ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE HP-RF MOS Modelling Workshop, Munich, February 15-16, 1999 EKV MOS Transistor Modelling & RF Application Matthias Bucher, Wladek Grabinski Electronics Laboratory (LEG) Swiss Federal Institute of Technology, Lausanne (EPFL) ☞Part I: Charge-based DC, AC and Noise Modelling ☞Part II: RF Application [email protected] [email protected] PART I: Charge-based DC, AC and Noise Modelling ☞Introduction: EKV v2.6 ☞Charge-based ☞Quasi-static ☞NQS Charge & Transcapacitances Model Model ☞Noise Model ☞Mobility © MB-WG 1999 Static Model Model & Short-Channel Effects EKV MOS Transistor Modelling & RF Application 2 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Introduction: EKV v2.6 MOS Transistor (MOST) Model ☞ Motivation: ✔RF ✔All ☞ circuit design requires complete MOST model from DC to RF, including noise. current levels need to be well modelled, in particular also moderate inversion. EKV v2.6 in summary: ✔A physics-based compact MOST model in the public domain. ✔Dedicated to analog circuit simulation for submicron CMOS. ✔Includes weak-moderate-strong inversion modelling, doping & mobility effects, short-channel effects, geometry- and bias-dependent matching. ✔Small number of intrinsic model parameters: EKV v2.6: < 20, BSIM3v3: > 65, MM9: > 55 © MB-WG 1999 3 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Charge-based Static Model VD B VG VS D D ID G S ID L VD G B tox p+ n+ Leff y n+ x S VG VS p substrate ☞ Bulk-reference, symmetric model structure. ☞ Drain current expression including drift and diffusion: dV ch I D = W ⋅ µ ⋅ ( – Q′ I ) ⋅ ----------dx © MB-WG 1999 EKV MOS Transistor Modelling & RF Application (1) 4 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Charge-based Static Model Inversion Charge Density – Q′ I ----------C′ ox ☞ n ⋅ VP W eff β = µ ⋅ C′ ox ⋅ ---------L eff strong inversion B I D = IF – I R g ms --------β ID ----β E g md --------β weak inversion Channel Voltage Vch C D VD VP A VS Integration of Q′ I from source to drain: ∞ ∫ VS © MB-WG 1999 β ∫ VS VD – ∫ β ∞ – Q′ -----------I ⋅ dV ch C′ ox (2) ID = β – Q′ -----------I ⋅ dV = ch C′ ox – Q′ -----------I ⋅ dV ch C′ ox VD IF ( VP – V S ) IR ( VP – VD ) 5 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Drain Current Normalization and Pinch-off Voltage ☞ Current normalization using the Specific current I S : 2 I D = I F – I R = I S ⋅ ( i f – i r ) = 2nβU T ⋅ ( i f – i r ) ☞ Pinch-off voltage V P accounts for... ✔threshold voltage V TO and substrate effect γ = ( 2qε s N sub ) ⁄ C′ ox V P = V G – V TO – γ ⋅ ☞ (3) γ 2 γ V G – V TO + Ψ 0 + --- – Ψ 0 + --- 2 2 (4) Slope factor n : ∂V P n = ∂ VG © MB-WG 1999 –1 γ = 1 + --------------------------2 Ψ0 + VP EKV MOS Transistor Modelling & RF Application (5) 6 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Charge-based Static Model 2 analytic interpolation 1.0 1 1/ √if 4 2 0.1 8 6 asymptotes analytical numerical (GAMMA=0.7 √V) 4 0.01 0.1 0.6 0.4 0.2 2 0.001 measured characteristics for: 0.5 µm, GAMMA=0.64 √V 0.7 µm, GAMMA=0.75 √V 1 µm, GAMMA=0.72 √V 0.8 gms·UT / ID gms·UT / ID 8 6 1 10 100 0.0 0.001 1000 0.01 0.1 if = ID / IS ☞ 1 10 100 1000 ID / I S Normalized transconductance-to-current ratio g ms ⋅ U T ⁄ I D vs. normalized current I D ⁄ I S from