Semiconductor Device Modeling & Characterization Lecture 15 Professor Ronald L. Carter ronc@uta.edu Spring 2001 L15 March 6

npn BJT topology xE x’E x’C xC z xJE xJC n-emitter p-Base n-collector IE IC IB xE x’E x’C xC z xJE xJC n-emitter p-Base n-collector Depletion Region Charge Neutral Region L15 March 6

Ebers-Moll npn injection current circuit model L15 March 6

Ebers-Moll npn transport current circuit model L15 March 6

Ebers-Moll npn linking current circuit model L15 March 6

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 L15 March 6

Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. L15 March 6

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 L15 March 6

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. L15 March 6

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 L15 March 6

Gummel-Poon Static Model Parameters name parameter units default area IS transport saturation current A 1.0e-16 * BF ideal maximum forward beta - 100 NF forward current emission coefficient - 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 coefficient - 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 for temperature eV 1.11 effect on IS XTI temperature exponent for effect on IS - 3 L15 March 6

Gummel-Poon Static Model Parameters name parameter units default area 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 L15 March 6

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 } L15 March 6

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 L15 March 6

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 L15 March 6

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec L15 March 6

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 L15 March 6

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec L15 March 6

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 L15 March 6

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 L15 March 6

Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L15 March 6

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. L15 March 6