6.012 Electronic Devices and Circuits Formula Sheet for Final Exam, Fall q = 1.6x10 19 Coul III IV V = x10 14 o. = 3.

Transcription

1 6.0 Elctc Dvcs ad Ccuts ula Sht f al Exa, all 003 Paat Valus: Pdc Tabl: q.6x0 9 Cul III IV V x0 4 /c,,s.7,,so 3.9 B C N 0 S /c, SO 3.5 x0 3 /c Al S P [S@R.T] 0 0 c 3 Ga G As /q 0.05 V ; ( /q) l V I S Sb x0 4 c Dft/Dffus: Elctstatcs: Dft vlcty : s ± E de(x) x x (x) E (x) ( x)dx Cductvty : q( + ) h d dx ( x) ( x) E (x)dx Dffus flux : D C E (x) dx x d ( x) D (x) (x) (x)dxdx Est lat : dx q Th v Basc Equats: ( x, t) J ( x, t) Elct cctat : (x, t) [( x,t) ( x,t) ](T) t q x ( x, t) J + h (x,t) Hl cctat : ( x, t) [(x,t) (x,t) ](T) t q x (x, t) Elct cut dsty : J (x, t) q ( x, t)e (x,t) + qd x (x, t) Hl cut dsty : J h (x, t) q h ( x, t)e (x,t) qd h x Pss's quat : E (x, t) q [ (x, t) (x, t) + N + d (x) x N a (x)] Uf d, full zat, TE - ty, N d >> N a N N D d N a N D,, l q - ty, N a >> N d N A N N d N A,, l a q Uf tcal xctat, uf d d' + ' + ' ' ' l (t) ( + + ')' dt w lvl ct, ',' << + : d' + ' l (t) wth ( ) dt

2 lw bls (ufly dd quasutal s wth quas-statc xctat ad lw lvl ct; -ty xal): Mty ca xcss : d '(x) '(x) ( x) dx D D Mty ca cut dsty : d'(t) J (x) qd dx Maty ca cut dsty : J h (x) J ( x) J Tt Elctc fld : E (x) J h (x) x D h J (x) q h D de (x) x Maty ca xcss : '(x) '( x) + q dx N-ufly dd scduct sal thal qulbu d (x) q { [ q ( x) q (x ) ] [N d ( x) N a( x)]} dx (x ) (x) ( x) q, (x) q, Dlt axat f abut - uct: (x) ( x) ( x) 0 f x < x qna f x < x < 0 NAx x q f 0 < x < x N A 0 f x < x b l q w(v AB ) S ( b v AB ) (N A + ) q ( b v AB ) N A E k q N A S (N A + ) N A qdp (v AB ) AqN A x (v AB ) A q S ( b v AB ) ( N A + ) Idal - uct dd -v lat: qv AB / ); (x ) qv AB / qv AB (-x / ) qv AB /, '(-x ) (, '(x ) ( ) D A q N A N A D h w,ff D + NA w,ff [ qv AB / -] w,ff tah[(w w x f >> w x ) ] f ~ w f << w -x w q QNR, -sd Aq '(x)dx, q QNR, -sd Aq '(x)dx, Nt : '(x) '(x) QNRs -w x