weak through moderate to strong inversion. ✔Comparison with numerical solution of the Poisson equation. ✔Comparison with three different CMOS processes (long-channel devices in saturation). ✔Almost technology independent! © MB-WG 1999 7 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Drain Current and Pinch-off Voltage -3 10 n-channel W=10 µm -5 L=10 µm 10 VD=3V -4 10 4.0 IS -7 10 -8 10 VS [V] -6 10 ID [A] W=20µm L=0.7µm 3.5 3.0 2.5 2.0 W=0.8µm L=20µm 1.5 1.0 -9 10 W=20µm L=20µm simulated measured n-channel VTO=0.752 V GAMMA=0.755 √V PHI=0.576 V LETA=0.503 WETA=0.256 0.5 10 -10 10 -11 10 -12 0.0 0.0 VS=0V 0.5 1V 0.5V 1.0 1.5 1.5V 2.0 2.5 -0.5 0 1 2 3.0 3 4 5 VG [V] VG [V] ☞ Valid from weak to strong inversion, and from linear to saturation. ☞ Accuracy of weak inversion slope and substrate effect. ✔no © MB-WG 1999 additional parameters used for adapting weak inversion slope EKV MOS Transistor Modelling & RF Application 8 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Charges normalized to WLCox [V] Quasistatic Charge- & Transcapacitances Model 0.6 0.5 0.4 QG (VD=0V) 0.3 0.2 QG (VD=2V) C OX = C′ ox ⋅ W ⋅ L 0.1 0 QS, QD (VD=2V) -0.1 QB QS & QD (VD=0V) -0.2 -0.3 -1 0 1 2 3 4 5 VG [V] ☞ Node charges: integration of inversion charge density along channel: L L x Q D = W ⋅ ∫ --- ⋅ Q I ′ ( x ) ⋅ dx L Q I = W ⋅ ∫ Q I ′ ( x ) ⋅ dx 0 (6) 0 n–1 Q B = – γ ⋅ C OX ⋅ V P + Ψ 0 – ------------ ⋅ Q I n ✔Drain QS = QI – QD Q G = – Q I – Q B – Q ox (7) and source charges are obtained using Ward’s charge partitioning scheme. ✔Single equation expressions are used from weak to strong inversion. © MB-WG 1999 9 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE (Trans-)Capacitances Model 0.8 TOX=6.6nm VD=VS=0V W=200µm, L=5µm 0.6 0.8 CGG 0.7 Normalized intrinsic capacitances Intrinsic Capacitances C/(CoxWL) 1.0 CGD=CGS 0.4 Simulated: 0.2 CGS (VG=2V) 0.6 0.5 CGD (VG=2V) 0.4 CGS (VG=0.8V) 0.3 CGB (VG=0.8V) 0.2 CBD (VG=2V) CGB (VG=2V) 0.1 Measured: CGD (VG=0.8V) CBD (VG=0.8V) CGB 0 0.0 -0.1 0 1 2 0 3 1 2 VDB [V] VG[V] ☞ Transcapacitances: derivation with respect to the terminal voltage: C MN = ± ✔Accurate M, N = G, D, S, B (8) capacitances through all inversion levels. ✔Symmetric © MB-WG 1999 ∂ (Q ) ∂ VN M CGS and CGD at VD=VS=0. EKV MOS Transistor Modelling & RF Application 10 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Intrinsic MOST - Small Signal Equivalent G C gs Ym g ∆V g Cgd C gb Ym s ∆V s S Transcapacitances are not shown D Ym d ∆V d Distributed time constant accounting for “transmission line effect” Cbd C bs B ✔First-order model for the transadmittances using bias-dependent time constant Y m ( g, d, s ) ≡ ∂i d g m ( g, d, s ) = -------------------1+s⋅τ ∂ v ( g, d, s ) τ: with τ = τ 0 ⋅ f ( i f, i r ) (9) 2 L τ 0 = ---------------------2 ⋅ µ ⋅ UT © MB-WG 1999 (10) 11 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Non-Quasistatic Model mag(Y21) phase(Y21) C (QS) Q (QS) C (QS) Q (NQS) Model: Q: charge C: capacitance W/L=36x9/2 ☞ C (NQS) C (NQS) Q (QS) Q (NQS) Intrinsic MOST: effect of QS/NQS models on charges-transcapacitances- and capacitances-only models. ✔Y21 Phase prediction is similar for all models except C-only QS model. ✔Y21 Magnitude prediction is incorrect for Q (QS) and C (QS) models. © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 