EKV MOS Transistor Modelling & RF Application

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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 matthias.bucher@epfl.ch wladyslaw.grabinski@epfl.ch PART I: Charge-based DC, AC and Noise Modelling Introduction: EKV v.6 Charge-based Static Model Quasi-static Charge & Transcapacitances Model NQS Model Noise Model Mobility Model & Short-Channel Effects MB-WG 1999 EKV MOS Transistor Modelling & RF Application

Introduction: EKV v.6 MOS Transistor (MOST) Model Motivation: RF circuit design requires complete MOST model from DC to RF, including noise. All current levels need to be well modelled, in particular also moderate inversion. EKV v.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 v.6: <, BSIM3v3: > 65, MM9: > 55 MB-WG 1999 EKV MOS Transistor Modelling & RF Application 3 Charge-based Static Model B p+ V S V G V D G S L n+ n+ L eff D t ox x V G G V S D S VD B y p substrate Bulk-reference, symmetric model structure. Drain current expression including drift and diffusion: dv ch = W µ ( Q I ) ---------- dx (1) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 4

Charge-based Static Model Q I ---------- C ox Inversion Charge Density n V P g ms -------- β B A V S I ----- D β strong inversion E D V D C V P = I F I R g md --------- β weak inversion V ch W eff β = µ C ox --------- Channel Voltage L eff Integration of V D Q I Q I = β ---------- d V = ch V S C ox from source to drain: β V S Q ---------- I d V ch C ox I F ( V P V S ) β V D Q ---------- I d V ch C ox I R ( V P V D ) () MB-WG 1999 EKV MOS Transistor Modelling & RF Application 5 Drain Current Normalization and Pinch-off Voltage Current normalization using the Specific current : I S = I F I R = I S ( i f i r ) = nβu T ( ) i f i r (3) Pinch-off voltage V P accounts for... threshold voltage V TO and substrate effect γ qε s N sub = ( ) C ox γ V P V G V TO γ V G V + TO Ψ + -- γ = Ψ + -- (4) Slope factor n: n 1 V P = = V G γ 1+ --------------------------- Ψ + V P (5) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 6

Charge-based Static Model g ms U T / 1 8 6 4.1 8 6 4 asymptotes analytical numerical (GAMMA=.7 V) 1 1.1 1 1 1 1 i f = / I S 1/ if g ms U T / 1..8.6.4. analytic interpolation measured characteristics for:.5 µm, GAMMA=.64 V.7 µm, GAMMA=.75 V 1 µm, GAMMA=.7 V 1 1.1 1 1 1 1 / I S Normalized transconductance-to-current ratio vs. normalized current 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! g ms U T MB-WG 1999 EKV MOS Transistor Modelling & RF Application 7 Drain Current and Pinch-off Voltage [A] 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-1 1-11 1-1 n-channel W=1 µm L=1 µm V D =3V VS=V.5V 1V 1.5V.5 1. 1.5 V G [V]..5 3. I S V S [V] 4. 3.5 3..5. 1.5 1..5 -.5 simulated measured 1 W=µm L=.7µm W=µm L=µm 3 V G [V] n-channel VTO=.75 V GAMMA=.755 V PHI=.576 V LETA=.53 WETA=.56 4 W=.8µm L=µm 5 Valid from weak to strong inversion, and from linear to saturation. Accuracy of weak inversion slope and substrate effect. no additional parameters used for adapting weak inversion slope MB-WG 1999 EKV MOS Transistor Modelling & RF Application 8

