MOSFET 2007 11 19 HiSIM HiSIM2 1
p/n Junction Shockley - - on-quasi-static - - - Y- HiSIM2 2
Wilson E f E c E g E v Bandgap: E g Fermi Level: E f HiSIM2 3
a Si 1s 2s 2p 3s 3p HiSIM2 4
Fermi-Dirac Distribution Density-of of-state 1 f(e) D g(e) Carrier Concentration [ ] D p Ev E f E f n i 1- f ( E) g( E) ( ) ( ) D g E f Ec n E E n= N N f E E c : effective density of state N v : E n i =1.4x10 10 /cm 3 n = c p= N E Ec E E v top v bottom exp exp ( ) ( ) g E f E de ( ) ( ) p = g E f E de Ec -E kt fn E -E fp kt D (1- ) D v HiSIM2 5
p n Si Si Si Si Si Si Si -q Si Si Si B Si +q Si Si Si Si Si Si Si Si Si Si p + Si Si Si Si +q -q n i =1.4x10 10 /cm 3 Ev E f Ec E Ev E f Ec E Ev E f Ec E HiSIM2 6
Fermi n= n p= n c - fn cexp E E N c kt - fp v vexp E E N v kt = n i exp(-q(φ fn -φ i )/kt) = n i exp(-q(φ i -φ fp )/kt) E c E fn E=-qφ N c N v exp(e g /kt)=n i 2 E i E fp pn=n 2 i E v HiSIM2 7
p/n p/n Junction Equilibrium Condition - +q - +q - +q - +q + -q + -q + -q + -q - +q - +q - +q - +q + -q + -q + -q + -q - +q - +q - +q - +q + -q + -q + -q + -q - +q - +q - - - +q - +q - - - +q - +q - - / + + + -q + -q + + + -q + -q + + + -q + -q - + : N A : N D depletion region) HiSIM2 8
Fermi E fp p-type qx qφ f p n-type qφ f n E 0 E E c fn E v p/n E fp E c E fn E v Depletion Region - - ε E c E E f i E v HiSIM2 9
Poisson (x) E(x)=-dφ/dx ε ε ε ε ε HiSIM2 10
HiSIM2 11
HiSIM2 12
MOSFET Vg SOURCE v d Metal Electrode Oxide z SOURCE GATE DRAIN y n + Tox r j n+ x Channel L P-Type w Vb HiSIM2 13
HiSIM2 14
MOSFET Meyer Model J. E. Meyer, RCA Rev., vol. 32, p. 42, 1971. C. T. Sah, IEEE TED, ED11, 324, 1964. HiSIM2 15
MOSFET V gs V ds E y E x I qnv q: n: v V gs V ds HiSIM2 16
Vgs Semiconductor Surface E C E g ( φ > ) S qφ S 0 qφ qφ B E i E F E V Insulator p-type Semiconductor x HiSIM2 17
E F V <0 p -type - - + + + + + + + + + ++ E C E i E F E V V 0 E F V >0 n -type --- -- - - - - - - - + + E C E F E i E V V >0 E F - - - + + + + + E C E i E F E V E F V <0 - - - - - + + + E E C E F i E V V >0 E F - --- - - - - - - - + + + + + E C E i E F E V E F V <0 - + ++ + + ++ + - - - - + + + E C E E F i E V HiSIM2 18
HiSIM2 19
