r c =r for BJTs = for MOSFETs

- 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 - μ Δ

- 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 - 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 - 2 3 { ( 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)] = 0.5 2 f +V SB

- 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 1 2 170 100 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 - 14.2v 2 gs - 8.5 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 - 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 0.1-0.3

- 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 - 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 - 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 1 + 1 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=0.700000 + TOX=9.6000E-09 XJ=0.200000U TPG=1 + VTO=0.7118 DELTA=2.3060E-01 LD=2.9830E-08 KP=1.8201E-04 + UO=506.0 THETA=1.9090E-01 RSH=1.8940E+01 GAMMA=0.6051 + 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 3.5700E-07 * Level 4 (BSIM) SPICE model for CMOS14TB 0.5 um.model CMOSNB5 NMOS LEVEL=4 + vfb=-9.65360e-01 lvfb= 4.11254E-02 wvfb=-1.21737e-01 + phi= 9.02436E-01 lphi= 0.00000E+00 wphi= 0.00000E+00 + k1= 9.33674E-01 lk1= -8.15872E-02 wk1= 2.03526E-01 + k2= 7.39228E-02 lk2= 1.48295E-02 wk2= 5.89097E-02 + eta=-2.77969e-03 leta= 1.12296E-02 weta= 1.25263E-03 + muz= 4.71133E+02 dl= 1.57937E-001 dw= 4.09563E-001 + u0= 1.98427E-01 lu0= 1.54850E-01 wu0= -1.05429E-01 + u1= 3.39403E-02 lu1= 3.59469E-02 wu1= -5.00497E-03 + x2mz=1.25728e+01 lx2mz=-1.24115e+01 wx2mz=1.77657e+01 + x2e=-9.95217e-05 lx2e=-5.16949e-03 wx2e= 2.83253E-03 + x3e=-4.27269e-04 lx3e=-1.62632e-03 wx3e=-1.60797e-03 + x2u0=-9.02747e-04 lx2u0=-1.66946e-02 wx2u0=2.48458e-02 + x2u1=-7.29822e-04 lx2u1=2.38803e-03 wx2u1=-9.76918e-04 + mus=5.36631e+02 lmus=2.18647e+01 wmus=4.43373e+00 + x2ms=5.97403e+00 lx2ms=-7.67105e+00 wx2ms=2.19614e+01 + x3ms=7.60054e+00 lx3ms=4.73779e+00 wx3ms=2.59952e+00 + x3u1=1.75532e-02 lx3u1=-1.21628e-03 wx3u1=-5.95548e-04 + tox=9.60000e-003 temp=2.70000e+01 vdd=3.30000e+00 + cgdo=4.26077e-010 cgso=4.26077e-010 cgbo=4.01709e-010 + xpart=1.00000e+000 + n0=1.00000e+000 ln0=0.00000e+000 wn0=0.00000e+000 + nb=0.00000e+000 lnb=0.00000e+000 wnb=0.00000e+000 + nd=0.00000e+000 lnd=0.00000e+000 wnd=0.00000e+000 + rsh=2 cj=6.02e-04 cjsw=2.0e-11 js=1e-08 pb=0.99 + 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=0.700000 + TOX=9.6000E-09 XJ=0.200000U TPG=-1 + VTO=-0.9016 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=0.4496 + 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 3.4860E-07 * Level 4 (BSIM) SPICE model for CMOS14TB 0.5 um.model CMOSPB5 PMOS LEVEL=4 + vfb=-2.80568e-01 lvfb=5.70163e-02 wvfb=-6.17493e-02 + phi=8.14689e-01 lphi=0.00000e+00 wphi=0.00000e+00 + k1=4.52973e-01 lk1=-9.19899e-02 wk1=1.20834e-01 + k2=-9.42157e-03 lk2=-2.25562e-03 wk2=3.13315e-02 + eta=-7.03956e-03 leta=1.92833e-02 weta=5.45445e-05 + muz=1.36047e+02 dl=1.85988e-001 dw=4.32366e-001 + u0=1.93813e-01 lu0=6.02231e-02 wu0=-4.90734e-02 + u1=8.52399e-03 lu1=2.60545e-02 wu1=-6.34371e-03 + x2mz=7.96258e+00 lx2mz=-2.15761e+00 wx2mz=2.30663e+00 + x2e=4.37912e-04 lx2e=-1.60046e-03 wx2e=-3.86750e-04 + x3e=-3.52725e-04 lx3e=-4.09096e-04 wx3e=-2.53471e-03 + x2u0=1.18873e-02 lx2u0=-4.81760e-03 wx2u0=8.80040e-03 + x2u1=2.26591e-03 lx2u1=7.96828e-04 wx2u1=-4.70527e-04 + mus=1.44421e+02 lmus=1.63665e+01 wmus=-7.31189e-01 + x2ms=8.18970e+00 lx2ms=-1.25158e+00 wx2ms=3.62233e+00 + x3ms=7.29640e-01 lx3ms=1.15206e+00 wx3ms=1.02833e+00 + x3u1=-3.51521e-03 lx3u1=-3.12374e-03 wx3u1=3.48134e-03 + tox=9.60000e-003 temp=2.70000e+01 vdd=3.30000e+00 + cgdo=5.01753e-010 cgso=5.01753e-010 cgbo=4.14187e-010 + xpart=1.00000e+000 + n0=1.00000e+000 ln0=0.00000e+000 wn0=0.00000e+000 + nb=0.00000e+000 lnb=0.00000e+000 wnb=0.00000e+000 + nd=0.00000e+000 lnd=0.00000e+000 wnd=0.00000e+000 + rsh=2.1 cj=9.34e-04 cjsw=2.41e-10 js=1e-08 pb=0.90 + 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=0.600000 TOX=4.3500E-08 XJ=0.2U TPG=1 + VTO=0.8756 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=0.4179 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=0.6604 CJS=2.1694E-10 + MJS=0.178543 PB=0.800000)

