Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L16 07Mar02 1
Gummel-Poon Static npn Circuit Model C RC Intrinsic Transistor B RBB ILC IBR I CC - I EC = B ILE IBF IS(exp(v BE /NFV t ) - exp(v BC /NRV t )/Q B RE E L16 07Mar02 2
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 L16 07Mar02 3
VAF Parameter Extraction (fearly) i C = I CC = (IS/Q B )exp(v BE /NFV t ), where I CE = 0, and Q -1 B = (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 Forward Active Operation L16 07Mar02 4 + - i B v BE i C v CE 0.2 < v CE < 5.0 0.7 < v BE < 0.9 + -
Forward Early Data for VAF At a particular data point, an effective VAF value can be calculated VAF eff = i C /[ i C / v BC ] vbe 0.003 0.002 0.001 v BE = 0.85 V v BE = 0.75 V The most accurate is at v BC = 0 (why?) 0.000 0 1 2 3 4 5 i C (A) vs. v CE (V) L16 07Mar02 5
Forward Early VAf extraction VAF eff = i C /[ i C / v BC ] vbe VAF was set at 100V for this data 105 103 101 v BE = 0.75 V v BE = 0.85 V When v BC = 0 v BE =0.75 VAR=101.2 v BE =0.85 VAR=101.0 99 0 1 2 3 4 VAF eff (V) vs. v CE (V) L16 07Mar02 6
VAR Parameter Extraction (rearly) i E = - I EC = (IS/Q B )exp(v BC /NRV t ), where I CC = 0, and Q -1 B = (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 Reverse Active Operation L16 07Mar02 7 i B + - v BC i E v EC 0.2 < v EC < 5.0 0.7 < v BC < 0.9 + -
Reverse Early Data for VAR At a particular data point, an effective VAR value can be calculated 0.0006 0.0004 0.0002 v BC = 0.85 V v BC = 0.75 V VAR eff = i E /[ i E / v BE ] vbc The most accurate is at v BE = 0 (why?) 0.0000 0 1 2 3 4 5 i E (A) vs. v EC (V) L16 07Mar02 8
Reverse Early VAR extraction VAR eff = i E /[ i E / v BE ] vbc VAR was set at 200V for this data When v BE = 0 v BC =0.75 VAR=200.5 v BC =0.85 VAR=200.2 204 202 200 198 v BC = 0.75 V v BC = 0.85 V 0 1 2 3 4 VAR eff (V) vs. v EC (V) L16 07Mar02 9
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 v BEx L16 07Mar02 10 + - i B i C R B v BC + + v BE R C - - R E
Sample fg data for parameter extraction 1.E-02 1.E-04 i C data 1.E-06 1.E-08 i B data 1.E-10 1.E-12 0.1 0.3 0.5 0.7 0.9 i C, i B vs. v BEext IS = 10f NF = 1 BF = 100 Ise = 10E-14 Ne = 2 Ikf =.1m Var = 200 Re = 1 Rb = 100 L16 07Mar02 11
Definitions of N eff and IS eff In a region where i C or i B is approximately 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 )] L16 07Mar02 12
Forward Gummel Data Sensitivities 1.E-02 1.E-04 1.E-06 1.E-08 1.E-10 1.E-12 v BCx = 0 e b i C i B d 0.1 0.3 0.5 0.7 0.9 i C (A),i B (A) vs. v BE (V) a c 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 L16 07Mar02 13
Region (b) fg Data Sensitivities Region b - IS, NF, VAR, RB, RE i C = F I BF /Q B = IS exp(v BE /NFV t ) (1-v BC /VAF-v BE /VAR ) {IKF terms } -1 L16 07Mar02 14
Region (e) fg Data Sensitivities Region e - ISE, NE i B = I BF + I LE = (IS/BF) expf(v BE /NFV t ) + ISE expf(v BE /NEV t ) L16 07Mar02 15
Simple extraction of IS, ISE from data 1.E-10 1.E-12 1.E-14 1.E-16 i C data i B data 0.1 0.3 0.5 0.7 0.9 IS eff vs. v BEext Data set used IS = 10f ISE = 10E-14 Flat IS eff for i C data = 9.99E-15 for 0.230 < v D < 0.255 Max IS eff value for i B data is 8.94E-14 for v D = 0.180 L16 07Mar02 16
Simple extraction of NF, NE from fg data 2.1 1.9 1.7 1.5 1.3 1.1 0.9 i B i C data data 0.1 0.3 0.5 0.7 0.9 NE eff vs. v BEext Data set used NF=1 NE=2 Flat N eff region from i C data = 1.00 for 0.195 < v D < 0.390 Max N eff value from i B data is 1.881 for 0.180 < v D < 0.181 L16 07Mar02 17
Region (d) fg Data Sensitivities Region d - IS/BF, NF i B = I BF + I LE = (IS/BF) expf(v BE /NFV t ) + ISE expf(v BE /NEV t ) L16 07Mar02 18
