© Estoril – 19 September 2003 Advanced Compact Modeling Workshop MOSFETs Flicker Noise Modeling For Circuit Simulation Montpellier University A. Laigle, F. Martinez, A. Hoffmann and M. Valenza

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Outline Introduction Methodology and Instrumentation 1/f modeling – 1/f theory – 1/f models Experimental results Conclusion

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Introduction (1) Low frequency noise is important for : Conduction phenomena and random noise - White noise (thermal & shot noise) - 1/f and origin (  N,  µ,  N-  µ); RTS & G.R. - High electric field : multiplication - Correlation between two noise sources Technologies evaluation - Reliability, quality, aging - Parasitic elements, defects - Equivalent circuit Analog applications with mixed CMOS technologies (LN amplifiers, oscillators, sensors …) We need models

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Introduction (2)

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop DRAIN CURRENT NOISE (3) - Fundamental thermal noise - Excess noise RTS 1/f

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop GATE CURRENT NOISE (4) - Fundamental level Shot noise - Excess noise RTS 1/f

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Introduction (5) - Drain current spectral density is dependent of : Technology process Oxide thickness Mobility Channel geometry (W, L) Access resistances Biases Are commercial simulators well suited ? - Gate current spectral density : few investigations up today

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Outline Introduction Methodology and Instrumentation 1/f modeling – 1/f theory – 1/f models Experimental results Conclusion

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop USED METHODOLOGY Good model for F.E.T devices. i c = source-drain noise generator  transistor channel i g = gate-source noise generator  command electrode /channel Direct measurement of Coherence

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Simultaneous measurements

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop EXPERIMENTAL SETUP Drain Gate channel B channel A IEEE Bus Amplifier voltageAmplifier Transimpedance Oscilloscope spectrum Analyser Transistor Batteries Faraday cage Batteries

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Transimpedance Amplifier

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Voltage Amplifier

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Cross Spectrum Measurements A A Analyser Input A Analyser Input B eAeA eAeA

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Low noise Amplifiers Voltage Amplifier Transimpedance Amplifier Bandwidth 0.5Hz-1MHz/200Hz-30MHz 1 Hz- 200 KHz Gain ; 10 7 ; 10 6  Input Imped. 1 M  - 15 pF/ 1 M  - 50 pF 1  - 10 k  Noise equival. 40  / 35  500 pA ; 50 nA ; 2  A Used for Direct measure of S I (f) Under low impedance Direct measure of S I (f) Under strong impedance

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Drain noise measurements V S (t) i R P G R C e A (t) i Rp (t) Ch (t)

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Drain noise measurements K V S (t) i ch (t) i A (t) RCRC

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Outline Introduction Methodology and Instrumentation 1/f modeling – 1/f theory – 1/f models Experimental results Conclusion

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop 1/f noise theory Noise source due to conductivity fluctuations :  = q µ n three models : Hooge model (  µ) SPICE Mc Whorter model (  N) correlated model (  N-  µ) BSIM

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop  N model Weak inversion Strong inversion : i) linear regime ii) saturation regime

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Typical NMOS results

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop  µ model Weak inversion Strong inversion : i) linear regime ii) saturation regime

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Typical PMOS results

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop CORRELATED MODEL (  N-  µ) Fluctuation of oxide Trapped carriers quantity Fluctuation of carriers number and of their mobility  : Coulomb scattering coefficient : the electron tunneling constant in the oxide N T : oxide trap density

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop CONTRIBUTION OF ACCESS RESISTANCES

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop CONTRIBUTION OF ACCESS RESISTANCES

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Access resistance noise

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop SPICE Simulations HSPICE SPICE [1980] SPICE [1996] NLEV=0 NLEV=1 NLEV=2 and 3

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop BSIM MODEL Weak inversion : Strong inversion : with and Continuity between weak and strong inversion :

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop BSIM MODEL

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Introduction Methodology and Instrumentation 1/f modeling – 1/f theory – 1/f models Experimental results Conclusion Outline

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Typical Results

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop PMOS Results T OX =1.5 nm

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop NMOS Results T OX =1.5 nm

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 2, (V -1.m -3 ) NOIB = 8, (V -1.m -1 ) NOIC = 8, (V -1.m) Ohmic Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 2, (V -1.m -3 ) NOIB = 8, (V -1.m -1 ) NOIC = 0 (V -1.m) Ohmic Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm NOIA = 2, (V -1.m -3 ) NOIB = 8, (V -1.m -1 ) NOIC = 8, (V -1.m) VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm NOIA = 2, (V -1.m -3 ) NOIB = 8, (V -1.m -1 ) NOIC = 0 (V -1.m) VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = (V -1.m -3 ) NOIB = 2, (V -1.m -1 ) NOIC = (V -1.m) Ohmic Range PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT V G =1V

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = (V -1.m -3 ) NOIB = 2, (V -1.m -1 ) NOIC = 0 (V -1.m) Ohmic Range PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT V G =1V

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range NOIA = (V -1.m -3 ) NOIB = 2, (V -1.m -1 ) NOIC = (V -1.m) PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range NOIA = (V -1.m -3 ) NOIB = 2, (V -1.m -1 ) NOIC = 0 (V -1.m) PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop PMOS T OX = 1.5 nm V DS = -25 mV

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Gate current noise (PMOS T OX = 1.5 nm) V DS = -25 mV

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Coherence measurements (PMOS T OX = 1.5 nm) V DS = -25 mV

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Conclusion SPICE and HSPICE models are not well suited for 1/f noise BSIM3 is a good fitting model Thinner and thinner gate oxide  new noise sources

© Estoril – 19 September 2003 Advanced Compact Modeling Workshop Conclusion i GD Source RSRS RDRD Grille Drain y1y1 y3y3 i GS