- 17 - * eff = drawn - Delta_ * The suggested Delta_ is -4.0460E-07 * Level 2 model pchan model for CN20.MODEL CMOSP PMOS (LEVEL=2 PHI=0.600000 TOX=4.3500E-08 XJ=0.2U TPG=-1 + VTO=-0.8889 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=0.7327 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=0.6044 CJS=2.5430E-10 + MJS=0.244194 PB=0.800000) * eff = drawn - Delta_ * The suggested Delta_ is -3.6560E-07 * BSIM model for n-channel CN20.MODEL CMOSNB NMOS (LEVEL=4 + VFB=-9.73820E-01 LVFB=3.67458E-01 VFB=-4.72340E-02 + phi=7.46556e-01 lphi=-1.92454e-24 wphi=8.06093e-24 + k1=1.49134e+00 lk1=-4.98139e-01 wk1=2.78225e-01 + k2=3.15199e-01 lk2=-6.95350e-02 wk2=-1.40057e-01 + eta=-1.19300e-02 leta=5.44713e-02 weta=-2.67784e-02 + muz=5.98328e+02 dl=6.38067e-001 dw=1.35520e-001 + u0=5.27788e-02 lu0=4.85686e-02 wu0=-8.55329e-02 + u1=1.09730e-01 lu1=7.28376e-01 wu1=-4.22283e-01 + x2mz=7.18857e+00 lx2mz=-2.47335e+00 wx2mz=7.12327e+01 + x2e=-3.00000e-03 lx2e=-7.20276e-03 wx2e=-5.57093e-03 + x3e=3.71969e-04 lx3e=-3.16123e-03 wx3e=-3.80806e-03 + x2u0=1.30153e-03 lx2u0=3.81838e-04 wx2u0=2.53131e-02 + x2u1=-2.04836e-02 lx2u1=3.48053e-02 wx2u1=4.44747e-02 + mus=7.79064e+02 lmus=3.62270e+02 wmus=-2.71207e+02 + x2ms=-2.65485e+00 lx2ms=3.68637e+01 wx2ms=1.12899e+02 + x3ms=1.18139e+01 lx3ms=7.24951e+01 wx3ms=-5.25361e+01 + x3u1=2.12924e-02 lx3u1=5.85329e-02 wx3u1=-5.29634e-02 + tox=4.35000e-002 temp=2.70000e+01 vdd=5.00000e+00 + cgdo=3.79886e-010 cgso=3.79886e-010 cgbo=3.78415e-010 + xpart=1.00000e+000 + n0=1.00000e+000 ln0=0.00000e+000 wn0=0.00000e+000 + nb=0.00000e+000 lnb=0.00000e+000 wnb=0.00000e+000 + nd=0.00000e+000 lnd=0.00000e+000 wnd=0.00000e+000 + rsh=27.9 cj=1.037500e-04 cjsw=2.169400e-10 js=1.0e-08 pb=0.8 + pbsw=0.8 mj=0.66036 mjsw=0.178543 wdf=0) * dell=0) * BSIM model for p-channel CN20.MODEL CMOSPB PMOS ( LEVEL=4

- 18 - + vfb=-2.65334e-01 lvfb=6.50066e-02 wvfb=1.48093e-01 + phi=6.75823e-01 lphi=-1.61406e-24 wphi=8.03764e-24 + k1=5.68962e-01 lk1=3.88845e-02 wk1=-5.33948e-02 + k2=-5.52938e-02 lk2=1.17906e-01 wk2=-6.89149e-02 + eta=-1.51784e-02 leta=5.87976e-02 weta=-7.51570e-04 + muz=2.10669e+02 dl=8.44240e-001 dw=1.62551e-001 + u0=1.04713e-01 lu0=5.50950e-02 wu0=-7.56659e-02 + u1=1.46638e-02 lu1=2.13581e-01 wu1=-1.22509e-01 + x2mz=8.76354e+00 lx2mz=-3.64793e+00 wx2mz=4.30934e+00 + x2e=-2.13631e-03 lx2e=-2.94140e-03 wx2e=-2.48293e-03 + x3e=2.78813e-04 lx3e=-1.60711e-03 wx3e=-4.57237e-03 + x2u0=3.93706e-03 lx2u0=-5.66051e-04 wx2u0=5.69621e-04 + x2u1=1.07707e-04 lx2u1=8.85125e-03 wx2u1=1.71537e-03 + mus=2.06464e+02 lmus=1.39151e+02 wmus=-4.95671e+01 + x2ms=5.86401e+00 lx2ms=6.98887e+00 wx2ms=5.55782e+00 + x3ms=-2.03430e-01 lx3ms=1.16170e+01 wx3ms=-3.44342e+00 + x3u1=-1.17893e-02 lx3u1=5.72098e-04 wx3u1=8.29791e-03 + tox=4.35000e-002 temp=2.70000e+01 vdd=5.00000e+00 + cgdo=5.02635e-010 cgso=5.02635e-010 cgbo=3.85017e-010 + xpart=1.00000e+000 + n0=1.00000e+000 ln0=0.00000e+000 wn0=0.00000e+000 + nb=0.00000e+000 lnb=0.00000e+000 wnb=0.00000e+000 + nd=0.00000e+000 lnd=0.00000e+000 wnd=0.00000e+000 + rsh=54.7 cj=3.245600e-04 cjsw=2.543000e-10 js=1.0e-08 pb=0.8 + pbsw=0.8 mj=0.60438 mjsw=0.244194 wdf=0) * dell=0)