Numerical Boltzmann/Spherical Harmonic Device CAD Overview and Goals

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Numerical Boltzmann/Spherical Harmonic Device CAD
Overview and Goals
Overview Further develop and apply the
Numerical Boltzmann/Spherical Harmonic method of
advanced device simulation. The method is based
on the direct solution to the Boltzmann equation.
It promises to be applicable at and below the
0.1µm range, where drift-diffusion models become
inaccurate. It gives virtually the same
information as Monte Carlo simulations (device
distribution function) and is 1000 times
faster. Goals Develop and apply new simulator
to model deep submicron behavior - Terminal
characteristics (I-V) - Substrate current
(impact ionization) - Oxide injection, gate
leakage current and FLASH programming - Quantum
effects
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Numerical Boltzmann/Spherical Harmonic Device CAD
Benefit to Intel
1) The semiconductor community recognized the
benefit of the Numerical Boltzmann model by
including it in the 1997 SIA Roadmap as one four
approaches to be pursued for future device
design. 2) Since Numerical Boltzmann/Spherical
Harmonic is based on fundamental transport
physics, it should be reliable for design of
ultra-small transistors (lt0.15µm), where the
drift-diffusion model becomes less and less
accurate. 3) Gives virtually a complete device
description (like Monte Carlo), and is practical
enough for day-to-day design. Applied to short
channel and hot-electron effects velocity
overshoot, impact ionization, oxide tunneling,
thermal emission. 4) The model will be useful
for predicting the limits of MOSFET scaling,
especially related to oxide thicknesses,
reliability and optimized doping, as well as
future devices (SOI, double gate MOSFETs, etc.).
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Numerical Boltzmann/Spherical Harmonic Device CAD
Scheduled Deliverables First Year (98-99)
All deliverables for first year were
achieved. 1) Benchmark Boltzmann solver for deep
submicron MOSFET Achieved 2) Deliver and
install Boltzmann solver at Intel
Achieved 3) Improve energy space discretization
for better convergence Achieved 4)
Benchmark to determine need for higher order
spherical Achieved harmonics 5)
Develop thin oxide gate leakage current model
Achieved
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Numerical Boltzmann/Spherical Harmonic Device
CADScheduled Deliverables 2nd Year (1999-2000)
1) Incorporate quantum mechanical effects. Two
Approaches a) Boltzmann/Wigner
method, Stage 1
Achieved b) Schrodinger, Stage 1

Achieved 2) Develop transient and
frequency domain capabilities
Achieved 3) Adapt and apply Numerical Boltzmann
to SOI devices. Achieved 4) Develop
thin oxide degradation model based on electron
In Progress and hole transport 5)
Develop Numerical Boltzmann simulator for PMOS
Achieved
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Numerical Boltzmann/Spherical Harmonic Device
CADScheduled Deliverables 3nd Year (2000-2001)
1) Continue incorporation of quantum mechanical
effects. a) Using Boltzmann/Wigner method.
Achieved b) Using
Boltzmann/Schrodinger method
Achieved 2) Continue to apply to
devices with geometries of 0.1 µm and
Achieved below, with focus on thin
oxides. 3) Improve user friendliness so
Numerical Boltzmann can be Achieved
easily transported into Intels TCAD platform,
especially with respect to Suprem. 4)
Explore boundary conditions at source and drain
In progress 5) Apply to futuristic
nonconventional devices In progress

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Numerical Boltzmann/Spherical Harmonic Device CAD
Doping Profile After Interpolation
Flow Chart
Start
Input from SUPREM
Sort Data
Interpolate to Rectangular Grid
Doping Profile after DD Simulation
Smoothen Doping Profile
Simulator
END
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Device Structure and Distribution
Function
Electron Concentration
MOS Cross Section
Distribution Function
Y0.0001mm
Y0.4mm
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Benchmark I-V with Experiment
Doping Profile
Leff 0.88mm
Leff 0.35mm
Leff 0.15mm
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Impact Ionization and Substrate Current
Agreement with experiment No fitting parameters!
Generation Rate
Leff 0.88mm
Leff 0.35mm
Leff 0.15mm
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Device Structure and I-V Characteristics
Device Structure
Doping Profile
I-V Characteristics Leff0.08mm
G0 Curves, Vds0.05 V
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Gate Tunneling and Thermal Emission
Current
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Lm50nm NMOSFET
Device Structure
Doping Profile
Distribution Function
Y0.0003 µm
Y0.1 µm
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Lm50nm NMOSFET
Electron Concentration
I-V Characteristics
G0 Curve
Substrate Current
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Lm50nm PMOSFET
Device Structure
Doping Profile
Distribution Function
Y0.0003 µm
Y0.1 µm
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results Lm50nm PMOSFET
I-V Characteristics
Hole Concentration
G0 Curve
Substrate Current
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Numerical Boltzmann/Spherical Harmonic Device CAD
Results SOI
Fully Depleted SOI Structure
Electron Distribution Function
Electron Energy
Impact Ionization Rate
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Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects Boltzmann/Wigner Results
Doping profile
Quantum Dist. Ftn.
Carrier Con. Ratio Clas/QM
IV Comparison
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Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects Schrodinger Results
..
Potential of QM System
Flow Chart
Carrier Comparison
Wave Functions
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Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects Schrodinger Results
..
Flow Chart
Band Diagram
Dispersion Relation of QM Well
Quantum Domain
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Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects Schrodinger Results
..
Electron Distribution Function
Electron Concentration
Effective and Classical Potential
2-D Electron Concentration
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Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects Schrodinger Results
..
Subthreshold Characteristics
I-V Charactistics
Current Vector(SHBTE)
Current Vector(QM-SHBTE)
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Numerical Boltzmann/Spherical Harmonic Device CAD
Direct Tunneling Gate Currents
..
Device Structure
Band Diagram
Wavefunction with lower energy
Wavefunction with higher energy
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Numerical Boltzmann/Spherical Harmonic Device CAD
Direct Tunneling Gate Currents
..
Ig vs. Vg at Vd1.0 V
Ig vs. Vg at Vd0.05 V
Distribution Function at Low Drain Bias
Distribution Function at Hign Drain Bias
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Numerical Boltzmann/Spherical Harmonic Device CAD
Summary
1)The Numerical Boltzmann/Spherical Harmonic
device simulation tool has been has been designed
and developed into a state of the art TCAD
simulator. 2) Since Numerical Boltzmann/Spherical
Harmonic is based on fundamental transport
physics, it is especially useful for design of
ultra-small transistors (lt0.10µm), where the
drift-diffusion model becomes less and less
accurate. 3) Gives virtually a complete device
description (like Monte Carlo), and is practical
enough for day-to-day design. Applied to short
channel and hot-electron effects velocity
overshoot, impact ionization, oxide tunneling,
thermal emission and quantum confinement. 4)The
Numerical Boltzmann/Spherical Harmonic simulator
has been transferred to Intel. It is compatible
with Suprem doping and should be ready for
incorporation into Intels TCAD platform.