Lecture #11. A Note of Caution

Transcription

1 ctur #11 OUTE uctos rvrs brakdow dal dod aalyss» currt flow (qualtatv)» morty carrr dstrbutos Radg: Chatr 6 Srg 003 EE130 ctur 11, Sld 1 ot of Cauto Tycally, juctos C dvcs ar formd by coutr-dog. Th quatos drvd class (ad th txtbook) ca b radly ald to such dods f t acctor dog o -sd ( - ) -sd t door dog o -sd ( - ) -sd Srg 003 EE130 ctur 11, Sld

2 EE130 ctur 11, Sld 3 Srg 003 ucto Elctrostatcs, 0 Bult- ottal b (o-dgrat dog): lto wdth W : l l l b q q q b s q x x W 1 1 ) ( W x W x EE130 ctur 11, Sld 4 Srg 003 Elctrc fld dstrbuto (x) Pottal dstrbuto (x) ) ( (0) that ot b

3 Pak Elctrc Fld 1 (0) W b For a o-sdd jucto: W s q ( b ) thrfor (0) ( ) q( ) b W b s Srg 003 EE130 ctur 11, Sld 5 ucto Brakdow Forward Currt BR Small lakag Currt P R (a) R Zr dod 3.7 C (b) Zr dod s dsgd to orat th brakdow mod. Srg 003 EE130 ctur 11, Sld 6

4 f rvrs - s so larg such that th ak lctrc fld xcds a crtcal valu crt, th th jucto wll brak dow (larg rvrs currt wll flow) ( ) q b crt s Thus, th rvrs bas at whch brakdow occurs s s crt BR b q BR Srg 003 EE130 ctur 11, Sld 7 valach Brakdow Mchasm Hgh E-fld: BR s crt q f BR >> b Small E-fld: crt crass slghtly wth : For cm -3 < < cm -3, 10 5 /cm < crt < 10 6 /cm Srg 003 EE130 ctur 11, Sld 8

5 Tulg (Zr) Brakdow Mchasm 0: E c omat brakdow mchasm wh both sds of a jucto ar vry havly dod. < 0: Flld Stats - E v Emty Stats E c s crt BR crt q b 10 6 /cm E v Tycally, BR < 5 for Zr brakdow Srg 003 EE130 ctur 11, Sld 9 Emrcal Obsrvatos of BR BR dcrass wth crasg BR dcrass wth dcrasg E G Srg 003 EE130 ctur 11, Sld 10

6 Brakdow Tmratur dc For th avalach mchasm: BR crass wth crasg T Ma fr ath dcrass For th tulg mchasm: BR dcrass wth crasg T Flux of valc-bad lctros avalabl for tulg crass Srg 003 EE130 ctur 11, Sld 11 Currt Flow a ucto od Wh a forward bas ( >0) s ald, th ottal barrr to dffuso across th jucto s rducd Morty carrrs ar jctd to th quasutral rgos > > 0, > 0 Morty carrrs dffus th quas-utral rgos, rcombg wth majorty carrrs Srg 003 EE130 ctur 11, Sld 1

7 Currt dsty (x) (x) d ( x) qµ q qµ q d ( x) qµ q qµ q d( ) d( ) s costat throughout th dod, but (x) ad (x) vary wth osto Srg 003 EE130 ctur 11, Sld 13 dal od alyss: ssumtos o-dgratly dod st jucto Stady-stat codtos ow-lvl jcto codtos rval th quas-utral rgos Rcombato-grato s glgbl th dlto rgo d d 0, 0.. & ar costat sd th dlto rgo Srg 003 EE130 ctur 11, Sld 14

8 dal od alyss: roach Solv th morty-carrr dffuso quatos quas-utral rgos to obta (x, ), (x, ) aly boudary codtos -sd: (-x ), (- ) -sd: (x ), ( ) trm morty-carrr currt dsts quasutral rgos d( ) d( ) ( x, ) q ( x, ) q Evaluat at x-x ad at xx ( ) ( ) x-x ( ) xx Srg 003 EE130 ctur 11, Sld 15 Carrr Coctratos at x, x Cosdr th qulbrum ( 0) carrr coctratos: -sd -sd 0 0 ) ) 0 0 ( x ( x ) ) f low-lvl jcto codtos rval th quas-utral rgos wh 0, th ) ( x ) Srg 003 EE130 ctur 11, Sld 16

9 aw of th ucto Th voltag ald to a jucto falls mostly across th dlto rgo (assumg that low-lvl jcto codtos rval th quas-utral rgos). W ca draw quas-frm lvls th dlto rgo: Srg 003 EE130 ctur 11, Sld 17 ( E ( F F )/ P E ) / ( E F ) / ( F F ) / P P q / ( F E ) / Excss Carrr Coctratos at x, x ) ) -sd 0 q / q / ( x -sd ) ( x ) q / 0 q / ) q / ( 1) ( x ) q / ( 1) Srg 003 EE130 ctur 11, Sld 18

10 Examl: Carrr jcto jucto has cm -3 ad cm -3. Th ald voltag s 0.6. Qusto: What ar th morty carrr coctratos at th dlto-rgo dgs? swr: q ) o 100 q ( x ) o cm cm -3-3 Qusto: What ar th xcss morty carrr coctratos? swr: Srg ) ) o ( x ) ( x ) o EE130 ctur 11, Sld cm cm -3-3 Excss Carrr strbuto From th morty carrr dffuso quato: d τ W hav th followg boudary codtos: ( x ) o ( q / 1) ( ) 0 For smlcty, w wll dvlo a w coordat systm: EW: x 0 0 x Th, th soluto s of th form: ( x' ) 1 x'/ x'/ Srg 003 EE130 ctur 11, Sld 0

11 ( x' ) 1 x'/ x'/ From th x boudary codto, 1 0. From th x x boudary codto, ( q / o 1) Thrfor, ( x' ) o ( q / 1) x'/, x' > 0 Smlarly, w ca drv ( x'') o ( q / 1) x''/, x'' > 0 Srg 003 EE130 ctur 11, Sld 1 -sd: -sd: od - Charactrstc q q d ( x'') q '' d q 0 ( 1) ( x') q q 0 ( 1) ' x'' x' q x x x x x 0 q ( x 0 1) Srg 003 EE130 ctur 11, Sld

12 EE130 ctur 11, Sld 3 Srg 003 1) ( 0 q q 0 EE130 ctur 11, Sld 4 Srg 003 od Saturato Currt 0 0 ca vary by ordrs of magtud, ddg o th smcoductor matral a asymmtrcally dod jucto, th trm assocatd wth th mor havly dod sd s glgbl: f th sd s much mor havly dod, f th sd s much mor havly dod, q 0 q 0 q 0