3 Ebs-Mll Mdl f Bla Juct Tasst (BJT) chaactstcs ( xal; bas wdth dulat): ] E D NDE we,ff he D h w D B,ff E he + E Aq h D + [ qv BE / N w DE E,ff w B,ff E D qv BE / w B,ff w B,ff C E ( B ) Aq [ ]( B ) wth B w B,ff D D qv BE / ( B ) [ ]( E + B ) w C B,ff B he + B E E ( E + B ) Aq B ( E + B ) a Sal BJT Mdl wad Actv R (AR) (; wth bas wdth d): qv BE B (v BE,v CE ) I BS [ ] wth I BS ( + ) I ES qv BE C (v BE,v CE ) [+ v CE ] B (v BE,v CE ) I BS [ ( + ) Aq ][+ v CE ] D B D + he w B,ff w E,ff N DE Bak - t dl : v BE, 0.6V, v CE,sat 0.V MOS Caact: lat - bad vlta : V B v GB at whch (0) S V B S Thshld vlta : v GC at whch (0) S + v BC ]} / S [ S V (v ) V T BC B S + C * { S qn A [ S v BC x DT (v BC ) x * * Ivs lay sht cha dsty : q N C x [v GC (v BC )] * Accuulat lay sht cha dsty : q P C * x [v GB V B (v BC )] qn A v BC ] Gadual Chal Ax. f MOSET chaactstcs (-chal; chal lth d.): Vald f v BS 0, ad v DS 0 : G ) 0 ad B ) 0 0 f [v GS )] < 0 < v DS * W D GS DS BS x [v GS )] f 0 < [v GS )] < v DS W * v C x v GS ) DS vds f 0 < v DS < [v GS )] wth ) V B S + C * { S qn A [ S x v ]} / BS / + * C x [ S qn A S v BS ] C * x x t x

4 a Sal MOSET Mdl Satuat (AR) (-chal; wth bas wdth d.): G ) D ) 0 B ) 0 K [ v GS )] [+ v DS ] W wth K C * x ad V B S + C * { S qn A [ S v BS x Sall sal la quvalt ccuts: - Dd BJT ( AR) d q I BS qv AB / q I D C d C d + C df, wh C d (V AB ) A q ( b ad N S A VAB ) q I D [w x ] [w x ] C d d wth df (V AB ) d D D ]} / q I C I C I C V A C b + B - E dlt caactac, wh b D C B- C dlt caactac MOSET ( satuat) w B ty. bas I K I D I D D K V -VT I D GS (V GS - ) V A b qn S A K I D wth * C x q V BS * C s W C x C sb, C b, C db : dlt caactacs 3 * * C d W C d wh C d s th at - t - da f ad vla caactac ut at wdth

5 Sl tasst aal ccut buld blck stas Bla:-basd stas Vlta Cut Iut Outut a, A v a, A sstac, R sstac, R C tt l [ + l ] ( l ') [ + l ] C bas [ + ] [ [ + ] + l ] ( l ') [ + ] l t + Ett fllw + [ + ] [ l ] [ + l ] l ' [ + ] Ett dat - l + [ + ]R (ss fdback) R [ G ] R l Shut fdback [ + G ] G + G [ A v ] R [ + G ] MOSET-basd stas Vlta Cut Iut Outut a, A v a, A sstac, R sstac, R C suc l ' C at [ + b ] l ' [ + b ] t Suc fllw Suc dat (ss fdback) Shut fdback + [ + b + ] [ + + l ] [ + + l ] - l R [ G ] R l R [ + G ] G G [ A v ] R [ + G ] OCTC/SCTC OCTC stat f HI : HI [ ] R C wth R dfd as th quvalt sstac aalll wth C, wth all th aastc dvc C's (C 's, C 's, C s 's, C d 's, tc.) ccutd. SCTC stat f O : O [RC ] wth R dfd as th quvalt sstac aalll wth C, wth all th bas ad cul C's (C I 's, C O 's, C E 's, C S 's, tc.) sht ccutd.

6 Dffc- ad C-d sals Gv tw sals, v ad v, w ca dcs th t tw w sals, (v C ) that s c t bth v ad v, ad (v D ) that aks a qual, but st laty, ctbut t v ad v : CMOS fac Tasf chaactstc vd v v ad v C [ v + v ] v D v v C + v D ad v v C I al : V O 0, V HI V DD, I ON 0, I O 0 Syty : V M V DD ad N M N MH K K ad Mu sz at :, W ( )W, W W Swtch ts ad Gat dlay :Pw dsat V DD C Ch a Dsch a K [V DD ] * * C ( + W W )C x 3W C x assus h V DD M.Cycl Ch a + Dsch a [V DD ] P Max. f C V DD f ax µ C V DD PD Max. f W C * V x DD [V DD ] M.Cycl Max. f P Max. f Ivt aa µ W V x DD [V DD ] t x