Lecture #21 OUTLINE The MOS apactor Electrotatc Readng: oure Reader EE130 Lecture 21, Slde 1 MOS apactor Structure MOS capactor (croectonal vew _ TE x EE130 Lecture 21, Slde 2 Typcal MOS capactor and trantor n I today employ heavly doped polycrytallne ( poly flm a the gateelectrode materal n type, for nchannel trantor (NMOS p type, for pchannel trantor (PMOS O 2 a the gate delectrc band gap 9 e ε r,o2 3.9 a the emconductor materal ptype, for nchannel trantor (NMOS ntype, for pchannel trantor (PMOS
ulk Semconductor Potental ψ qψ E ( bulk E F ptype : kt ψ q ln( N / n > 0 E F qψ E Ev ntype : kt ψ q D ln( N / n < 0 E F qψ E EE130 Lecture 21, Slde 3 MOS Equlbrum Energyand Dagram 3.1 e 3.1 e N polylcon O 2 Plcon body gate 9e body E f (a How doe one arrve at th energyband dagram? (b EE130 Lecture 21, Slde 4
udelne for Drawng MOS and Dagram Ferm level E F flat (contant wth dtance x n the nce no current flow n the x drecton, we can aume that equlbrum condton preval and bendng lnear n the de No charge n the de > d /dx 0 o contant > d /dx contant From au Law, we know that the electrc feld trength n the at the urface,, related to the electrc feld trength n the de, : ε ε 3 dec dec o 3 dx dx de ( at the urface EE130 Lecture 21, Slde 5 MOS anddagram udelne (cont. The barrer heght for conductonband electron flow from the nto O 2 3.1 e Th equal to the electronaffnty dfference (χ and χ O2 The barrer heght for valenceband hole flow from the nto O 2 4.8 e The vertcal dtance between the Ferm level n the metal, E FM, and the Ferm level n the, E FS, equal to the appled gate voltage: q E FS E FM EE130 Lecture 21, Slde 6
oltage Drop n the MOS Sytem In general, where q φ MS φ M φ S the voltage dropped acro the de ( total amount of band bendng n the de ψ the voltage dropped n the lcon (total amount of band bendng n the lcon qψ E ( bulk E ( urface For example: When, ψ 0.e. there no band bendng EE130 Lecture 21, Slde 7 ψ Specal ae: Equal Work Functon Φ M Φ S What happen when the work functon dfferent? EE130 Lecture 21, Slde 8
eneral ae: Dfferent Work Functon EE130 Lecture 21, Slde 9 Flatand ondton χ O2 0.95 e E 0 qφ M 3.1 e 3.1 e χ qφ χ ( E F, E F N E 0 : acuum level E 0 E f : Work functon E 0 : Electron affnty /O 2 energy barrer poly 9e O 4.8 e Ptype E f EE130 Lecture 221, Slde 10
MOS and Dagram (ntype Decreae (toward more negatve value > move the gate energyband up, relatve to the decreae decreae ccumulaton > Electron accumulate at urface Depleton < Electron repelled from urface Inveron < T Surface become ptype EE130 Lecture 21, Slde 11 ang ondton for ptype ncreae ncreae < T > > EE130 Lecture 21, Slde 12
ccumulaton (n poly gate, ptype M O S < 3.1 e q E FM _ TE ptype 4.8 e q qψ mall, 0 E FS Moble carrer (hole accumulate at urface EE130 Lecture 21, Slde 13 ccumulaton Layer harge Denty < _ TE ptype Q acc (/cm 2 From au Law: t Q where acc t / ε O 2 Q ε acc / / t O2 (unt: F/cm 2 Q acc ( > 0 EE130 Lecture 21, Slde 14
Depleton (n poly gate, ptype T > > M O S q W d _ TE ptype E FM 3.1 e qψ q E FS 4.8 e urface depleted of moble carrer (hole > Surface charge due to onzed dopant (acceptor EE130 Lecture 21, Slde 15 Depleton Wdth W d (ptype Depleton pprmaton: The urface of the depleted of moble carrer to a depth W d. The charge denty wthn the depleton regon Poon equaton: ρ d dx qn ρ ε Integrate twce, to obtan ψ S : ( 0 x Wd qn ε (0 x W d ψ qn W 2ε 2 d W d 2ε ψ qn To fnd ψ for a gven, we need to conder the voltage drop n the MOS ytem EE130 Lecture 21, Slde 16
oltage Drop n Depleton (ptype TE _ Q dep (/cm 2 ptype From au Law: Q ε dep / O2 t Q dep Q dep the ntegrated charge denty n the : Q dep qn W d / ε ψ ψ ψ ε ψ EE130 Lecture 21, Slde 17 Surface Potental n Depleton (ptype ψ Solvng for ψ S, we have ε ψ 2 qn ε 2 ( ψ 1 1 2 qn ε 2 qn 2 ( 1 1 2 2 ε ψ qn ε 2 EE130 Lecture 21, Slde 18
Threhold ondton ( T When ncreaed to the pont where ψ reache 2ψ Β, the urface ad to be trongly nverted. (The urface ntype to the ame degree a the bulk ptype. Th the threhold condton. T ψ 2ψ n E ( bulk E ( urface urface E ( urface E N F 2[ E( bulk EF ] [ E ( bulk E ] F EE130 Lecture 21, Slde 19 MOS and Dagram at Threhold (ptype ψ 2ψ 2 W d W dm kt q N ln n 2ε (2ψ qn M O S q qψ F W dm qψ qψ E FS q E FM EE130 Lecture 21, Slde 20
For ptype : T Threhold oltage ψ 2ψ ε (2ψ ψ ε ψ For ntype : T 2ψ ε 2ψ D EE130 Lecture 21, Slde 21 Strong Inveron (ptype ncreaed above T, the negatve charge n the ncreaed by addng moble electron (rather than by depletng the more deeply, o the depleton wdth reman ~contant at W d W dm TE W dm ρ(x M O S _ ptype x gnfcant denty of moble electron at urface (urface ntype ψ 2ψ W d W dm 2ε (2ψ qn EE130 Lecture 21, Slde 22
Inveron Layer harge Denty (ptype T ψ Q S nv ( Qdep Qnv 2ψ ε (2ψ 2ψ Q nv Q nv ( T EE130 Lecture 21, Slde 23