r c =r for BJTs = for MOSFETs

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1 - 1 - VCC RL vout vin Transistor + i=v/r + i= vc/rt = gm vc v vc - - Resistor Trans-Resistor=Transistor + vc rc - i=gm vc r c =r for BJTs = for MOSFETs g m = I C V T for BJTs = I DS (V GS -V TH )/2 for MOSFETs

2 - 2 - μ Δ

3 - 3 - V GS -V FB =V oxide +V semi = Q G C ox +[ 2 f +V( y)] = -Q d -Q n +[ 2 C f + V( y)] ox Q n =- C ox [ V GS - V FB - 2 f -V(y)] - Q d (y) Q d =- qn A =- C ox 2 f + V SB + V( y) Q d -C ox 2 f + V SB V I DS =- n C DS ox Q n (y) dv 0 I DS = n C ox L [ ( V GS - V TH )V DS - V2 DS /2] V DS V GS - V TH I DS = 1 2 n C ox L ( V GS -V TH ) 2 V DS > V GS -V TH V TH = V FB +2 f + - Q d C ox = V FB +2 f + 2 f LEVEL = 1, KP( = n C ox ), TOX( C ox = TOX ), VT0( = V TH0 ), PHI( = 2 f ) GAMMA( = ), LAMBDA( = )

4 - 4 - Q d =- qn A =- C ox 2 f + V SB + V( y) I DS = n C ox L [ ( V GS -V fb -2 f - V DS 2 )V DS { ( V GS +2 f +V SB ) 3/2 -( 2 f +V SB ) 3/2 }] Q d =-C ox 2 f +V SB +V( y) -C ox [ 2 f +V SB + V( y)] = f +V SB

5 - 5 - V TH = 0.7V, KP = 170 A/V 2 i DS = 1 2 nc ox L ( V GS +v gs -V TH ) 2 v OUT =V DD -R L i DS =3.3-1k m 0.6 m ( 0.3 +v gs ) 2 =2-8.5v gs -14.2v 2 gs =V OUT +v out v out =- 8.5 v gs v 2 gs v gs v 2 gs A v = v out v gs =- 8.5 V/V i DS = 1 2 n C ox L [ ( V GS +v gs )-V TH ] 2 = 1 2 nc ox L (V GS -V TH ) 2 (1+ I DS (1+2 = I DS +i ds v gs V GS -V TH ) v gs V GS -V TH ) 2 i ds = I DS (V GS -V TH )/2 v gs g mv gs g m = I DS (V GS -V TH )/2 = 2 n C ox /LI DS = n C ox /L( V GS -V TH )

6 - 6 - V GS -V FB = - Q d -Q n C ox + [ 2 f + V( y)] V TH = V FB +2 f - Q d ( s = 2 f +V SB ) C ox Q d =-qn A =- 2 s qn A ( 2 f +V SB ) V TH = V TH0 + ( 2 f +V SB - 2 f ) V TH0 = V FB +2 F - Q d ( s = 2 f ) C ox and = 2 s qn A /C ox g mb =- i ds =- I DS = v sb V n C ox SB L ( V GS -V TH )( V TH ) V SB g mb = g m 2 2 f +V SB = g m

7 - 7 - V DS V GS - V TH I DS = 1 2 nc ox L (V GS - V TH )2 (1 + V DS ) r o [ I DS V DS ] -1 V GS = constant = [ nc ox 2 L (V GS - V TH ] -1 )2 r o = 1 = V A I DS I DS

8 - 8 - I DS = 1 2 nc ox L ( V GS -V TH ) 2 I DS =I D0 e V GS nv T ( = 1 n ) V Channel V GS = 1 1 +C d /C ox I DS = I D0 e V Channel V T = I D0 e V GS nv T Δ S dv GS d( log I DS ) = ln (10) dv GS d( ln I DS ) = ln (10) kt q n = ln (10) kt q [1+C d/c ox ]

9 - 9 - C sb, C db C gs, C gd, C gb C gs = 1 2 LC ox +CGSO C gd = 1 2 LC ox +CGDO C gb = CGBO L C gs = 2 3 LC ox +CGSO C gd = CGDO C gb = CGBO L C gs = CGSO C gd = CGDO C gb = LC ox +CGBO L C ox = TOX CGSO, CGDO, CGBO L

