1. 1 Numerical Simulation of Electronic Noise in Si MOSFETs C. Jungemann Institute for Electronics Bundeswehr University Munich, Germany Acknowledgments: B. Neinhüs, B. Meinerzhagen, A. Scholten, A. Heringa EIT4

2. 2 Outline Introduction Theory Acceleration Effects Noise source modeling Noise in NMOSFETs Noise in a BJT Noise in an IMOS Conclusions

3. 3 Introduction

4. 4 Noise is a fundamental property of electron transport and cannot be avoided Fluctuation-dissipation theorems (e.g.: Nyquist theorem) are only valid at equilibrium (Shot and thermal noise are macroscopic manifestations of microscopic noise.) Transport in nanoscale devices is nonlocal and quasi-ballistic Physics-based methods required for device level simulations!

5. 5 Introduction Terminal current fluctuations are due to electron scattering within the device via displacement and conduction currents Noise theory describes the variance and the correlation of the fluctuations N + NN + structure at zero bias 5*10 17 2*10 15 5*10 17

6. 6 Introduction PSD vanishes at very high frequencies due to acceleration effects (finite electron mass means no real white noise) nonquasistationary Plasma resonance at very high frequencies (>1THz) in silicon Power spectral density (PSD)

7. 7 Theory

8. 8 LBE is the basis for LHD and LDD models

9. 9 Theory

10. 10 Theory

11. 11 Theory Transport and noise parameters of the LDD are calculated consistently under homogeneous bulk conditions based on the single particle LBE The parameters are generated for a wide range of doping concentrations, lattice temperatures, strain conditions, driving fields etc, and stored in lookup tables for later use.

12. 12 Impact of the Acceleration Term

13. 13 Acceleration Effects In the DD approximation the mobility and the PSD of the velocity fluctuations are assumed to be frequency independent Up to about 100GHz this is correct for silicon The macroscopic relaxation time approximation fails N dop =10 17 /cm 3

14. 14 Acceleration Effects N + NN + structure (Full LBE) Up to about 100GHz acceleration effects can be neglected in silicon

15. 15 Acceleration Effects Undoped silicon at room temperature E(t) = 30kV/cm[1+cos(2  ft)] Above 100GHz nonquasistationary effects occur in silicon

16. 16 Noise source modeling

17. 17 Noise source modeling N + NN + structure Diffusion noise source yields the best results HD model yields similar good results Device results strongly deviate from thermal or shot noise Bulk, N D =10 17 /cm 3

18. 18 Noise source modeling N + NN + structure biased at 6V Generation noise due to impact ionization Noise source is given by microscopic white shot noise

19. 19 Noise source modeling N + NN + structure biased at 0 and 1V Terminal current noise is due to cold and warm electrons Hot electrons can produce noise via impact ionization

20. 20 Noise in NMOSFETs

21. 21 Noise in NMOSFETs Measurements and Tsuprem simulations by Philips (A. Scholten) Simulation includes quantum correction for channel DD and HD simulations performed without any parameter matching 180nm Technology, t ox = 3nm, V drain = 1.8V, f=2.5GHz L gate =1  m

22. 22 Noise in NMOSFETs Also in MOSFETs drain noise is not due to hot electrons 180nm gate length, t ox = 3nm, V drain = 1.8V, V gate =1.0V Gate noise Drain noise

23. 23 Noise in NMOSFETs 50nm channel length, 1.3nm oxide, V drain =0.9V, f=10GHz Noise specs of small NMOSFETs increase only moderately

24. 24 Noise in a BJT

25. 25 Noise in a BJT Overestimation of shot noise is caused by model failure 1D 50nm Si NPN bipolar transistor Fano factor of electron collector noise at V CE =0.5V Doping profile

26. 26 Noise in a BJT Quasiballistic transport leads to model failure 50nm Si bipolar transistor V CE =0.5V, V BE =0.65V

27. 27 Noise in an IMOS F. Mayer et al., TED, Vol. 53, p. 1852, 2006

28. 28 Noise in an IMOS CMOS has a Fano factor of less than one for inversion IMOS generates two or more orders of magnitude more noise CIMPAT, V gate/drain =-3.5V, L channel =5.0  m

29. 29 Conclusions

30. 30 Conclusions Consistent hierarchy of noise models (DD, HD, LBE) Transport and noise parameters are consistently generated for the DD and HD models by LBE bulk simulations The transport and noise parameters are local in real space and frequency independent Acceleration effects can be neglected below 100GHz in silicon Modified noise sources (diffusion noise) give good results

31. 31 Conclusions Good agreement of measurements and simulations for MOSFETs Terminal current noise is produced by cold or warm electrons Hot electrons can produce noise via impact ionization No dramatic increase of noise in scaled MOSFETs IMOS suffers from huge noise due to avalanche breakdown