1

Numerical Simulation of Electronic Noise

in Si MOSFETs

C. Jungemann

Institute for ElectronicsBundeswehr University

Munich, Germany

Acknowledgments: B. Neinhüs, B. Meinerzhagen, A. Scholten, A. Heringa

EIT4

2

Outline

• Introduction

• Theory

• Acceleration Effects

• Noise source modeling

• Noise in NMOSFETs

• Noise in a BJT

• Noise in an IMOS

• Conclusions

3

Introduction

4

Introduction

• 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

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

NN++NNNN++ structure at zero bias structure at zero bias

5*105*101717 2*102*101515 5*105*101717

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)Power spectral density (PSD)

detItIES tiII )()(2

7

Theory

8

Theory

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LBE is the basis for LHD and LDD modelsLBE is the basis for LHD and LDD models

9

Theory

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10

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mobility for the corrected is of forceLangevin theof PSD

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

Impact of the Acceleration Term

13

Acceleration Effects

In the DD approximation the mobility and the PSD of the In the DD approximation the mobility and the PSD of the velocity fluctuations are assumed to be frequency independentvelocity fluctuations are assumed to be frequency independent

Up to about 100GHz this is correct for siliconUp to about 100GHz this is correct for siliconThe macroscopic relaxation time approximation failsThe macroscopic relaxation time approximation fails

NNdopdop=10=101717/cm/cm33

14

Acceleration Effects

NN++NNNN++ structure (Full LBE) structure (Full LBE)

Up to about 100GHz acceleration effects Up to about 100GHz acceleration effects can be neglected in siliconcan be neglected in silicon

15

Acceleration Effects

Undoped silicon at room temperatureUndoped silicon at room temperatureE(t) = 30kV/cm[1+cos(2E(t) = 30kV/cm[1+cos(2ft)]ft)]

Above 100GHz nonquasistationary effects occur in siliconAbove 100GHz nonquasistationary effects occur in silicon

16

Noise source modeling

17

Noise source modelingNN++NNNN++ structure structure

Diffusion noise source yields the best resultsDiffusion noise source yields the best resultsHD model yields similar good resultsHD model yields similar good results

Device results strongly deviate from thermal or shot noiseDevice results strongly deviate from thermal or shot noise

Bulk, NBulk, NDD=10=101717/cm/cm33

18

Noise source modeling

NN++NNNN++ structure biased at 6V structure biased at 6V

Generation noise due to impact ionizationGeneration noise due to impact ionizationNoise source is given by microscopic white shot noiseNoise source is given by microscopic white shot noise

19

Noise source modeling

NN++NNNN++ structure biased at 0 and 1V structure biased at 0 and 1V

Terminal current noise is due to cold and warm electronsTerminal current noise is due to cold and warm electronsHot electrons can produce noise via impact ionizationHot electrons can produce noise via impact ionization

20

Noise in NMOSFETs

21

Noise in NMOSFETs

Measurements and Tsuprem simulations by Philips (A. Scholten)Measurements and Tsuprem simulations by Philips (A. Scholten)Simulation includes quantum correction for channelSimulation includes quantum correction for channel

DD and HD simulations performed without any parameter matchingDD and HD simulations performed without any parameter matching

180nm Technology, t180nm Technology, toxox = 3nm, V = 3nm, Vdraindrain = 1.8V, f=2.5GHz = 1.8V, f=2.5GHz

Lgate=1m

22

Noise in NMOSFETs

Also in MOSFETs drain noise is not due to hot electronsAlso in MOSFETs drain noise is not due to hot electrons

180nm gate length, t180nm gate length, toxox = 3nm, V = 3nm, Vdraindrain = 1.8V, V = 1.8V, Vgategate=1.0V=1.0V

Gate noiseDrain noiseDrain noise

23

Noise in NMOSFETs

50nm channel length, 1.3nm oxide, V50nm channel length, 1.3nm oxide, Vdraindrain=0.9V, f=10GHz=0.9V, f=10GHz

Noise specs of small Noise specs of small NMOSFETs increase NMOSFETs increase

only moderatelyonly moderately

24

Noise in a BJT

25

Noise in a BJT

Overestimation of shot noise is caused by model failure Overestimation of shot noise is caused by model failure

1D 50nm Si NPN bipolar transistor1D 50nm Si NPN bipolar transistor

Fano factor of electron collector noise at VCE=0.5V

Doping profileDoping profile

26

Noise in a BJT

Quasiballistic transport leads to model failureQuasiballistic transport leads to model failure

50nm Si bipolar transistor50nm Si bipolar transistor

VCE=0.5V, VBE=0.65V

27

Noise in an IMOS

F. Mayer et al., TED, Vol. 53, p. 1852, 2006F. Mayer et al., TED, Vol. 53, p. 1852, 2006

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Noise in an IMOS

CMOS has a Fano factor of less than one for inversionCMOS has a Fano factor of less than one for inversionIMOS generates two or more orders of magnitude more noiseIMOS generates two or more orders of magnitude more noise

CIMPAT, VCIMPAT, Vgate/draingate/drain=-3.5V, L=-3.5V, Lchannelchannel=5.0=5.0mm

29

Conclusions

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

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