12 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Noise Model 3-Feb-99 File : noise.cou 13:54:29 ELDO v4.6_1.1 (production) : * M.BUCHER - LEG/DE/EPFL DB(INOISE)_1:3 dB DB(INOISE)_2:3 DB(INOISE)_3:3 DB(INOISE)_4:3 DB(INOISE)_5:3 -120 input noise PSD -125 -130 -210 -135 f = 1kHz KF = 0 (no 1/f noise) Noise PSD [dBv/√Hz] -140 -145 -150 -155 -160 -165 5e-01 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 Hz DB(ONOISE)_1:3 dB DB(ONOISE)_2:3 DB(ONOISE)_3:3 DB(ONOISE)_4:3 DB(ONOISE)_5:3 -190 output noise PSD -200 -220 -230 EKV model -240 -250 LEVEL 3 -210 -260 0.0 -220 0.2 -230 0.4 0.6 0.8 1.0 1.2 VDS [V] -240 -250 5e-01 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 Hz Thermal noise is proportional to total inversion charge Q I . ☞ ✔Valid for all inversion levels, and from linear to saturation. 1/f noise modelling included. ☞ © MB-WG 1999 13 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Mobility Model -6 4x10 14x10 n-channel W=L=10µm VDS=0.05 V 12 10 -6 p-channel W=L=10µm VDS=0.05 V 3 EKV v2.6 for 0.5um CMOS (NMOS, PMOS) ID ID 8 2 6 4 Measured Simulated VB=0 2 Measured Simulated 1 VB=0 VB=1.5V VB=-1.5V 0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 -0.5 -2.0 -2.5 -3.0 Field- and position-dependent mobility: µ 0' µ ( x ) = -------------------------E eff ( x ) 1 + ---------------E0 ☞ -1.5 VGS VGS ☞ -1.0 where: Q' B ( x ) + η ⋅ Q' inv ( x ) E eff ( x ) = -------------------------------------------------ε 0 ε si (11) One parameter: E0 vertical critical field in the oxide ✔ η = 1 ⁄ 2 for n-channel, η = 1 ⁄ 3 for p-channel) ✔No back-bias dependence needed due to inclusion of bulk charge. © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 14 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Short-channel Effects 50 n-channel 3.0 W=10 µm L=0.5 µm 2.5 VS=0 V 40 VG=3V 2.5V 2.0 2V 1.5 1.0 ∆VT [mV] ID [A] 3.5x10-3 20 10 0 Measure Simulation -10 1.5V 0.5 30 -20 0.1 1V 1 0.0 -2 10 -3 10 -4 10 -5 10 -2 10 -3 n-channel W=10 µm L=0.5 µm 10-4 VD=3V ID [A] gds [A/V] 10 10 -5 10 -6 10 -7 10 -8 10 -9 -10 10 10 -6 0.0 IS VS=0V 1.5V 1V 0.5V -11 10 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 VD [V] ☞ 10 Ldrawn [µm] 1.5 2.0 2.5 3.0 VG [V] Includes short-channel effects (here: 0.5um CMOS) ✔Velocity saturation, Channel length modulation (CLM), 2D-charge sharing, RSCE © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 15 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Summary ☞ EKV v2.6 MOST model is a charge-based compact model ✔Continuous, ✔Includes physics-based and valid for all bias conditions. charge-based static and dynamic models, and noise. ✔Non-quasistatic ☞ (NQS) model for small-signal. Availability early ‘99: ✔Eldo, SmartSpice, Saber, Spectre, HSpice, PSpice, Aplac, Smash (check model versions). ☞ EKV v2.6 on the web: <http://legwww.epfl.ch/ekv/> © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 16 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE PART II: RF Application of the EKV v2.6 MOST Model ☞Intrinsic ☞RF MOST and Extrinsic Parasitic Elements Test Structure ☞Simulation and Measurement Environment ☞DC Measurements and Simulations ☞RF Measurements and Simulations © MB-WG 1999 17 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Intrinsic