( x ) Poisson :φ s 2 d φ ρ = 2 dx ε S ρ ( x) = q( N D N A + p n) N D N A = np0 pp0 p n = p exp ( βφ) n exp ( βφ) p0 Gradual Channel p0 x 2 φ = q ( ) ( ) ε p exp βφ 1 n exp βφ 1 2 p0 p0 x S φ/ x q φ ( ) ( ) d = ε p exp φ 1 n exp 1 d 0 x x 0 p0 p0 E 2 S φ φ β βφ φ 2 qp β 2kT n p0 = ( β q exp φ) + βφ+1 + p0 ( βφ) βφ 2ε p exp 1 E S si p0 ε = E ε = Q S : E ox ox s s HiSIM2 20
MOS HiSIM2 21
φ S Q b =sqrt(βφ s ) Q i =function(φ s ) charge-sheet HiSIM2 22
HiSIM2 23
V gs V ds E y E x I qnv q: n: v V gs V ds HiSIM2 24
d I = φ ds Wµ qn dy Ids dy = Wµ qndφ φ y = φ + V y ( ) ( ) 0 (y) Gauss Eoxε ox = ESiε Si = QS Vgs Vfb φ ( xy) = 0) ε T ox = Q Q ox n b ( ) 2 ( ) Q n = qn= Vgs Vfb φ0 V y Cox + εsiqnsub φ0 + V y L I dy = Wµ ds V ds 0 0 Q dv n W 1 I = µ C ( Vgs V ) V V L 2 2 ds ox th ds ds φ 0 =2Φ B ; V th = 2Φ + B 2E qn 2Φ C Si sub B ox HiSIM2 25
I ds V th V ds HiSIM2 26
HiSIM2 27
MOS φ f : (0 V ds ) φ s? V gs HiSIM2 28
φ φ φ SL : Gradual-Channel HiSIM2tut028 29
(y) ( ) ( ) ( ) dlnn y 1 dn y = dy n y dy ( ) ( ) I dφ y dn y ds s + n( y) β = W qµ dy dy eff L 0 ( ) I = I y dy ds ( ) ( ) C V y Q qn y ox G φs = B + ds HiSIM2 30
HiSIM2 32
HiSIM2 33
φ φ 2Φ B φ SL : Gradual-Channel HiSIM2tut028 34
- - HiSIM2 35
HiSIM2 36
Gradual-Channel φ φ HiSIM2 37
Channel-Length Modulation HiSIM2 38
HiSIM2 39
HiSIM2 40
Drift : : : HiSIM2 41
I x (t)=i x (V(t))+dQ x /dt HiSIM2 42
HiSIM2 43
HiSIM2 44
tut041 HiSIM2 45
tut042 HiSIM2 46
HiSIM2105 tut051 HiSIM2 47
IdVd gds NMOS Large HiSIM2 Measurement IdVg_low IdVg_low gm_low gm2_low gm3_low IdVg_high IdVg_high gm_high gm2_high gm3_high HiSIM2 48
L gate =40nm HiSIM2 49
HiSIM2 50
s SPICE ) HiSIM2 51
Donald O. Pederson You don t get any credit for doing 95 percent of the job. SPICE: Simulation Program with Integrated Circuit Emphasis HiSIM2 52
Circuit Simulator : Finding a set of for SPICE I ( I, I, I,... I ) s 1 2 3 n V = ( V, V, V,... V ) s 1 2 3 n by fulfilling the kirchhof law. m m+1 m V =V - I m g g V = - I + g V m I m m+1 m m m m+1 V m V Newton s Method HiSIM2 53
2 (V 2 ) I 21 Device1 1 (V 1 ) I 11 I 12 I I 13 31 I 22 Device2 I 42 I 1 =I 11 +I 12 +I 13 I 2 =I 21 +I 22 I 3 =I 31 +I 13 3 (V 3 ) Device3 I 33 I 43 m m m m m m I11 I11 I 11 I11 I11 I 11 + + + + + + V1 V2 V3 m+1 m V1 V2 V 3 V 1 +I m 11 V 1 m m m m I21 I21 I m m 21 m+1 m I21 I 21 I m + + + V 2 = - +I 21 + 21 + + + V2 V1 V2 V3 V m+1 m 1 V2 V3 m m m m V 3 +I31 I31 I31 I m m m V3 31 + + + I31 I31 I 31 + + + V1 V2 V 3 V1 V2 V 3 HiSIM2 54