C - University of California, Santa Barbara
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ECE145A /218CA notes, M. Rodwell, copyrighted ECE145a / 218a: Notes Set 5 device models & device characteristics: Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax Content: Bipolar Transistor M odels M OSFET M odels HEM T (JFET) models Cutoff frequencie s. ECE145A /218CA notes, M. Rodwell, copyrighted ECE145A /218CA notes, M. Rodwell, copyrighted Active Devices: Bipolar Transistors HBT Physical Structure ECE145A /218CA notes, M. Rodwell, copyrighted Increasing total emitter area ECE145A /218CA notes, M. Rodwell, copyrighted J E I E /( total emitter area) Increasing the emitter area (increasin g LE , or multiple fingers) increases the maximum current. Emitter area generally selected to reach peak bandwidth at some specified current. ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor: DC characteristics: common-emitter 10 -2 10 -4 10 -6 10 -8 20 c 2 I 10 -10 10 -12 I b mA/m c b I , I (A) Vce,sat 15 I c I b 10 5 0 0 0.25 0.5 0.75 1 V be 0 1 (V) Approximately : I c I s e qVbe / nkT and I b I c / These relationships are approximate, and fail at higher current densities 2 V 3 4 ce Vbr,ceo ECE145A /218CA notes, M. Rodwell, copyrighted HBT hybrid-Pi equivalent-circuit model Ccbx Rbe / g m f b c f base collector g mo I C IC VBE (nkT / q) g m g mo e j c 0 1 (typically~ 0.8) B Rbb Ccbi Rbe Cbe,diff =gm f Cje Rc C gm Vbee -jc Vbe Rex E C je , Ccbi , Ccbx : depletion capacitances Cbe,diff : diffusion capacitance b , c : carrier transit times in base and collector Rb , Re , Rc : parasitic resitances The term e j c , though often neglected, can be significan t in some circuits. ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor T-model 1 exp j c 1 j b 1 1 0 1 j b 1 j c ( ) 0 1 0 1 j ( b c ) The approximations above, if taken to first order in , produce the hybrid pi model. The T model is more convenient for common-base amplifier analysis. ECE145A /218CA notes, M. Rodwell, copyrighted How model varies as emitter area is increased Ccbx B Rbb Ccbi Rbe Cbe,diff =gm f Cje Rc C gm Vbee -jc Vbe Rex E Increasing the emitter area by N : 1 same as wiring N HBTs in parallel. All capacitances increase N : 1, all resistances decrease 1 : N. Cbe , Rbe and g m are given by theformulas on the previous pages. ECE145A /218CA notes, M. Rodwell, copyrighted Active Devices: Silicon MOSFETs ECE145A /218CA notes, M. Rodwell, copyrighted Planar Bulk MOSFET Cross-Section gate metal (silicide) Layout (multi-finger) dielectric sidewall G S gate oxide N+ poly gate Wg source contact (silicide) drain contact (silicide) G N+ source N+ drain P substrate gate dielectric inversion layer P substrate N+ polysilicon gate D S D S D S ECE145A /218CA notes, M. Rodwell, copyrighted MOSFET DC Characteristics mobility-limited ID Id increasing VGS velocity-limited Vgs VDS Vth For drain voltages larger tha n the knee voltage : mobility limited current I D , coxWg (Vgs Vth )2 / 2 Lg velocity limited current I D ,v coxWg vsat (Vgs Vth ) Generalized Expression 2 ID ID I I D ,v D , 1 ECE145A /218CA notes, M. Rodwell, copyrighted The knee voltage defines the boundary between ID Ohmic Knee Voltage: Mobility-Limited Case constant-current the Ohmic and constant - current regions increasing VGS In the mobility - limited regime, the knee in curve occurs when Vdg Vds Vgs Vth VDS VGD=Vth The Knee Voltage is further increased by voltage VGD=Vth IDRD drops across the parasitic source & drain resistances. IDRS ECE145A /218CA notes, M. Rodwell, copyrighted Knee Voltage: Velocity-Limited Case In the velocity - limited regime, the knee in curve occurs when Vds vsatLg / Again, the Knee Voltage is further increased by voltage drops across the parasitic source & drain resistances. VDS=vsatLg/ IDRD VDS=vsatLg/ IDRS ECE145A /218CA notes, M. Rodwell, copyrighted