Quasistatic Charge- & Transcapacitances Model Charges normalized to WLCox [V].6.5.4.3..1 -.1 -. QB QG (VD=V) QG (VD=V) QS, QD (VD=V) QS & QD (VD=V) C OX = C ox W L -.3-1 1 3 4 5 Node charges: integration of inversion charge density along channel: L Q I = W Q I ( x) dx Q D = W x L -- Q I ( x ) dx Q S = Q I Q D n 1 Q B = γ C OX V P + Ψ ----------- Q n I Q G = Q I Q B Q ox Drain and source charges are obtained using Ward s charge partitioning scheme. Single equation expressions are used from weak to strong inversion. VG [V] L (6) (7) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 9 (Trans-)Capacitances Model Intrinsic Capacitances C/(C ox WL) 1..8.6.4. T OX =6.6nm V D =V S =V W=µm, L=5µm C GG C GD =C GS C GB 1 V G [V] Simulated: Measured: 3 Normalized intrinsic capacitances.8.7.6.5.4.3..1 CGD (VG=V) CBD (VG=V) CGD (VG=.8V) CBD (VG=.8V) CGS (VG=V) CGS (VG=.8V) CGB (VG=.8V) CGB (VG=V) -.1 1 VDB [V] Transcapacitances: derivation with respect to the terminal voltage: C MN = ± ( Q M ) MN, = G, D, S, B Accurate capacitances through all inversion levels. Symmetric C GS and C GD at V D =V S =. V N (8) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 1

Intrinsic MOST - Small Signal Equivalent G Cgs Ymg Vg Cgd S Yms Vs Cgb D Transcapacitances are not shown Ymd Vd Cbs Cbd Distributed time constant accounting for transmission line effect B First-order model for the transadmittances using bias-dependent time constant : τ i d Y mgds (,, ) v ( gds,, ) g mgds (,, ) = -------------------- with τ = τ 1+ s τ fi ( f, i r ) L τ = --------------------- µ U T (9) (1) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 11 Non-Quasistatic Model mag(y1) phase(y1) C (QS) Q (QS) C (QS) Q: charge C: capacitance Model: W/L=36x9/ C (NQS) Q (NQS) Q (NQS) C (NQS) Q (QS) Intrinsic MOST: effect of QS/NQS models on charges-transcapacitances- and capacitances-only models. Y1 Phase prediction is similar for all models except C-only QS model. Y1 Magnitude prediction is incorrect for Q (QS) and C (QS) models. MB-WG 1999 EKV MOS Transistor Modelling & RF Application 1

Noise Model 3-Feb-99 13:54:9 File : noise.cou ELDO v4.6_1.1 (production) : * M.BUCHER - LEG/DE/EPFL DB(INOISE)_1:3 DB(INOISE)_:3 DB(INOISE)_3:3 DB(INOISE)_4:3 db -1-15 -13-135 -14-145 -15-155 -16-165 db -19 - -1 DB(INOISE)_5:3 input noise PSD 5e-1 1e+1 1e+ 1e+3 1e+4 1e+5 1e+6 Hz DB(ONOISE)_1:3 DB(ONOISE)_:3 DB(ONOISE)_3:3 DB(ONOISE)_4:3 DB(ONOISE)_5:3 output noise PSD Noise PSD [dbv/ Hz] -1 - -3-4 -5 f = 1kHz KF = (no 1/f noise) LEVEL 3 EKV model - -3-6..4.6 V DS [V].8 1. 1. -4-5 5e-1 1e+1 1e+ 1e+3 1e+4 1e+5 1e+6 Hz Thermal noise is proportional to total inversion charge. Valid for all inversion levels, and from linear to saturation. 1/f noise modelling included. Q I MB-WG 1999 EKV MOS Transistor Modelling & RF Application 13 Mobility Model 14x1-6 4x1-6 1 1 8 6 n-channel W=L=1µm V DS =5 V 3 p-channel W=L=1µm V DS =5 V EKV v.6 for.5um CMOS (NMOS, PMOS) 4 V B = V B =-1.5V Measured Simulated 1 V B = V B =1.5V Measured Simulated.5 1. 1.5..5 3. -.5-1. -1.5 -. -.5-3. V GS V GS Field- and position-dependent mobility: µ ( x) µ ' = ------------------------- where: E E eff ( x) eff ( x) 1+ ---------------- E = Q' B ( x) + η Q' inv ( x) ------------------------------------------------- ε ε si (11) One parameter: E vertical critical field in the oxide η = 1 η = 1 3 for n-channel, for p-channel) No back-bias dependence needed due to inclusion of bulk charge. MB-WG 1999 EKV MOS Transistor Modelling & RF Application 14

