1. © 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 valenza@cem2.univ-montp2.fr

2. © 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

3. © 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

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

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

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

7. © 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

8. © 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

9. © 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

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

11. © 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

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

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

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

15. © 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 1000 10 8 ; 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

16. © 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)

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

18. © 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

19. © 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

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

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

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

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

24. © 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

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

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

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

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

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

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

31. © 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

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

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

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

35. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 2,2.10 20 (V -1.m -3 ) NOIB = 8,7.10 6 (V -1.m -1 ) NOIC = 8,6.10 -8 (V -1.m) Ohmic Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm VTVT

36. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 2,2.10 20 (V -1.m -3 ) NOIB = 8,7.10 6 (V -1.m -1 ) NOIC = 0 (V -1.m) Ohmic Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm VTVT

37. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm NOIA = 2,2.10 20 (V -1.m -3 ) NOIB = 8,7.10 6 (V -1.m -1 ) NOIC = 8,6.10 -8 (V -1.m) VTVT

38. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range PMOS T OX = 1.3 nm W=10µm, L=0.35µm NOIA = 2,2.10 20 (V -1.m -3 ) NOIB = 8,7.10 6 (V -1.m -1 ) NOIC = 0 (V -1.m) VTVT

39. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 1.10 22 (V -1.m -3 ) NOIB = 2,6.10 6 (V -1.m -1 ) NOIC = 7.10 -11 (V -1.m) Ohmic Range PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT V G =1V

40. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop NOIA = 1.10 22 (V -1.m -3 ) NOIB = 2,6.10 6 (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

41. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range NOIA = 1.10 22 (V -1.m -3 ) NOIB = 2,6.10 6 (V -1.m -1 ) NOIC = 7.10 -11 (V -1.m) PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT

42. © Estoril – 19 September 2003 Advanced Compact Modeling Workshop Saturation Range NOIA = 1.10 22 (V -1.m -3 ) NOIB = 2,6.10 6 (V -1.m -1 ) NOIC = 0 (V -1.m) PMOS T OX = 1.5 nm W=0.3µm, L=10µm VTVT

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

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

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

46. © 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

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