DC Characteristics---Far Above Threshold Id V Vth Vgs I D coxWg vsat (Vgs Vth V ) for (Vgs Vth ) / V 1 where V vsat Lg / ECE145A /218CA notes, M. Rodwell, copyrighted MOSFET Transconductance mobility limited Id I D , coxWg (Vgs Vth ) / 2 Lg 2 V I D gm coxWg (Vgs Vth ) / Lg VGS Vgs Vth mobility-limited velocity limited I D ,v coxWg vsat (Vgs Vth ) gm velocity-limited V I D gm coxWg vsat VGS Vth Vgs ECE145A /218CA notes, M. Rodwell, copyrighted Linear vs. Square-Law Characteristics: 90 nm 90 nm MOSFET DC Characteristics N - channel g m / Wg coxv sat 1.4 mS / μm 1.4 S / mm Vth 0.6 V 1/ ~ 3V P - channel g m / Wg coxv sat 0.7 mS / μm 0.7 S / mm | Vth | 0.6 V 1/ ~ 3V ECE145A /218CA notes, M. Rodwell, copyrighted ECE145A /218CA notes, M. Rodwell, copyrighted Device Structure and Model: multi-finger device G Rg Cgd gmVg’s’ Gds Rd G S D S D S D S D Ri Cgs Wg Vg’s’ Cdb G Csb Rs S gm Teq veff NWg or Teq NWg Vgs Vth C gd koWg ko (0.3 0.5)fF/m C gs Teq Lg NWg koWg G Cgd s Wg Rend 12 Lg N 2 N Rd 1 / NWg Rg ~ Rg gmVg’s’ Gds D Ri Cgs Vg’s’ Cdb Rs 1 / NWg Gds NWg Csb NWg Increase f max using Ri ~ 1 / g m Cdb NWg - short gate fingers - ample substrate contacts Rs S Csb ECE145A /218CA notes, M. Rodwell, copyrighted Oversimplified Model For rough hand analysis, etc gm g mx ~ 1 g m Rs C gsx ~ Gdsx ~ G Rg Cgd gmVg’s’ Gds D Ri Cgs Vg’s’ Cdb C gs 1 g m Rs Rs Gds 1 g m Rs Csb S Rin ~ Rs Rg Ri G Rin Cgd gmxVg’s’ G dsx D Approximate cutoff frequencie s 1 / 2f ~ Cgs / g m Cgd / g m ( Rs Rd )Cgd f max ~ Cgsx Vg’s’ f 2 ( Rs Rg Ri )Gds 2Rg Cgd Cdb Csb S ECE145A /218CA notes, M. Rodwell, copyrighted Active Devices: III-V Field-Effect Transistors ECE145A /218CA notes, M. Rodwell, copyrighted FET with Heterojunction for Gate Barrier→ HEMT drawing : B. Brar. Gate Source Drain N+ InGaAs contact layer InAlAs gate barrier layer undoped InGaAs channel drawing: K. Shinohara, HRL HEMT : FET with semiconduc tor heterojunc tion for barrier between channel and gate. ECE145A /218CA notes, M. Rodwell, copyrighted HEMTs: Typical interdigitated structure gate source drain Note multiple gate fingers. ECE145A /218CA notes, M. Rodwell, copyrighted HEMT: approximate equivalent circuit model Idss. Cgs, Cgd, gm, Gds all scale proportionally with gate periphery Ri, Rs scale proportionally with (1/ gate periphery) Rg scales proportionally to (gate finger length)/(number fingers) ECE145A /218CA notes, M. Rodwell, copyrighted HEMT DC-IV characteristics Data : K. Shinohara, Teledyne Scientific Schottky diode between gate and channel; gate will draw current for Vgs more positive than c.a. 0.6 V ECE145A /218CA notes, M. Rodwell, copyrighted Figures of Merit ECE145A /218CA notes, M. Rodwell, copyrighted Transistor figures of Merit Transistor small-signal bandwidth is typically stated in terms of the figures of merit f and fmax In order to understand these figures of merit, we must introduce device power gain. These power gains will be studied in more detail later in the course. ECE145A /218CA notes, M. Rodwell, copyrighted Definition of short-circuit current gain G Ri gmVg's Rds D Cgs G Vg's D example: FET small-signal model S S Iin Ri Cgs gmVg's Rds Vg's Vgs I in / jC gs Iout short-circuit current gain: drive input with AC current, short output, measure Iout/Iin I out g mVgs g m f jC jf I in I in gs ECE145A /218CA notes, M. Rodwell, copyrighted Variation of H21 with frequency: Bipolar Transistors 50 h 21 Gains (dB) 40 30 U 20 V f 2 CE = 1 V, J = 1.5 mA/um = 295 GHz H21 is plotted in dB. because H21 is a current gain: dB( H 21) 20 * log10 ( H 21) C 10 f MAX = 295 GHz 0 1 10 Frequency (GHz) Ccbx 6.9 fF B Vb'e C diff C je 172 fF 34 fF g m g mo exp( j c ) C diff g mo f r cb 7000 Ccbi 2.3 fF Rbb 48 R g m 10 R 433 C g mVb 'e Rex 4.7 E r ce 500 2 Because of effect of R / g m : H 21( f ) 1 1 / f / jf ECE145A /218CA notes, M. Rodwell, copyrighted Current-gain