1EE130 Lecture 19, Slide 1Spring 2003Lecture #19ANNOUNCEMENT• Quiz #4 (Thursday 4/3) to cover Chapters 10 & 11OUTLINE• BJT transient response• BJT small-signal model, fTReading: Chapter 12EE130 Lecture 19, Slide 2Spring 2003BJT Switching - Qualitative2EE130 Lecture 19, Slide 3Spring 2003Turn-on transient• We know:• The general solution is:• Initial condition: QB(0)=0. since transistor is in cutoffBBBBBQIdtdQτ−=BtBBBBAeItQττ/)(−+=)1()(/BtBBBBeItQττ−−=≥≤≤+==−rLCCrttBBBtBCttRVttAeItQtiBLL0)()(/ττττwhere IBB=VS/RS−=BBBLCCBrIRVtττ/11lnEE130 Lecture 19, Slide 4Spring 2003Turn-off transient• We know:• The general solution is:• Initial condition: QB(0)=IBBτBBBBBBQIdtdQτξ−−=BtBBBBAeItQττξ/)(−+−=()[]ξξττ−+=−BtBBBBeItQ/1)(()[]≥=≤≤=−+−sdteBBBtBsdCCCttItQttItiBtLLτττξξτ/1)(0)(++≅ξττξτBBBtCCBsdIIt1ln3EE130 Lecture 19, Slide 5Spring 2003kTqVFFCBEeII/α=transconductance:)//()(//qkTIeIkTqeIdVddVdIgCkTqVFFkTqVFFBEBECmBEBE===≡ααAt 300 K, for example,gm=IC /26mV.vberπ gmvbeCE B ECπ +−)//( qkTIgCm=Small-Signal ModelForward-active mode,Common-emitter configuration:EE130 Lecture 19, Slide 6Spring 2003This is the minority-carrier charge-storage capacitance, better known as the diffusion capacitance.Add the depletion-layer capacitance, CJBE:dBEmFCgC +=τπSmall-Signal Model (cont.)()mFBECFBEFmdcmdcdcmBECdcBEBgdVIddVdQCgrgrgdVdIdVdIrττββββππππ========114EE130 Lecture 19, Slide 7Spring 2003Forward Transit Time τF• To reduce the forward transit time, the emitter as well as the depletion layers must be kept thin.=====+++=BCtBEECFBCtBEEFwhereIQτττττττττemitter delay timeemitter-base depletion region transit timebase transit timebase-collector depletion-region transit timeEE130 Lecture 19, Slide 8Spring 2003A BJT is biased at IC= 1 mA and VCE= 3 V. βdc=90,τF=5 ps, and T = 300 K. Find (a) gm, (b) rπ, (c) Cπ.Solution: (a)(b) rπ= βdc/ gm= 90/0.039 = 2.3 kΩc) Example: Small-Signal Model Parameterssiemens)(milliqkTIgCm mS 39VmA39mV26mA 1)//( ====ad)(femto fargCmFfF 19F109.1039.01051412=×≈××==−−τπ5EE130 Lecture 19, Slide 9Spring 2003Once the model parameters have been determined, one can analyze circuits with arbitrary source and load impedance.The parameters are routinely determined through comprehensivemeasurement of the BJT ACand DC characteristics.vberπ gmvbeCE B ECπ +-SignalsourceLoadvberπ gmvbe C BECπ +−ro CdBC rbrcre CµApplication of Small-Signal ModelFull BJT equivalent circuit:EE130 Lecture 19, Slide 10Spring 2003The load is a short circuit, and the signal source is a current source, ib, at frequency, f. At what frequency does the a.c. current gain fall to unity?CdBEFFmbcbemcbbbeqIkTCjjCjrgiivgiCjriiv//11/1)(/1admittanceinput ωωτβωωβωππππ++=+===+==vberπ gmvbeCE B ECπ +-SignalsourceLoadCutoff Frequency fT()CJBEFTacqIkTCf/21at 1+==τπβ6EE130 Lecture 19, Slide 11Spring 2003fTis commonly used as a metric for the speed of a transistor.SiGe HBT by IBM()()()()cedBCCdBCdBEFTrrCqIkTCCf++++=/21τπFor the full BJT equivalent circuit:EE130 Lecture 19, Slide 12Spring 2003Cutoff Frequency fT•To maximize ft:– Increase IC– Minimize CdBE, CdBC– Minimize re, rc– Minimize τF()()()()cedBCCdBCdBEFTrrCqIkTCCf++++=/21τπ7EE130 Lecture 19, Slide 13Spring 2003• At very high current densities (> 0.5 mA/µm2), base widening occurs*, so QBincreases. →ttand τBCincrease, so τFincreases and fTdecreases. Top to bottom : VCE = 0.5V, 0.8V, 1.5V, 3V.Base Widening at High IC: the Kirk Effect*For an NPN BJT, the electron density in the collector (n = NC) becomes insufficient to support the collector current even if the electrons move at the saturation velocity.Eventually, ρ changes sign as ICincreases (for fixed VBC), and the base width is effectively widened.satCCCCdepsatCAvIqNqnqNqAnvI−=−==,ρEE130 Lecture 19, Slide 14Spring 2003• Narrow base • n+ poly-Si emitter• Self-aligned p+ poly-Si base contacts• Lightly-doped collector• Heavily-doped epitaxial subcollector• Shallow trenches and deep trenches filled with SiO2for electrical isolationB EC p+p+ P base N collectorN+ subcollector P− substrateN+polySiN+DeeptrenchDeep trench ShallowtrenchP+polySiP+po lySiBJT Structure for High
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