Short-channel Effects 3.5x1-3 [A] 3..5. 1.5 1..5 n-channel W=1 µm L=.5 µm V S = V VG=3V.5V V 1.5V 1V V T [mv] 5 4 3 1-1 Measure Simulation -.1 1 1 L drawn [µm] g ds [A/V] 1-1 -3 1-4 1-5 1-6.5 1. 1.5 V D [V]..5 3. [A] 1 - n-channel 1-3 W=1 µm L=.5 µm 1-4 V D =3V 1-5 1-6 1-7 1-8 1-9 1-1 VS=V.5V 1V 1.5V 1-11.5 1. 1.5..5 V G [V] 3. I S Includes short-channel effects (here:.5um CMOS) Velocity saturation, Channel length modulation (CLM), D-charge sharing, RSCE MB-WG 1999 EKV MOS Transistor Modelling & RF Application 15 Summary EKV v.6 MOST model is a charge-based compact model Continuous, physics-based and valid for all bias conditions. Includes 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 v.6 on the web: <http://legwww.epfl.ch/ekv/> MB-WG 1999 EKV MOS Transistor Modelling & RF Application 16

PART II: RF Application of the EKV v.6 MOST Model Intrinsic MOST and Extrinsic Parasitic Elements RF Test Structure Simulation and Measurement Environment DC Measurements and Simulations RF Measurements and Simulations MB-WG 1999 EKV MOS Transistor Modelling & RF Application 17 Intrinsic MOST and Extrinsic Parasitic Elements Structure of the MOST Corresponding small-signal EKV model G Lov S intrinsic part G Lov D Cgso Rg intrinsic part Cgs Cgd Ymg Vg Cgbo Cgdo As L W Ad S Rs gs Cjs Yms Vs Ymd Vd Cbs Cgb Cbd Cjd gd Rd D B C js(d) = A s(d) * C j + P s(d) * C jsw C ov = W * L ov * C ox P s, P d - perimeter A s, A d - area Rb MB-WG 1999 EKV MOS Transistor Modelling & RF Application 18

Simulation and Measurement Environment Measurements: HP851 and HP 8719 Network Analyzers HP4145 and HP4156 DC Parameter Analyzers Cascade HF Probe Station Ground-Signal-Ground (GSG) probes Test Devices: RF MOS transistor matrix with 36 parallel devices in GSG pad frame Geometry of single circular MOST: L =.5 um, W = 9.um OPEN pad frame for de-embedding thru Y parameters Parameter Extraction and Simulation: IC-CAP 5 ELDO v4.6 with EKV v.6 (LEVEL=44) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 19 RF Test Structure courtesy A.-S. Porret The GSG pad frame and matrix of the RF MOSTs Minimized extrinsic drain capacitance using circular layout MB-WG 1999 EKV MOS Transistor Modelling & RF Application

DC Measurements and Simulations vs. V G g m vs. V G Transfer current and conductance characteristics VD = 5mV MB-WG 1999 EKV MOS Transistor Modelling & RF Application 1 DC Measurements and Simulations vs. V D g ds vs. V D Output current and conductance characteristics MB-WG 1999 EKV MOS Transistor Modelling & RF Application

RF Measurements and Simulations S11, S S1, S1 S1 S S1 S11 Measured de-embedded and simulated S-parameters Frequency sweep 45MHz - GHz DC bias ID=18mA @ VG = 1.5 V VD = 3.V MB-WG 1999 EKV MOS Transistor Modelling & RF Application 3 RF Measurements and Simulations Re(Y1) Im(Y1) Real and Imaginary parts of the forward admittance Y 1 MB-WG 1999 EKV MOS Transistor Modelling & RF Application 4

RF Measurements and Simulations Re(Y 11 ) Re(Y ) Real parts of the input and output admittances Y 11, Y MB-WG 1999 EKV MOS Transistor Modelling & RF Application 5 RF Measurements and Simulations G max Maximum power gain G max MB-WG 1999 EKV MOS Transistor Modelling & RF Application 6

Summary Application of the physics-based EKV v.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 - GHz) MB-WG 1999 EKV MOS Transistor Modelling & RF Application 7

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