10 C db = C sb = CJ AD (1+ V + DB PB ) MJ CJ AS (1+ V + SB PB ) MJ CJS PD (1+ V DB PBS ) MJS CJS PS (1+ V SB PBS ) MJS

11 AS = AD = 6 14 = 84 m 2 PS = PD = 2(6+ 14)= 40 m C sb =C db =C sb, bottom +C sb, sidewall CJ AS CJS PS = ( 1 + V + SB PB ) MJ ( 1 + V =17.6fF SB PBS ) MJS C gb = CGBO L = 3.8fF C gd = CGDO = 5.3fF ( sat.) C gs = 2 3 C' oxl + CGSO = 75fF ( sat.)

12 I o = g m V gs - sc gd V gs I o g m V gs V gs = I i /s(c gs + C gd ) I o I i = g m s(c gs + C gd ) I o I i ( = T ) =1 T = g m /(C gs + C gd ) f T = g m 2 (C gs + C gd )

13 V TH VFB + PHI + K1 PHI + V SB - K2(PHI + V SB ) KP n = M UZ*C ox I DS = MU0' [1 + U0Z'(V GS - V THN )] C ox ' -D L-DL ( 1 + U1Z' L-DL V DS) [ (V GS - V THN)V DS - a 2 DS] V2 I DS MUZ C ox L [ (V GS - V TH )V DS - I DS = V 2 DS 2 ] MUZ C ox (V 2L GS - V TH ) 2 [1 + ( c + m )V DS ] c m I DS MUZ C ox L ( kt q ) 2 e 1.8 e q(v GS - V TH)/N'kT (1 - e -qv DS /kt )

14 V TH = V TH0 + K 1 ( S + V SB - S ) + K 2 V SB + K 1 ( 1 + NLX L eff - 1 ) S - V TH V TH I DS = eff C ox L V DS /L [ VGS - VTH - VDS 2 ]V DS E crit I DS = v sat C ox (V GS - V TH - V DSsat )[ 1 + V DS - V TH - V DSsat V A ] I DS = eff L ( kt q ) 2 C d e ( V GS - V TH - V off)q/nkt (1 - e -qv DS /kt )

15 ***** MOSIS 0.5um Parameters ***** * Level 3 SPICE model for CMOS14TB 0.5 um.model CMOSN5 NMOS LEVEL=3 PHI= TOX=9.6000E-09 XJ= U TPG=1 + VTO= DELTA=2.3060E-01 LD=2.9830E-08 KP=1.8201E-04 + UO=506.0 THETA=1.9090E-01 RSH=1.8940E+01 GAMMA= NSUB=1.4270E+17 NFS=7.1500E+11 VMAX=2.4960E+05 ETA=2.5510E-02 + KAPPA=1.8530E-01 CGDO=9.0000E-11 CGSO=9.0000E-11 + CGBO=3.7295E-10 CJ=6.02E-04 MJ=0.805 CJS=2.0E-11 + MJS=0.761 PB=0.99 * eff = drawn - Delta_ * The suggested Delta_ is E-07 * Level 4 (BSIM) SPICE model for CMOS14TB 0.5 um.model CMOSNB5 NMOS LEVEL=4 + vfb= e-01 lvfb= E-02 wvfb= e-01 + phi= E-01 lphi= E+00 wphi= E+00 + k1= E-01 lk1= E-02 wk1= E-01 + k2= E-02 lk2= E-02 wk2= E-02 + eta= e-03 leta= E-02 weta= E-03 + muz= E+02 dl= E-001 dw= E u0= E-01 lu0= E-01 wu0= E-01 + u1= E-02 lu1= E-02 wu1= E-03 + x2mz= e+01 lx2mz= e+01 wx2mz= e+01 + x2e= e-05 lx2e= e-03 wx2e= E-03 + x3e= e-04 lx3e= e-03 wx3e= e-03 + x2u0= e-04 lx2u0= e-02 wx2u0= e-02 + x2u1= e-04 lx2u1= e-03 wx2u1= e-04 + mus= e+02 lmus= e+01 wmus= e+00 + x2ms= e+00 lx2ms= e+00 wx2ms= e+01 + x3ms= e+00 lx3ms= e+00 wx3ms= e+00 + x3u1= e-02 lx3u1= e-03 wx3u1= e-04 + tox= e-003 temp= e+01 vdd= e+00 + cgdo= e-010 cgso= e-010 cgbo= e xpart= e n0= e+000 ln0= e+000 wn0= e nb= e+000 lnb= e+000 wnb= e nd= e+000 lnd= e+000 wnd= e rsh=2 cj=6.02e-04 cjsw=2.0e-11 js=1e-08 pb= pbsw=0.99 mj=0.805 mjsw=0.761 wdf=0 dell=0 * Level 3 SPICE model for CMOS14TB 0.5 um.model CMOSP5 PMOS LEVEL=3 PHI= TOX=9.6000E-09 XJ= U TPG=-1 + VTO= DELTA=4.2020E-01 LD=4.3860E-08 KP=4.1582E-05

