L27 23Apr021 Semiconductor Device Modeling and Characterization EE5342, Lecture 27 -Sp 2002 Professor Ronald L. Carter
L27 23Apr022 Ebers-Moll Model (No G-R curr) -J E A E = I E J C A C = I C E B C RIRRIR FIFFIF (Fig Semiconductor Physics & Devices, by Neamen, Irwin, Chicago, 1997, * throughout)
L27 23Apr023 Source of Ebers- Moll Equations (E)
L27 23Apr024 Source of Ebers- Moll Equations (C)
L27 23Apr025 Common emitter current gain,
L27 23Apr026 Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.
L27 23Apr027 Gummel-Poon Static npn Circuit Model C E B B’ ILC ILE IBF IBR I CC - I EC = IS(exp(v BE /NFV t ) - exp(v BC /NRV t )/Q B RC RE RBB Intrinsic Transistor
L27 23Apr028 Recombination/Gen Currents (FA)
L27 23Apr029 Gummel Poon npn Model Equations I BF = IS expf(v BE /NFV t )/BF I LE = ISE expf(v BE /NEV t ) I BR = IS expf(v BC /NRV t )/BR I LC = ISC expf(v BC /NCV t ) I CC - I EC = IS(exp(v BE /NFV t - exp(v BC /NRV t )/Q B Q B = { + + (BF IBF/IKF + BR IBR/IKR) 1/2 } (1 - v BC /VAF - v BE /VAR ) -1
L27 23Apr0210 VAF Parameter Extraction (fEarly) iCiC iBiB v CE v BE 0.2 < v CE < < v BE < 0.9 Forward Active Operation i C = I CC = (IS/Q B )exp(v BE /NFV t ), where I CE = 0, and Q B -1 = (1-v BC /VAF-v BE /VAR )* {IKF terms } -1, so since v BC = v BE - v CE, VAF = i C /[ i C / v BC ] vBE
L27 23Apr0211 i E = - I EC = (IS/Q B )exp(v BC /NRV t ), where I CC = 0, and Q B -1 = (1-v BC /VAF-v BE /VAR ) {IKR terms } -1, so since v BE = v BC - v EC, VAR = i E /[ i E / v BE ] vBC VAR Parameter Extraction (rEarly) iEiE iBiB v EC v BC 0.2 < v EC < < v BC < 0.9 Reverse Active Operation
L27 23Apr0212 BJT Characterization Forward Gummel v BCx = 0 = v BC + i B R B - i C R C v BEx = v BE +i B R B +(i B +i C )R E i B = I BF + I LE = IS exp(v BE /NFV t )/BF + ISE expf(v BE /NEV t ) i C = F I BF /Q B = IS exp (v BE /NFV t ) (1-v BC /VAF-v BE /VAR ) {IKF terms } -1 iCiC RCRC iBiB RERE RBRB v BEx v BC v BE
L27 23Apr0213 Definitions of N eff and IS eff In a region where i C or i B is approxi- mately a single exponential term, then i C or i B ~ IS eff exp (v BEext /(NF eff V t ) where N eff = {dv BEext /d[ln(i)]}/V t, and IS eff = exp[ln(i) - v BEext /(N eff V t )]
L27 23Apr0214 Region a - IKF IS, RB, RE, NF, VAR Region b - IS, NF, VAR, RB, RE Region c - IS/BF, NF, RB, RE Region d - IS/BF, NF Region e - ISE, NE Forward Gummel Data Sensitivities i C (A),i B (A) vs. v BE (V) iCiC v BCx = 0 iBiB a b c d e
L27 23Apr0215 Simple extraction of IS, ISE from data Data set used IS = 10f ISE = 10E-14 Flat IS eff for i C data = 9.99E-15 for < v D < Max IS eff value for i B data is 8.94E-14 for v D = IS eff vs. v BEext i B data i C data
L27 23Apr0216 Simple extraction of NF, NE from fg data Data set used NF=1 NE=2 Flat N eff region from i C data = 1.00 for < v D < Max N eff value from i B data is for < v D < NE eff vs. v BEext i B data i C data
L27 23Apr0217 Simple extraction of BF from data Data set used BF = 100 Extraction gives max i C /i B = 92 for 0.50 V < v D < 0.51 V 2.42 A < i D < 3.53 A Minimum value of N eff =1 for slightly lower v D and i D i C /i B vs. i C
L27 23Apr0218 BJT Characterization Reverse Gummel iEiE RCRC iBiB RERE RBRB v BCx v BC v BE v BEx = 0 = v BE + i B R B - i E R E v BCx = v BC +i B R B +(i B +i E )R C i B = I BR + I LC = (IS/BR) expf(v BC /NRV t ) + ISC expf(v BC /NCV t ) i E = R I BR /Q B = IS expf (v BC /NRV t ) (1-v BC /VAF-v BE /VAR ) {IKR terms } -1
L27 23Apr0219 Sample rg data for parameter extraction IS=10f Nr=1 Br=2 Isc=10p Nc=2 Ikr=.1m Vaf=100 Rc=5 Rb=100 i E, i B vs. v BCext i B data i E data
