ECE 340 Lecture 33 : MOS Capacitor I 4/17/14. Class Outline: Ideal MOS Capacitor. Things you should know when you leave. Ideal MOS Capacitor

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1 ECE 34 Lctur 33 : MO Capacitor I Class Outlin: Things you should know whn you lav Ky Qustions What ar th diffrnt bias rgions in MO capacitors? What do th lctric fild and lctrostatic potntial look lik? What is th Dby lngth? What dos th capacitanc look lik as a function of bias? Last tim, w discussd th basic opration of th MOET And how it oprats as w vary V D Pinch off V D Dpltion Rgion Channl Rgion Whn th barrir rgion is sufficintly rducd, thn a currnt flows from th sourc to th drain. V G As w put mor positiv charg on th gat, mor hols ar rplld dplting th concntration nar th surfac and populating it with lctrons. Th point in th gat voltag swp whn significant currnt bgins to flow is th thrshold voltag, V T. This corrsponds to th point whn th channl is formd undr th gat. Wr w to hav mad a PP dvic th application of a ngativ VG would rpl lctrons and attract hol forming a channl. Dpltion Rgion Channl Rgion With V D swpt in small positiv incrmnts, th channl mrly acts lik a rsistor and th drain currnt is proportional to th drain voltag. Past a fw tnths of a volt of bias, th voltag drop from th sourc to th drain associatd with currnt flow bgins to ngat th invrting ffct of th gat. Channl carrirs bgins to dcras lading to a rduction in th channl conductivity. This is du to th lctron flow not bing through th channl but a largr rgion about th drain. Drain currnt is said to b in saturation as changs in V D produc no changs in I D. 1

2 But w saw that th opration in most rgims was controlld by th channl Th channl of a MOET is an xampl of a MO capacitor Usful for: Digital and analog logic Mmory functionality Imaging (CCD) and displays (LCD) What is th structur of a MO capacitor? Havily dopd polycrystallin i film as th gat lctrod matrial. -typ for n-channl transistors (MO). P-typ for p-channl transistors (PMO). io as th gat dilctric Band gap = 9 V. Rlativ dilctric constant ε r = 3.9. i as th smiconductor matrial. P-typ for n-channl dvics. -typ for p-channl dvics. Rmmbr all of th componnts Lt s start with th idal situation, Ф M Chargs only xist at th surfac = Ф of th mtal. W assum that thr ar no chargs or dopants locatd in th oxid rgion. W cannot achiv thrmal quilibrium through th oxid layr. To achiv thrmal quilibrium w nd to us a wir to connct th mtal to th smiconductor. Lt s now apply a ngativ gat voltag to our MO capacitor Applying a ngativ gat voltag dposits ngativ charg on th mtal. W xpct to s this charg compnsatd by a nt positiv charg on th smiconductor. Th applid ngativ voltag dprsss th potntial of th mtal. As a rsult th lctron nrgis ar raisd in th mtal rlativ to th smiconductor. Moving E M up causs a tilt in th oxid bands and th smiconductor bands p = n i Ei E E ( x) 1 dei = q dx Mor hols accumulat at th surfac of th smiconductor. ow apply a positiv gat voltag Dposition of positiv charg on th gat rquirs compnsation by ngativ chargs in th smiconductor. Th ngativ charg in a p- typ smiconductor ariss from th dpltion of hols from th surfac. This lavs bhind uncompnsatd ionizd accptors. Th bands bnd downward nar th smiconductor surfac (E I closr to E ). Incrasd lctron concntration What happns if w kp incrasing th amount of positiv gat voltag w apply to th mtal rlativ to th smiconductor?