cutoff frequency: Bipolar Transistors Web We emitter contact base BC grade emitter base contact collector EB grade Tc B base contact N+ sub collector Rbb Ccbi Rc C collector contact N- drift collector Tb Ccbx Wb,cont Wunder semi-insulating InP substrate Wc Rbe gm Vbee -jc Vbe Cbe,diff =gm f Cje Rex E kT 1 kT base collector C je Cbc Rex Rcoll 2f qI E qI E base Tb2 2Dn collector Tc 2vsat ECE145A /218CA notes, M. Rodwell, copyrighted Current-gain cutoff frequency: Field-Effect Transistors gate metal (silicide) dielectric sidewall G Rg Cgd gmVg’s’ Gds gate oxide source contact (silicide) D Ri N+ poly gate Cgs Vg’s’ Cdb drain contact (silicide) N+ source N+ drain Rs S P substrate f gm 2 (C gs C gd ) Csb ECE145A /218CA notes, M. Rodwell, copyrighted Maximum Power Transfer Theorem generator Xgen load Rgen Xload Rload Vgen M aximum power is transferred from generator to load if X load X gen and Rload Rgen this is called * * * conjugate impedance matching * * * The power delivered, called the available generator power is Pavg 2 Vgen ,( RMS ) 4 Rgen ECE145A /218CA notes, M. Rodwell, copyrighted Impedance Matching Maximum power transfer can be obtained by adding a ***lossless*** (no resistances) impedance matching network between the generator and the load: generator Xgen match Rgen load Xload Vgen * Z gen Z gen * Z load Z load Rload ECE145A /218CA notes, M. Rodwell, copyrighted Maximum Available Power Gain (if it exists) generator Rgen Vgen load gmVg's Rds Ri lossless matching network Cgs Vg's lossless matching network RL The transistor or amplifier is connected to generator and load via lossless matching networks. If it is possible to match at both input and output, then the power gain is called the *maximum available gain* (MAG) Detailed microwave circuit theory (see later notes) indicates that this procedure often produces an oscillator (if the device is “potentially unstable”) . In that case we must define Maximum stable gain ECE145A /218CA notes, M. Rodwell, copyrighted Maximum Stable Power Gain (if MAG does not exist) generator Rgen Vgen load Rds Ri lossless matching network resistive loss (stabilization) Cgs lossless matching network Vg's RL gmVg's If the device is potentially unstable (usually due to strong feedback through Cgd as indicated), addition of a minimum amount of series/shunt resistance to the device input/output will prevent oscillation, and the device can then be matched. The resulting power gain is called the Maximum stable power gain. ECE145A /218CA notes, M. Rodwell, copyrighted Unilateral power gain shunt feedback generator Rgen Vgen load gmVg's Rds Ri lossless matching network Cgs Vg's lossless matching network RL series feedback If the device is potentially unstable (due to strong feedback ), addition of lossless reactive feedback as indicated can cancel the feedback and prevent oscillation. The device can then be matched. The resulting power gain is called Mason’s invariant power gain **or** the Unilateral power gain , U. ECE145A /218CA notes, M. Rodwell, copyrighted Power-Gain Cutoff Frequency (Fmax) This is the frequency at which the device Unilateral power gain reaches unity. The maximum available gain (either in the forward or reverse direction) also reaches unity at the same frequency G For Field - Effect Transistors : f max Rg Cgd gmVg’s’ Gds D Ri Cgs Vg’s’ f 2 ( Ri Rs Rg )Gds 2f Rg Cdg Rs Cdb Csb S Ccbx For Bipolar Transistors ( Rce being large) : B f max f f 8RbbCcbi 2 Rbb / Rce 2f RbbCcbi Rbb Ccbi Rbe Cbe,diff =gm f Cje Rc C gm Vbee -jc Vbe Rex E ECE145A /218CA notes, M. Rodwell, copyrighted Power gains of a typical transistor 40 U: all 3 35 Gains, dB 30 25 MAG/MSG common emitter 20 15 MAG/MSG common base 10 5 MAG/MSG common collector 0 1 10 Frequency, GHz 100 fmax The inflection in the curves is the break between unstable (MSG) at lower frequencies and