L27 23Apr0220 Simple extraction of BR from data Data set used Br = 2 Extraction gives max i E /i B = 1.7 for 0.48 V < v BC < 0.55V 1.13 A < i E < 14.4 A Minimum value of N eff =1 for same range i E /i B vs. i E
L27 23Apr0221 Simple extraction of IS, ISC from data Data set used IS = 10fA ISC = 10pA Min IS eff for i E data = 9.96E-15 for v BC = Max IS eff value for i B data is 8.44E-12 for v BC = IS eff vs. v BCext i B data i E data
L27 23Apr0222 Simple extraction of NR, NC from rg data Data set used Nr = 1 Nc = 2 Flat N eff region from i E data = 1.00 for < v BC < Max N eff value from i B data is for < v BC < NE eff vs. v BCext i B data i E data
L27 23Apr0223 Fully biased n-MOS capacitor 0 y L VGVG V sub =V B E Ox,x > 0 Acceptors Depl Reg e - e - e - e - e - e - n+ VSVS VDVD p-substrate Channel if V G > V T
L27 23Apr0224 Flat band with oxide charge (approx. scale) EvEv AlSiO 2 p-Si E Fm E c,Ox E g,ox ~8eV E Fp EcEc EvEv E Fi q( fp - ox ) q(V ox ) q( m - ox ) q(V FB ) V FB = V G -V B, when Si bands are flat ExEx + -
L27 23Apr0225 Flat-band parameters for p-channel (n-subst)
L27 23Apr0226 Fully biased n- channel V T calc
L27 23Apr0227 Fully biased n- channel V T calc
L27 23Apr0228 Q’ d,max and x d,max for biased MOS capacitor Fig 8.11** x d,max (microns) |Q’ d,max |/q (cm -2 )
L27 23Apr0229
L27 23Apr0230 Fully biased p- channel V T calc
L27 23Apr0231 I-V relation for n-MOS (ohmic reg) IDID V DS V DS,sa t I D,sat ohmic non-physical saturated
L27 23Apr0232 Universal drain characteristic 9I D1 IDID 4I D1 I D1 V GS =V T +1V V GS =V T +2V V GS =V T +3V V DS saturated, V DS >V GS -V T ohmic
L27 23Apr0233 Characterizing the n-ch MOSFET VDVD IDID D S G B V GS VTVT
L27 23Apr0234 Substrate bias effect on V T (body-effect)
L27 23Apr0235 Body effect data Fig 9.9**
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L27 23Apr0237
L27 23Apr0238 Values for ms with silicon gate
L27 23Apr0239 SPICE mosfet model levels Level 1 is the Schichman-Hodges model Level 2 is a geometry-based, analytical model Level 3 is a semi-empirical, short- channel model Level 4 is the BSIM1 model Level 5 is the BSIM2 model, etc.
L27 23Apr0240 Level 1 Static Const. For Device Equations Vfb = -TPG*EG/2 -Vt*ln(NSUB/ni) - q*NSS*TOX/eOx VTO = as given, or = Vfb + PHI + GAMMA*sqrt(PHI) KP = as given, or = UO*eOx/TOX CAPS are spice pars., technological constants are lower case
L27 23Apr0241 Level 1 Static Const. For Device Equations = KP*[W/(L-2*LD)] = 2*K, K not spice GAMMA = as given, or = TOX*sqrt(2*eSi*q*NSUB)/eOx 2*phiP = PHI = as given, or = 2*Vt*ln(NSUB/ni) I SD = as given, or = JS*AD I SS = as given, or = JS*AS
L27 23Apr0242 Level 1 Static Device Equations vgs < VTH, ids = 0 VTH < vds + VTH < vgs, id = KP*[W/(L-2*LD)]*[vgs-VTH-vds/2] *vds*(1 + LAMBDA*vds) VTH < vgs < vds + VTH, id = KP*[W/(L-2*LD)]*(vgs - VTH)^2 *(1 + LAMBDA*vds)
L27 23Apr0243 Level 2 Static Device Equations Accounts for variation of channel potential for 0 < y < L For vds < vds,sat = vgs - Vfb - PHI + 2 *[1-sqrt(1+2(vgs-Vfb-vbs)/ 2 ] id,ohmic = [ /(1-LAMBDA*vds)] *[vgs - Vfb - PHI - vds/2]*vds -2 [vds+PHI-vbs) 1.5 -(PHI-vbs) 1.5 ]/3
L27 23Apr0244 Level 2 Static Device Eqs. (cont.) For vds > vds,sat id = id,sat/(1-LAMBDA*vds) where id,sat = id,ohmic(vds,sat)
L27 23Apr0245 Level 2 Static Device Eqs. (cont.) Mobility variation KP’ = KP*[(esi/eox)*UCRIT*TOX /(vgs-VTH-UTRA*vds)] UEXP This replaces KP in all other formulae.
L27 23Apr0246 References CARM = Circuit Analysis Reference Manual, MicroSim Corporation, Irvine, CA, M&A = Semiconductor Device Modeling with SPICE, 2nd ed., by Paolo Antognetti and Giuseppe Massobrio, McGraw-Hill, New York, M&K = Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, Semiconductor Physics and Devices, by Donald A. Neamen, Irwin, Chicago, 1997