- 81 -

q M -q ox = 3.15eVq ox -q Si = 3.1eVq s = q Si +E g/2+(E i -E Fs)

- 82 -

V G = V FB = M - S= MS =- 0.8V

- 83 -

(x)≡[E i (bulk)-E i(x)]/q

s≡[E i (bulk)-E i(0)]/q

F≡[Ei (bulk)-EF]/q = kTq ln (NA/n i) for p-type =- kTq ln (ND/n i) for n-type

s =2 F

≈-qNA ...0≤x≤W

W≈W max = 2 sqN A(2 F)

- 84 -

∙

∴

∴

s = 2 F

VT = VFB +2 F + |-Qd ( s = 2 F)|C oxQd=-qNAW=- 2 sqNA(2 F)

- 85 -

V QC = Q/ V

C(accu)≈C ox

C(depl) = C sC oxC s+C ox

QC( inv,LF)≈C ox

C( inv,HF) = C sC oxC s+C ox

- 86 -

μ

Δ

- 87 -

- 88 -

Q d( s = 2 F +V c)≈Q d( s = 2 F)V G≈V FB +2 F + - Q d ( s = 2 F)

C ox+V c+ - Q nC ox

= V TH+V c+ - Q nC ox

Q n =-C ox(V G -V T -V c)

V TH = V FB+2 F + - Q d ( s = 2 F)C oxQ d =-qN A W=- 2 sqN A(2 F)

- 89 -

J n≈J ny = q nnE y + qD ndn/dx≈q nnE y =- q nn dV cdyI D =- J nydxdz =-W x c(y)

0 J nydx

I D =-W nQ ndV cdy

Q d( s = 2 F +V c)≈Q d( s = 2 F) Q n≈- C ox (V G -V TH-V c)L

0 I Ddy≈ V D

0 W nC ox(V G -V TH-V c)dV c

I D = nC oxWL [ ( V G -V TH)V D -V 2D /2]

I Dsat = 12 nC oxWL ( V G -V TH) 2

- 90 -

i D = 12 nC oxWL [ (VG +v g)-VT] 2

= 12 nC oxWL (VG-VT) 2(1+ v gVG-VT

) 2

≈I D(1+2 v gVG-VT)

= I D +i d

∴i d = I D(V G-V T)/2 v g≡g mv g

Cgs≈23 C oxWL for saturation region

C gd≈CoxWL ov for saturation region

g d = IDVA

g m = I D(V G-V T)/2

i i = jW(Cgs +Cgd)vg i o(vd=0)≈gmvg

| i oi i(f=fT)|= gm2 fT(Cgs+Cgd) =1

f T = gm2 (C gs+C gd)

- 92 -

s = 2 F -VBS

V TH = V FB+2 F - Q IC ox- Q d( s = 2 F -VBS)

C oxQ d =-qNAW=- 2 sqNA(2 F -V BS)

V TH = V TH0+ ( 2 F -VBS- 2 F)V TH0 = V FB+2 F - Q IC ox

- Q d( s = 2 F)C oxand = 2 sqN A/C ox

- 93 -

I D = 12 nC oxWL (VG-VT) 2

ID=ID0eqVGnkT

(= 1n )≡ d sdVG= 11+d ox/d s

= 11+C d/C ox

n or ≡ ΔΔΔΔ

S≡ dVGd( log ID) = ln(10) dVGd( ln ID) = ln(10) kTq n = ln(10) kTq [1+Cd/Cox]

- 94 -

V DS≥V GS - V T

1 = 1lattice

+ 1impurity

+ 1surface

≈ 1surface

s = 01+U 0(V GS -V TH)

= s[1+[ E yE crit] 2]1/2

I D = 0[1+U 0 (V GS-V TH)] ×C 'oxW eff/L eff(1+ U 1L eff

V DS) × [ ( V GS -V T)V DS - a2 V2DS]

- 95 -

- 96 -

VT-VFB =2| B|+ |QD( eff)|Cox

Q'D = 1ZL [qx dmZ L+L'2 NA] = fQDwhere f=1- r jL {[1+ 2x dmr j

]1/2-1} < 1

VT =- qNAx dmr jC oxL ( 1+ 2x dmr j-1)

- 97 -

VT = 1+ x dmW

- 98 -

- 99 -

VT = V FB +2 F + -Q d ( s = 2 F)-Q IC ox

Q I =-qN I and Qd =-qNAW=- 2 sqNA(2 F)N I = 2.6×10 11boron ions/cm 2, x o=0.1 m

- Q I /C ox =+ 1.22V, V T= 1.0V