Mobility in UTB-SOI PFETS: Local Coordinate-Based Modeling with the Density Gradient Method Daniel Connelly, Acorn Technologies D. E. Grupp, Acorn Technologies Daniel Yergeau, Paco Leon: Mixed Technology Associates ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
FDSOI Mobility Modeling Current practice: Use E perp or E eff to model µ reduction with increasing inversion layer density. Technology Trend: Length scaling of FDSOI � ever- decreasing t Si . Problem: E perp or E eff don’t predict µ reduction with decreasing t Si . Ballisticity ∝ µ 1/2 . Result: Excessively optimistic scaling forecasts by simulation engineers. Unsatisfying Kludge: “Manually adjust” global µ APS scale factor based on theoretical or experimental data. Better Approach: A local model which includes structural effects. ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Mobility Composition Agostinelli new approach, et al, TED 1991 using Agostinelli et al, TED 1991 1 1 1 = + + surface coulombic APS mobility mobility mobility 1 1 + surface roughness thickness variation scattering mobility scattering mobility use E eff -based new term, after model Uchida et al, IEDM 2002 ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Confinement and APS Bulk: electric field predicts confinement. FDSOI: structural information needed. confinement � k -space dispersion � APS ������ ������ confinement ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ due to electric ������ ������ ������ ������ ������ ������ E F ������ ������ ������ ������ field ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ SiO 2 SiO 2 ������ ������ ������ ������ SiO 2 ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ E F ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ confinement ������ ������ ������ ������ ������ ������ ������ ������ due to structure ������ ������ ������ ������ ������ ������ ������ ������ ������ ������ bulk channel FDSOI channel ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
APS Modeling Philosophy New idea: Use position to model confinement effects on mobility. Advantage: Structural confinement effects can be modeled. Efficiency: Calculation done only at start of simulation, not after each iteration. New Requirement: An accurate determination of carrier distributions near interfaces. Tool for the Job: The Density Gradient Method. ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Obligatory Density Gradient Validation Slide m h *N dim = 0.48 Density Gradient (Prophet) vs. Schrödinger-Poisson (Schred) 4 2 1.0 Prophet 1×10 13 Schred 3 1.5 0.8 ∆ V G [volts] t Si =7.5nm N holes [cm -2 ] 0.6 2 1 3 ) 19 /cm 0.4 5×10 12 t ox =1.5nm all curves : 1 0.5 0.2 2×10 12 hole concentration (10 t Si =5nm N holes =5×10 12 /cm 2 1×10 12 0.0 0 0 3 5 7 10 20 0 0.5 1 1.5 2 2.5 0 1 2 3 silicon thickness [nm] 2 2 5 hole centroid (t Si /2) [nm] 20 t Si =15nm t Si =10nm t Si [nm] 15 1.5 1.5 3 10 7.5 1 1 2 5 4 0.5 0.5 3 1 2.5 0 0 0 1 2 3 4 5 0 2 4 6 10 12 10 13 N holes (t Si /2) [cm -2 ] position from oxide interface (nm) ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Methodology Development Basis: µ APS proportional to inversion layer thickness. Challenge: defining and calculating “inversion layer thickness” in arbitrary structures is difficult. Observation: For planar “bulk” channel, inversion layer thickness is roughly proportional to mean distance from Si/SiO 2 . Planar “Bulk” Channel: Consider APS mobility proportional to distance from SiO 2 . 2 = 1/z 1 2 + 1/z 2 2 . FDSOI Channel: use 1/z eff Extension: treat arbitrary distribution of Si, SiO 2 . ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Bulk PFET Mobility Modeling variable N D , T=300K variable T, N D =7.8×10 17 /cm 3 200 200 2 effective hole mobility [cm 2 /volt-sec] 2 3 K 150 297K N D [cm -3 ] 343K 150 393K 120 443K 120 6 100 1 7 5.1×10 100 1 5 2.7×10 90 1 6 8.9×10 1 90 1.6×10 80 6.6×10 17 80 70 70 60 γ -based 60 E eff -based simulated: NF=3×10 10 /cm 2 50 50 2 3 5 7 10 20 30 50 2 3 5 7 10 20 30 50 Neff (10 11 /cm 2 ) Neff (10 11 /cm 2 ) ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
FDSOI PFET Mobility Model vs. Data Prophet: N F =3×10 11 /cm 3 from Ren et. al. 200 200 500Å effective hole mobility [cm 2 /volt-sec] 175Å 500Å 150 150 175Å 111Å 111Å 120 120 68Å 68Å 100 100 54Å 54Å 90 90 80 80 43Å 43Å 70 70 60 60 50 50 2 3 5 7 10 20 30 50 2 3 5 7 10 20 30 50 Ns (10 11 /cm 2 ) Ns (10 11 /cm 2 ) ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
Extension to Multiple Dimensions: Acoustic Phonon Scattering a heuristic approach ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
APS Mobility Determination Convert γ to an effective field: E γ = (q/ ε Si )(k γ γ ) 3 where here: k γ = 25.1 µ m 1/3 Heuristic approach: Use E γ in place of E eff in Agostinelli et al nonlocal µ eff (E eff ) APS term to yield a local APS µ field. Result: µ roughly proportional to 1/ γ, proportional to distance from SiO 2 . ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc ACORN Technologies Inc http://www.acorntech acorntech.com .com http://www.
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