16 UO=115.6 THETA=3.7990E-02 RSH=9.0910E-02 GAMMA= NSUB=7.8780E+16 NFS=6.4990E+11 VMAX=2.3130E+05 ETA=2.8580E-02 + KAPPA=9.9270E+00 CGDO=9.0000E-11 CGSO=9.0000E-11 + CGBO=3.6835E-10 CJ=9.34E-04 MJ=0.491 CJS=2.41E-10 + MJS=0.222 PB=0.90 * eff = drawn - Delta_ * The suggested Delta_ is E-07 * Level 4 (BSIM) SPICE model for CMOS14TB 0.5 um.model CMOSPB5 PMOS LEVEL=4 + vfb= e-01 lvfb= e-02 wvfb= e-02 + phi= e-01 lphi= e+00 wphi= e+00 + k1= e-01 lk1= e-02 wk1= e-01 + k2= e-03 lk2= e-03 wk2= e-02 + eta= e-03 leta= e-02 weta= e-05 + muz= e+02 dl= e-001 dw= e u0= e-01 lu0= e-02 wu0= e-02 + u1= e-03 lu1= e-02 wu1= e-03 + x2mz= e+00 lx2mz= e+00 wx2mz= e+00 + x2e= e-04 lx2e= e-03 wx2e= e-04 + x3e= e-04 lx3e= e-04 wx3e= e-03 + x2u0= e-02 lx2u0= e-03 wx2u0= e-03 + x2u1= e-03 lx2u1= e-04 wx2u1= e-04 + mus= e+02 lmus= e+01 wmus= e-01 + x2ms= e+00 lx2ms= e+00 wx2ms= e+00 + x3ms= e-01 lx3ms= e+00 wx3ms= e+00 + x3u1= e-03 lx3u1= e-03 wx3u1= e-03 + tox= e-003 temp= e+01 vdd= e+00 + cgdo= e-010 cgso= e-010 cgbo= e xpart= e n0= e+000 ln0= e+000 wn0= e nb= e+000 lnb= e+000 wnb= e nd= e+000 lnd= e+000 wnd= e rsh=2.1 cj=9.34e-04 cjsw=2.41e-10 js=1e-08 pb= pbsw=0.90 mj=0.491 mjsw=0.222 wdf=0 dell=0 ***** MOSIS 2.0um Parameters ***** * Level 2 model nchan model for CN20.MODEL CMOSN NMOS(LEVEL=2 PHI= TOX=4.3500E-08 XJ=0.2U TPG=1 + VTO= DELTA=8.5650E+00 LD=2.3950E-07 KP=4.5494E-05 + UO=573.1 UEXP=1.5920E-01 UCRIT=5.9160E+04 RSH=1.0310E+01 + GAMMA= NSUB=3.3160E+15 NFS=8.1800E+12 VMAX=6.0280E+04 + LAMBDA=2.9330E-02 CGDO=2.8518E-10 CGSO=2.8518E-10 + CGBO=4.0921E-10 CJ=1.0375E-04 MJ= CJS=2.1694E-10 + MJS= PB= )

