Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 17 Spring 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L17 11Mar03

npn BJT currents (F A region, ©RLC) IC = JCAC IB=-(IE+IC ) JnE JnC IE = -JEAE JRB=JnE-JnC JpE JGC JRE JpC L17 11Mar03

Ebers-Moll Model (Neglecting G-R curr) Fig. 9.30* -JEAE = IE JCAC = IC E B C aRIR aFIF L17 11Mar03

E-M model equations L17 11Mar03

Linking current version of E-M model L17 11Mar03

Linking current E-M model (cont) L17 11Mar03

Linking current E-M circuit model L17 11Mar03

Hybrid-pi circuit model Adapted from linking current version of E-M model with parasitic Rs and CSubstr C-E branch is linking current B-E branch is the reduced B-E diode with diffusion (for and rev) resistance and capacitance and junction cap. B-C branch is the reduced B-C diode with diffusion (for and rev) resistance and capacitance and junction cap. L17 11Mar03

Hybrid-pi Circuit model Fig 9.33* L17 11Mar03

Ebers-Moll npn injection current circuit model L17 11Mar03

Ebers-Moll npn transport current circuit model L17 11Mar03

Ebers-Moll npn linking current circuit model L17 11Mar03

Non-ideal effects in BJTs Base-width modulation (FA: xB changes with changes in VBC) Current crowding in 2-dim base High-level injection (minority carriers g.t. dopant - especially in the base). Emitter Bandgap narrowing (NE ~ density of states at cond. band. edge) Junction breakdown at BC junction L17 11Mar03

Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. L17 11Mar03

Gummel-Poon Static npn Circuit Model B RBB ILC IBR ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B’ ILE IBF RE E L17 11Mar03

Gummel-Poon Model General Form QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T> Netlist Examples Q5 11 26 4 Q2N3904 IC=0.6, 5.0 Q3 5 2 6 9 QNPN .67 NC, NB and NE are the collector, base and emitter nodes NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name, AREA is the area factor, and TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog. L17 11Mar03

Gummel-Poon Static Model Gummel Poon Model Parameters (NPN/PNP) Adaptation of the integral charge control model of Gummel and Poon. Extends the original model to include effects at high bias levels. Simplifies to Ebers-Moll model when certain parameters not specified. Defined by parameters IS, BF, NF, ISE, IKF, NE determine forward characteristics IS, BR, NR, ISC, IKR, NC determine reverse characteristics VAF and VAR determine output conductance for for and rev RB(depends on iB), RC, and RE are also included L17 11Mar03

Gummel-Poon Static Par. NAME PARAMETER UNIT DEFAULT IS transport saturation current A 1.0e-16 BF ideal maximum forward beta - 100 NF forward current emission coef. - 1.0 VAF forward Early voltage V infinite ISE B-E leakage saturation current A 0 NE B-E leakage emission coefficient - 1.5 BR ideal maximum reverse beta - 1 NR reverse current emission coeff. - 1 VAR reverse Early voltage V infinite ISC B-C leakage saturation current A 0 NC B-C leakage emission coefficient - 2 EG energy gap (IS dep on T) eV 1.11 XTI temperature exponent for IS - 3 L17 11Mar03

Gummel-Poon Static Model Parameters NAME PARAMETER UNIT DEFAULT IKF corner for forward beta A infinite high current roll-off IKR corner for reverse beta A infinite RB zero bias base resistance W 0 IRB current where base resistance A infinite falls halfway to its min value RBM minimum base resistance W RB at high currents RE emitter resistance W 0 RC collector resistance W 0 TNOM parameter - meas. temperature °C 27 L17 11Mar03

Gummel Poon npn Model Equations IBF = ISexpf(vBE/NFVt)/BF ILE = ISEexpf(vBE/NEVt) IBR = ISexpf(vBC/NRVt)/BR ILC = ISCexpf(vBC/NCVt) QB = (1 + vBC/VAF + vBE/VAR )  { + [ + (BFIBF/IKF + BRIBR/IKR)]1/2 } L17 11Mar03

Gummel Poon Base Resistance If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 Regarding (i) RBB and (x) RTh on slide 22, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L17 11Mar03

BJT Characterization Forward Gummel iC RC iB RE RB vBEx vBC vBE + - vBCx= 0 = vBC + iBRB - iCRC vBEx = vBE +iBRB +(iB+iC)RE iB = IBF + ILE = ISexpf(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexpf(vBE/NFVt)/QB L17 11Mar03

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec L17 11Mar03

BJT Characterization Reverse Gummel iE RC iB RE RB vBCx vBC vBE + - vBEx= 0 = vBE + iBRB - iERE vBCx = vBC +iBRB +(iB+iE)RC iB = IBR + ILC = ISexpf(vBC/NRVt)/BR + ISCexpf(vBC/NCVt) iE = bRIBR/QB = ISexpf(vBC/NRVt)/QB L17 11Mar03

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec L17 11Mar03

Distributed resis- tance in a planar BJT emitter base collector reg 4 reg 3 reg 2 reg 1 coll. base & emitter contact regions The base current must flow lateral to the wafer surface Assume E & C cur-rents perpendicular Each region of the base adds a term of lateral res.  vBE diminishes as current flows L17 11Mar03

Simulation of 2- dim. current flow =  DV  Both sources have same current iB1 = iB. The effective value of the 2-dim. base resistance is Rbb’(iB) = DV/iB = RBBTh Distributed device is repr. by Q1, Q2, … Qn Area of Q is same as the total area of the distributed device. Both devices have the same vCE = VCC L17 11Mar03

Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L17 11Mar03

Distributed base resistance function Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax. FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997. L17 11Mar03

References * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997. * Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print). L17 11Mar03