An Improved Model for Electron Mobility Degradation by ... · An Improved Model for Electron Mobility Degradation by Remote Coulomb Scattering in Ultra-Thin SOI MOSFETs David Esseni

David Esseni ESSDERC 2002 1

An Improved Model for Electron Mobility Degradation by Remote Coulomb Scattering in

Ultra-Thin SOI MOSFETs

David Esseni and Antonio Abramo

DIEGM – University of Udine


Motivations• Limits to Gate Oxide Scaling in terms of

Reliability and/or Leakage Current• Effect of oxide thickness and Polysilicon

Proximity on Electron Transport• Experimental Reduction of On-Current

for TOX < 1.3nm [Timp-IEDM ’98]• Previous papers on RCS use Simplified

Models Large µrcs Underestimate


Purpose of the Work• Numerical Calculation of RCS:

– Wave functions of the 2D Electron Gas– CS Potential induced by a point charge

including Screening in Poly and Substrate– Momentum Relaxation Time (MRT)

• Discuss Importance of Poly Screening and Multi-Subband Transport

• Dependence of µeff on TOX and NPOLY


Outline• Numerical Evaluation of µRCS

– The Screened CS Potential– Momentum Relaxation Time (MRT)

• Results for RCS Limited Mobility

• Total µeff in Ultra-Thin Oxide MOSFETs

• Conclusions


Determine φ(q,z,z0): z0: Charge Positionq: Spacial Freq. Vectorz: Normal to Interfaceξi: i-th Subband Eigenf.

Non-Local Screening [Stern - 1967]


φ(q,z,z0) in Poly/Oxide/Substrate Stack

Boundary Conditions for φ and (dφ/dz)give the unknown constants A1 .. A4


Calculation of the CS Potential φ(q,z,z0)

• Poly Screening strongly reduces φ(q,z,z0)• QM Depletion Region [Spinelli-TED ’00]



– The Screened CS Potential

– Momentum Relaxation Time (MRT)



• Conclusions


Scattering Matrix Elements:

Momentum Relaxation Time:

Inter-Subband Transitions Couple MRTs Calculation !!


Momentum Relaxation Time:

Isotropic Bands: τi(E) DOES NOT depend on the angle βi

Set of Non-Linear Algebraic Equations:


CS Momentum Relaxation Time

• Inter-Subband Transitions do affect MRTs• Subband Mobility is finally obtained from

the average MRT in the Subband


Outline

• Numerical Evaluation of µRCS– The Screened CS Potential




• Conclusions


RCS Mobility: Effect of Poly Screening

• Large µRCS Underest. w/o Poly Screen.

• CL Poly gives much Larger µRCS


RCS Mobility: Multi Subband Transport

• CS Potential decays in the substrate so lowest Subbands have largest Coupling

• µRCS is much Larger than in QL Approx.



– The Screened CS Potential




• Conclusions


Mobility of Thick Oxide MOSFETs

• Phonons [Jungemann - SSE 1993] and Surface Roughness [Ando - 1982]

• DAC and Roughness adjusted for Nsub=2x1016


Mobility of Thin Oxide MOSFETs

• ~20% Reduction for TOX=1.2nm at Ninv~1012

• Larger Reductions with Simplified Models


• At Ninv=1013 Mobility is Independent of TOX• ~7% Reduction for TOX=3nm at Ninv~1012

• Simplified Models: µeff Degradation for TOX>5nmcontrary to Data [Liang-TED 1986]

Mobility vs. Oxide Thickness


Mobility vs. Polysilicon Doping Concentration

• Increased Density of CS Centers and Poly Screening result in Weak Npoly Dependence


Conclusions• Numerical Model for µRCS:

– Polysilicon and Substrate Screening– MRTs Including Inter-Subband Transitions

• Large Underestimates w/o Poly Screening

• QL Approximation NOT Applicable• RCS Effects for TOX<3nm at Low Ninv

• Approach suitable for RCS due to Oxide Charges in High-K Dielectrics


Temperature Dependence

• Low Temperatures Confine Electrons in the Lowest Subband and Decrease µRCS


Alternative High-K Dielectrics

• For a given Teq High-K Improves µRCS

• For a given TOX High-K Reduces µRCS


High-K Dielectrics: Effect of Fixed Charges

• Control of Fixed Charges is Very Critical

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An Improved Model for Electron Mobility Degradation by ... · An Improved Model for Electron Mobility Degradation by Remote Coulomb Scattering in Ultra-Thin SOI MOSFETs David Esseni