17 * eff = drawn - Delta_ * The suggested Delta_ is E-07 * Level 2 model pchan model for CN20.MODEL CMOSP PMOS (LEVEL=2 PHI= TOX=4.3500E-08 XJ=0.2U TPG=-1 + VTO= DELTA=4.8720E+00 LD=2.9230E-07 KP=1.5035E-05 + UO=189.4 UEXP=2.7910E-01 UCRIT=9.5670E+04 RSH=1.8180E+01 + GAMMA= NSUB=1.0190E+16 NFS=6.1500E+12 VMAX=9.9990E+05 + LAMBDA=4.2290E-02 CGDO=3.4805E-10 CGSO=3.4805E-10 + CGBO=4.0305E-10 CJ=3.2456E-04 MJ= CJS=2.5430E-10 + MJS= PB= ) * eff = drawn - Delta_ * The suggested Delta_ is E-07 * BSIM model for n-channel CN20.MODEL CMOSNB NMOS (LEVEL=4 + VFB= E-01 LVFB= E-01 VFB= E-02 + phi= e-01 lphi= e-24 wphi= e-24 + k1= e+00 lk1= e-01 wk1= e-01 + k2= e-01 lk2= e-02 wk2= e-01 + eta= e-02 leta= e-02 weta= e-02 + muz= e+02 dl= e-001 dw= e u0= e-02 lu0= e-02 wu0= e-02 + u1= e-01 lu1= e-01 wu1= e-01 + x2mz= e+00 lx2mz= e+00 wx2mz= e+01 + x2e= e-03 lx2e= e-03 wx2e= e-03 + x3e= e-04 lx3e= e-03 wx3e= e-03 + x2u0= e-03 lx2u0= e-04 wx2u0= e-02 + x2u1= e-02 lx2u1= e-02 wx2u1= e-02 + mus= e+02 lmus= e+02 wmus= e+02 + x2ms= e+00 lx2ms= e+01 wx2ms= e+02 + x3ms= e+01 lx3ms= e+01 wx3ms= e+01 + x3u1= e-02 lx3u1= e-02 wx3u1= e-02 + tox= e-002 temp= e+01 vdd= e+00 + cgdo= e-010 cgso= e-010 cgbo= e xpart= e n0= e+000 ln0= e+000 wn0= e nb= e+000 lnb= e+000 wnb= e nd= e+000 lnd= e+000 wnd= e rsh=27.9 cj= e-04 cjsw= e-10 js=1.0e-08 pb=0.8 + pbsw=0.8 mj= mjsw= wdf=0) * dell=0) * BSIM model for p-channel CN20.MODEL CMOSPB PMOS ( LEVEL=4

18 vfb= e-01 lvfb= e-02 wvfb= e-01 + phi= e-01 lphi= e-24 wphi= e-24 + k1= e-01 lk1= e-02 wk1= e-02 + k2= e-02 lk2= e-01 wk2= e-02 + eta= e-02 leta= e-02 weta= e-04 + muz= e+02 dl= e-001 dw= e u0= e-01 lu0= e-02 wu0= e-02 + u1= e-02 lu1= e-01 wu1= e-01 + x2mz= e+00 lx2mz= e+00 wx2mz= e+00 + x2e= e-03 lx2e= e-03 wx2e= e-03 + x3e= e-04 lx3e= e-03 wx3e= e-03 + x2u0= e-03 lx2u0= e-04 wx2u0= e-04 + x2u1= e-04 lx2u1= e-03 wx2u1= e-03 + mus= e+02 lmus= e+02 wmus= e+01 + x2ms= e+00 lx2ms= e+00 wx2ms= e+00 + x3ms= e-01 lx3ms= e+01 wx3ms= e+00 + x3u1= e-02 lx3u1= e-04 wx3u1= e-03 + tox= e-002 temp= e+01 vdd= e+00 + cgdo= e-010 cgso= e-010 cgbo= e xpart= e n0= e+000 ln0= e+000 wn0= e nb= e+000 lnb= e+000 wnb= e nd= e+000 lnd= e+000 wnd= e rsh=54.7 cj= e-04 cjsw= e-10 js=1.0e-08 pb=0.8 + pbsw=0.8 mj= mjsw= wdf=0) * dell=0)

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