3 Whn V G is larg nough, th surfac is invrtd. Th n-typ surfac that forms as a rsult of th applid lctric fild is th ky to transistor opration! Dfin a potntial q which dtrmins how much band bnding thr is at th surfac. Whn q = w ar in flat band condition. Whn q < w hav hol accumulation at th surfac. Whn q > w hav lctron accumulation at th surfac. Whn q > q w hav invrsion at th surfac. urfac should b as strongly n-typ as th body is p-typ. IV IV q = E bulk I E k bt = = ln q ni k bt = = ln q ni A D What othr physical information can w obtain from this structur? Elctron and hol concntrations ar rlatd to th potntial n = n E EI i = n q i W thn know th lctron (hol) concntration at any x q( ) q n = n = n Elctrons p = p q Hols But w still nd th potntial, how do w gt it? Poisson Equation Total Charg Dnsity Us Poisson quation and total charg dnsity to gt th total charg ubstitut in our knowldg of carrir concntrations and w gt d q = = p x x x ε Elctric ild q d = x x ε dx q p k 1 n q T 1 q b q 1 n 1 d Intgrat from th bulk (whr th bands ar flat, thr ar no lctric filds, and th doping alon sts th carrir concntrations) towards th surfac W now intgrat and xamin th rsult at th surfac (x = ) whr th prpndicular lctric fild bcoms Dby lngth distanc at which charg fluctuations ar scrnd out to look lik nutral ntitis. o what dos th surfac charg dnsity look lik? Us Gauss Law to find th charg: Qs = ε sξs At s = thr is no spac charg. Whn s is ngativ w accumulat majority hols at th surfac. Whn s is positiv initially th linar trm in th lctric fild solution dominats as a rsult of th xposd, immobil dopants. Dpltion xtnds ovr svral hundrd nm until w rach strong invrsion and th xponntial fild trm dominats. 3

4 What is th charg distribution on an invrtd surfac? or simplicity, lt s assum complt dpltion for < x < W and nutral matrial for x > W. Charg du to uncompnsatd accptors is q a W. Positiv charg on th mtal Q M is balancd by ngativ charg Q in th smiconductor which is th dpltion layr charg plus th charg du to th invrsion rgion Q. Q M = Q = q W Q Th dpltion width hr is xaggratd and is typically only on th ordr of 1 nm. a What about th lctric fild and th potntial? Th lctric fild dos not pntrat th mtal. It is constant across th oxid as thr ar no chargs or impuritis in th oxid. Th lctric fild in th smiconductor drops linarly, as w would xpct. Th potntial is constant in th mtal. It is drops linarly across th oxid (V I ). Th potntial is also droppd across th dpltion rgion of th smiconductor,. Q will b ngativ for an n-channl giving a positiv V I. Lt s xplor th dpltion rgion mor rom considrations basd on othr systms (p-n junction), w can us th dpltion approximation to show that What about th capacitanc of our structur? Th capacitanc dpnds on th voltag Lngth of dpltion rgion Th dpltion rgion grows with voltag until strong invrsion is rachd. o what is th maximum valu of th dpltion width? And th charg in th dpltion rgion at strong invrsion. Which must b drivn by an applid voltag. Th applid voltag rquird for strong invrsion is Assums ngativ charg at surfac is du to dpltion charg. MO Capacitor is th sris combination of th oxid and th voltag dpndnt smiconductor capacitancs. In accumulation: Th capacitanc is hug. tructur acts lik a paralll plat capacitor piling hols up at th surfac. 4

5 tart incrasing th voltag across th capacitor Th surfac bcoms dpltd and th dpltion layr capacitanc nds to b addd in Total capacitanc: In dpltion: Capacitanc dcrass as W grows until invrsion is rachd. Charg in dpltion layr of MO capacitor incrass as ~ ( ) 1/ so dpltion capacitanc dcrass as th invrs. If signal applid to mak masurmnt is too fast, invrsion layr carrirs can t rspond and do not contribut. lowly varying signals allow tim for minority carrirs to b gnratd, drift across dpltion rgion, or rcombin. Majority carrirs in th accumulation rgion rspond much fastr. 5