MOST and Extrinsic Parasitic Elements Corresponding small-signal EKV model Structure of the MOST G Rg intrinsic part Lov G S intrinsic part Lov C gs D Cgso Y m g ∆Vg C gd C gbo C gdo C gb S L Y m s ∆Vs Rs Rd D Y m d ∆Vd gs As W Ad Cjs C jd gd C bd C bs B Cjs(d) = As(d) * Cj + Ps(d) * Cjsw Cov = W * Lov * Cox Rb Ps, Pd - perimeter As, Ad - area © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 18 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Simulation and Measurement Environment ☞ Measurements: ✔HP8510 and HP 8719 Network Analyzers ✔HP4145 and HP4156 DC Parameter Analyzers ✔Cascade HF Probe Station ✔Ground-Signal-Ground ☞ Test Devices: ✔RF MOS transistor matrix with 36 parallel devices in GSG pad frame ✔Geometry ✔OPEN ☞ (GSG) probes of single circular MOST: L = 0.5 um, W = 9.2um pad frame for de-embedding thru Y parameters Parameter Extraction and Simulation: ✔IC-CAP ✔ELDO 5 v4.6 with EKV v2.6 (LEVEL=44) © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 19 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE RF Test Structure courtesy A.-S. Porret ☞ The GSG pad frame and matrix of the RF MOSTs ✔Minimized © MB-WG 1999 extrinsic drain capacitance using circular layout EKV MOS Transistor Modelling & RF Application 20 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE DC Measurements and Simulations ID vs. VG ☞ gm vs. VG Transfer current and conductance characteristics ✔VD = 50mV © MB-WG 1999 21 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE DC Measurements and Simulations ID vs. VD ☞ gds vs. VD Output current and conductance characteristics © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 22 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE RF Measurements and Simulations S11, S22 S12, S21 S21 S22 S12 S11 ☞ Measured de-embedded and simulated S-parameters ✔Frequency ✔DC sweep 45MHz - 20 GHz bias ID=18mA @ VG = 1.5 V VD = 3.0V © MB-WG 1999 23 EKV MOS Transistor Modelling & RF Application ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE RF Measurements and Simulations Re(Y21) ☞ Im(Y21) Real and Imaginary parts of the forward admittance Y21 © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 24 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE RF Measurements and Simulations Re(Y22) Re(Y11) ☞ Real parts of the input and output admittances Y11 , Y22 © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 25 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE RF Measurements and Simulations Gmax ☞ Maximum power gain Gmax © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 26 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE Summary ☞ Application of the physics-based EKV v2.6 MOST model for RF simulation has been presented ✔DC parameter set was verified on the RF MOST test structure measurements ✔The small-signal characteristics were corrected for interconnections and bond pads parasitics ✔Effective gate and bulk (substrate) resistances were introduced to allow proper small signal simulation ✔Simulated small-signal S- and Y- parameters match on-the-wafers measurements over wide range of frequencies (45MHz - 20GHz) © MB-WG 1999 EKV MOS Transistor Modelling & RF Application 27 ÉCOLE POLYTECHNIOUE FÉDÉRALE DE LAUSANNE
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