MOSFET HiSIM HiSIM2 1

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れんかはしかわ
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1 MOSFET HiSIM HiSIM2 1

2 p/n Junction Shockley - - on-quasi-static Y- HiSIM2 2

3 Wilson E f E c E g E v Bandgap: E g Fermi Level: E f HiSIM2 3

4 a Si 1s 2s 2p 3s 3p HiSIM2 4

5 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

6 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

7 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

8 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

9 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

10 Poisson (x) E(x)=-dφ/dx ε ε ε ε ε HiSIM2 10

11 HiSIM2 11

12 HiSIM2 12

13 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

14 HiSIM2 14

15 MOSFET Meyer Model J. E. Meyer, RCA Rev., vol. 32, p. 42, C. T. Sah, IEEE TED, ED11, 324, HiSIM2 15

16 MOSFET V gs V ds E y E x I qnv q: n: v V gs V ds HiSIM2 16

17 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

18 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 < E E C E F i E V V >0 E F E C E i E F E V E F V < E C E E F i E V HiSIM2 18

19 HiSIM2 19

20 ( 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

21 MOS HiSIM2 21

22 φ S Q b =sqrt(βφ s ) Q i =function(φ s ) charge-sheet HiSIM2 22

23 HiSIM2 23

24 V gs V ds E y E x I qnv q: n: v V gs V ds HiSIM2 24

25 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

26 I ds V th V ds HiSIM2 26

27 HiSIM2 27

28 MOS φ f : (0 V ds ) φ s? V gs HiSIM2 28

29 φ φ φ SL : Gradual-Channel HiSIM2tut028 29

30 (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

31 HiSIM2 32

32 HiSIM2 33

33 φ φ 2Φ B φ SL : Gradual-Channel HiSIM2tut028 34

34 - - HiSIM2 35

35 HiSIM2 36

36 Gradual-Channel φ φ HiSIM2 37

37 Channel-Length Modulation HiSIM2 38

38 HiSIM2 39

39 HiSIM2 40

40 Drift : : : HiSIM2 41

41 I x (t)=i x (V(t))+dQ x /dt HiSIM2 42

42 HiSIM2 43

43 HiSIM2 44

44 tut041 HiSIM2 45

45 tut042 HiSIM2 46

46 HiSIM2105 tut051 HiSIM2 47

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

48 L gate =40nm HiSIM2 49

49 HiSIM2 50

50 s SPICE ) HiSIM2 51

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

52 Circuit Simulator : Finding a set of for SPICE I ( I, I, I,... I ) s n V = ( V, V, V,... V ) s 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

53 2 (V 2 ) I 21 Device1 1 (V 1 ) I 11 I 12 I I 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 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 V2 V1 V2 V3 V m+1 m 1 V2 V3 m m m m V 3 +I31 I31 I31 I m m m V I31 I31 I V1 V2 V 3 V1 V2 V 3 HiSIM2 54

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untitled MOSFET 17 1 MOSFET.1 MOS.1.1 MOS.1. MOS.1.3 MOS 4.1.4 8.1.5 9. MOSFET..1 1.. 13..3 18..4 18..5 0..6 1.3 MOSFET.3.1.3. Poon & Yau 3.3.3 LDD MOSFET 5 3.1 3.1.1 6 3.1. 6 3. p MOSFET 3..1 8 3.. 31 3..3 36