the fxe ccetors: ρ( q( ) x < x < Sce the hole cocetrto s reuce o the se, the et chrge s egtve: > ρ ( < Crrer Cocetrto Potetl If we let the oe come to therml equlbrum, the electro hole curret estes ech must be zero everywhere: Where ( ( = = q( µ E( q x ( µ q = ( E ( x = kt x V th kt ( = = V q ( kt = q th ( ( Chrge o Se Crrer Cocetrto Potetl () Alogous to the se, the chrge o the se s gve by: ρ( x ) q( ) < x < x The et chrge here s ostve sce: > = E ff ρ ( > = We hve equto reltg the otetl to the crrer cocetrto kt ( ( = = Vth q ( ( If we tegrte the bove equto we hve ( x) = Vth l ( x ) We efe the otetl referece to be trsc S: x ) = for ( x ) = eleto Rego 4

5 Crrer Cocetrto Versus Potetl P oe equlbrum Voltge The crrer cocetrto s thus fucto of otetl φ ( / V ( = th e Check tht for zero otetl, we hve trsc crrer cocetrto (referece). If we o smlr clculto for holes, we rrve t smlr equto φ ( / V ( = th e ote tht the lw of mss cto s uhel t every ot x: φ ( / Vth φ ( / Vth ( = e e = ( So therml equlbrum, t room temerture, slco P oe wll hve otetl fferece betwee the ses of: ( ( φ 6mV log 6mV log φ ( ( 6mV log The og Chges Potetl Hve we vete bttery? ue to the logrthm, the otetl chges lerly for exoetl crese og: = V th ( ( ( l = 6mV l 6mV llog ( 6mV log ( 6mV log Quck clculto : For tye cocetrto of 16 cm 3, the otetl s 36 mv tye mterls hve ostve otetl wth resect to trsc S (To remember ths: tye mterl ees ostve otetl to kees ts electros from lekg out to the trsc mterl ext to t!) C we hress the P jucto tur t to bttery? A A φb φ φ = V th l l = Vth l umercl exmle:? 15 A φb = 6mV l = 6mV log 15 = 6mV 5

6 B ege grm Abrut jucto, full eleto moel If we rw grm of the eerges of the eges of the vlece b the coucto b, we c see tht the Ferm level, the level tht the electros re flle u to, s the sme cross the jucto. The otetl we clculte ws the fferece betwee the eerges of the coucto b the two regos. I my cses, t s suffcet to coser brut chge from tye to tye ot If the umber of oors o the se, the umber of ccetors o the se re >>, the we c mke the roxmto tht the et chrge esty ρ( s: P tye φ The Ferm level s lwys flt therml equlbrum x q tye x Where x x re the wths of the eleto regos exteg to ther resectve oe regos q B ege grm Forwr bs If the oe s lghtly oe o ech se, the the eutrl regos hve fewer crrers, the Ferm level s further from the b ege ech cse, the otetl fferece s less. Uer forwr bs, voltge s le whch reuces the bult fel, lettg the moble crrers ffuse towr ech other, bult u oulto whch s lrger th the equlbrum oulto. The curret c become very lrge (hures of ms for bg oe) P tye φ The Ferm level s lwys flt therml equlbrum φ Smller th equlbrum tye P tye tye > ( ( 6

7 Reverse bs Alcto: rectfer Uer reverse bs, voltge s le whch creses the bult fel, ullg the moble crrers out of the eleto rego. The rft curret rses oly slghtly, becuse oly the morty crrers geerte crrers get ulle cross the rego. φ Lrger th equlbrum The P jucto c block curret oe recto, whle lettg t ss f the voltge s reverse I the forwr bse (curret ssg) coto, voltge s le to ush the moble crrer regos towr ech other. They recombe t hgher rte, the oe coucts. I the reverse bse coto, the moble crrers re ulle wy from ech other, there s lttle curret. P tye tye < ( ( Forwr or reverse bs (brut jucto, full eleto moel) Alcto: Solr Cell Forwr bs Reverse Bs q x x q x eleto rego rrows q eleto rego s lrger If we ut P jucto brght lght, the lght s bsorbe by rsg electros from the vlece b to the coucto b, thereby cretg electro hole for ech hoto bsorbe. The excess electros holes get swet out of the eleto rego, there s et curret. If the voltge s llowe to rse lttle, the ostve curret voltge ct just lke bttery, sulyg C ower. q x I y cse: q x = q x 7

8 Alcto: Lghtwve recever (etector) P ucto Cctor Smlrly to solr cell, lght hts P oe, electros holes re geerte. Ths cuses excess rft curret, c be mlfe to ct s recever for otcl sgls from otcl fber. Uer therml equlbrum or reverse bs, the P jucto oes ot rw y curret But otce tht P jucto stores chrge the sce chrge rego (trsto rego) Sce the evce s storg chrge, t s ctg lke cctor Postve chrge s store the rego, egtve chrge s the rego: q x = q x o o Alcto: Lght Emttg oe Reverse Bse P ucto I LE, oe me of rect bg semcouctor such s Gllum Arsee s forwr bse. The excess holes electros the recombe, emt lght. Semcouctor lsers for otcl commuctos work smlr wy. Wht hes f we reversebs the P jucto? φ V b V < Sce o curret s flowg, the etre reverse bse otetl s roe cross the trsto rego To ccommote the extr otetl, the chrge these regos must crese If o curret s flowg, the oly wy for the chrge to crese s to grow (shrk) the eleto regos V 8

9 Curret Uer Reverse Bs V φ Uer therml equlbrum curret s zero If we ly reverse bs, we re cresg the brrer gst ffuso curret rft curret s low sce the fel oly moves morty crrers cross jucto I fct, curret s ot zero but very smll sce the morty crrer cocetrto s low. Morty crrers wth oe ffuso legth of jucto c cotrbute to reverse bs curret. Ths s more or less eeet of the le bs φ φ V E E φ X X ( V ) Abrut jucto, full eleto moel We f the otetl from: φ ( ρ( = x ε Itegrtg twce, we f: q = x Ax B x < x < ε q = x A x B < x < x ε I the ext lecture, we wll use the boury cotos to f x, the vlues of the costts. x Abrut jucto, full eleto moel For the Abrut jucto, full eleto moel of the P oe, we c f the otetl s fucto of osto by tegrtg over the chrge strbuto ρ( x q x Where x x re the wths of the eleto regos exteg to ther resectve oe regos q 9