Simple extraction of BF from data 100 75 50 25 0 1.E-10 1.E-06 1.E-02 i C /i B vs. i C 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 L16 07Mar02 19
Region (a) fg Data Sensitivities Region a - IKF IS, RB, RE, NF, VAR i C = F I BF /Q B = IS exp(v BE /NFV t ) (1-v BC /VAF-v BE /VAR ) {IKF terms } -1 L16 07Mar02 20
Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE i B = I BF + I LE = (IS/BF) expf(v BE /NFV t ) + ISE expf(v BE /NEV t ) L16 07Mar02 21
BJT Characterization Reverse Gummel 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 L16 07Mar02 22 - + v BCx i B R B i E v BC + + v BE R C - - R E
Sample rg data for parameter extraction 1.E-02 i B data 1.E-04 1.E-06 1.E-08 i E data 1.E-10 0.1 0.3 0.5 0.7 0.9 i E, i B vs. v BCext IS=10f Nr=1 Br=2 Isc=10p Nc=2 Ikr=.1m Vaf=100 Rc=5 Rb=100 L16 07Mar02 23
Definitions of N eff and IS eff In a region where i C or i B is approximately a single exponential term, then i C or i B ~ IS eff exp (v BCext /(NR eff V t ) where N eff = {dv BCext /d[ln(i)]}/v t, and IS eff = exp[ln(i) - v BCext /(N eff V t )] L16 07Mar02 24
Reverse Gummel Data Sensitivities 1.E-02 1.E-04 1.E-06 1.E-08 1.E-10 i B v BCx = 0 e i E b 0.1 0.3 0.5 0.7 0.9 i E (A),i B (A) vs. v BC (V) d c a Region a - IKR IS, RB, RC, NR, VAF Region b - IS, NR, VAF, RB, RC Region c - IS/BR, NR, RB, RC Region d - IS/BR, NR Region e - ISC, NC L16 07Mar02 25
Region (d) rg Data Sensitivities Region d - BR, IS, NR i B = I BR + I LC = IS/BR expf(v BC /NRV t ) + ISC expf(v BC /NCV t ) L16 07Mar02 26
Simple extraction of BR from data 2.0 1.5 1.0 0.5 0.0 1.E-10 1.E-06 1.E-02 i E /i B vs. i E 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 L16 07Mar02 27
Region (b) rg Data Sensitivities Region b - IS, NR, VAF, RB, RC i E = R I BR /Q B = IS exp(v BC /NRV t ) (1-v BC /VAF-v BE /VAR ) {IKR terms } -1 L16 07Mar02 28
Region (e) rg Data Sensitivities Region e - ISC, NC i B = I BR + I LC = IS/BR expf(v BC /NRV t ) + ISC expf(v BC /NCV t ) L16 07Mar02 29
Simple extraction of IS, ISC from data 1.E-10 1.E-12 1.E-14 1.E-16 i B data i E data 0.2 0.4 0.6 IS eff vs. v BCext Data set used IS = 10fA ISC = 10pA Min IS eff for i E data = 9.96E-15 for v BC = 0.200 Max IS eff value for i B data is 8.44E-12 for v BC = 0.200 L16 07Mar02 30
Simple extraction of NR, NC from rg data 2.1 1.9 1.7 1.5 1.3 1.1 0.9 i B i E data data 0.1 0.3 0.5 0.7 0.9 NE eff vs. v BCext Data set used Nr = 1 Nc = 2 Flat N eff region from i E data = 1.00 for 0.195 < v BC < 0.375 Max N eff value from i B data is 1.914 for 0.195 < v BC < 0.205 L16 07Mar02 31
Region (c) rg Data Sensitivities Region c - BR, IS, NR, RB, RC i B = I BR + I LC = IS/BR expf(v BC /NRV t ) + ISC expf(v BC /NCV t ) L16 07Mar02 32
Region (a) rg Data Sensitivities Region a - IKR IS, RB, RC, NR, VAF i E = R I BR /Q B ~[IS IKR] 1/2 exp(v BC /NRV t ) (1-v BC /VAF-v BE /VAR ) L16 07Mar02 33
RE-flyback data extraction of RE Qintr o.c. v CE R E v CE / i B (from IC-CAP Modeling Reference, p. 6-37) v BE R BB i B B E R E R BM (v BE - v CE )/ i B (adapted by RLC from IC-CAP Modeling Reference, p. 6-39) L16 07Mar02 34
Extraction of RE from refly data 0.08 0.07 0.06 y=7.1373x+0.0517 RE vce/ ib Slope gives RE 7.1 Ohm 0.05 0.04 0.000 0.001 0.002 0.003 vce(v) vs. ib(a) Model data assumed RE = 1 Ohm L16 07Mar02 35
Extraction of RBM from refly data 1.00 y=107.72x+0.6714 RBM (v BE - v CE )/ i B 0.90 0.80 0.70 0.000 0.001 0.002 0.003 vbc(v) vs. ib(a) Slope gives RBM 108 Ohm Model data assumed RB = RBM = 100 Ohm L16 07Mar02 36