stable (MAG) at higher frequencies. MAG/MSG is directly relevant for RF/microwave/mm-wave IC design. Because U has -20 dB/decade slope, it is used to extrapolate measurements to determine fmax ECE145A /218CA notes, M. Rodwell, copyrighted End ECE145A /218CA notes, M. Rodwell, copyrighted Appendix (optional) ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor Operation ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor ~ MOSFET Below Threshold Vce Because emitter energy distribution is thermal (exponential) I c exp( qVbe / kT ) Almost all electrons reaching base pass through it I c varies little with collector voltage ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor ~ MOSFET Below Threshold Vbe Vce Ic Because emitter energy distribution is thermal (exponential) I c exp( qVbe / kT ) Almost all electrons reaching base pass through it I c varies little with collector voltage ECE145A /218CA notes, M. Rodwell, copyrighted HBT Equivalent Circuit Model ECE145A /218CA notes, M. Rodwell, copyrighted Physical structure, symbolic Device Stripe Length LE perpendicular to drawing Web We emitter contact base BC grade emitter base contact collector Wb,cont EB grade base contact collector contact N- drift collector Tb Tc N+ sub collector semi-insulating InP substrate Wc Wunder ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor DC-IV Characteristics ECE145A /218CA notes, M. Rodwell, copyrighted Bipolar Transistor: Carrier Transit Times ECE145A /218CA notes, M. Rodwell, copyrighted Base resistance & collector-base capacitance Device Stripe Length LE perpendicular to drawing Rbb contact term spreading under contact spreading under emitter Rbb Ccb contact 2 LE Wb,cont 1 Wb,contact 1 WE base_ sheet base_ sheet 6 LE 12 LE semiconductorWc Le Tc Rbb and Ccb are distributed splitting of Ccb into Ccbx and Ccbi Details beyond scope of class (see Rodwell IEEE EDL Nov. 2001, Proc. IEEE Feb. 2008 HBT RC Parasitics ECE145A /218CA notes, M. Rodwell, copyrighted base contact width < 2 transfer lengths → simple analysis Limiting case of Pulfrey / Vaidyanathan fmax model. ECE145A /218CA notes, M. Rodwell, copyrighted HBT RC Parasitics Rex contact,emitter / Aemitter emitter length LE Rspread sWe / 12 LE Rgap sWgap / 4 LE Rspread,contact sWbc / 6LE Rcontact contact,baseWbc / Abase_ contacts Ccb,e Aemitter / Tc Ccb,gap Agap / Tc Ccb,contact Abase_ contacts / Tc Base-Collector Time Constant & Fmax. f max f where 8RbbCcbi cb RbbCcbi Ccb ,contactRcontact Ccb , gap( Rcontact Rspread,contact Rgap / 2) Ccb ,e ( Rcontact Rspread,contact Rgap Rspread ) ECE145A /218CA notes, M. Rodwell, copyrighted ECE145A /218CA notes, M. Rodwell, copyrighted Relationship to HBT Equivalent Circuit Model Ccbx Ccbi Ccb,e Ccb,gap Ccb,contact Rbb Rspread Rgap Rcontact,spread Rcontact RbbCcbi Ccb ,contactRcontact Ccb, gap( Rcontact Rspread,contact Rgap / 2) Ccb ,e ( Rcontact Rspread,contact Rgap Rspread ) ECE145A /218CA notes, M. Rodwell, copyrighted Field-Effect Transistor Operation (Approximate) Field-Effect Transistor Operation source ECE145A /218CA notes, M. Rodwell, copyrighted gate drain Positive Gate Voltage → reduced energy barrier → increased drain current Field-Effect Transistor Operation source ECE145A /218CA notes, M. Rodwell, copyrighted gate drain Positive Gate Voltage → reduced energy barrier → increased drain current FETs: Basic Operation Cgs ~ A / D Id Q / ECE145A /218CA notes, M. Rodwell, copyrighted Cd ch where Lg / velectron Q CgsVgs Cd chVds I d g m Vgs Gds Vds where g m Cgs / and Ggd Cd ch / FET Characteristics ECE145A /218CA notes, M. Rodwell, copyrighted ID increasing VGS Cgs ~ A / D Cd ch VDS I d g m Vgs Gds Vds g m Cgs / Ggd Cd ch / Lg / velectron FET Parasitic Capacitances (Estimate) Cgd / Wg ~ gm / Wg ~ v / Tox Cgs / Wg ~ Lg / Tox Cgs, f / Wg ~ Csb / Wg ~ Lc / Tsub ECE145A /218CA notes, M. Rodwell, copyrighted
