Transcript Numerical Boltzmann/Spherical Harmonic Device Modeling

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
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
(<0.15µm), 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.).
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
harmonics:
Achieved
5) Develop thin oxide gate leakage current model:
Achieved
Numerical Boltzmann/Spherical Harmonic Device CAD
Scheduled Deliverables: 2nd Year (1999-2000)
1) Incorporate quantum mechanical effects. Two Approaches:
a) Boltzmann/Wigner method, Stage 1:
b) Schrodinger, Stage 1:
Achieved
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
and hole transport:
In Progress
5) Develop Numerical Boltzmann simulator for PMOS:
Achieved
Numerical Boltzmann/Spherical Harmonic Device CAD
Scheduled Deliverables: 3nd Year (2000-2001)
1) Continue incorporation of quantum mechanical effects.
a) Using Boltzmann/Wigner method.
b) Using Boltzmann/Schrodinger method
Achieved
Achieved
2) Continue to apply to devices with geometries of 0.1 µm and
below, with focus on thin oxides.
Achieved
3) Improve user friendliness so Numerical Boltzmann can be
easily transported into Intel’s TCAD platform, especially
with respect to Suprem.
Achieved
4) Explore boundary conditions at source and drain
In progress
5) Apply to futuristic nonconventional devices
In progress
Numerical Boltzmann/Spherical Harmonic Device CAD
Flow Chart
Doping Profile After Interpolation
Start
Input from SUPREM
Sort Data
Interpolate to Rectangular Grid
Smoothen Doping Profile
Simulator
END
Doping Profile after DD Simulation
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Device Structure and Distribution Function
Electron Concentration
MOS Cross Section
Distribution Function
Y=0.0001mm
Y=0.4mm
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Benchmark I-V with Experiment
Doping Profile
Leff = 0.35mm
Leff = 0.88mm
Leff = 0.15mm
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Impact Ionization and Substrate Current
Agreement with experiment: No fitting parameters!
Generation Rate
Leff = 0.35mm
Leff = 0.88mm
Leff = 0.15mm
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Device Structure and I-V Characteristics
Device Structure
I-V Characteristics Leff=0.08mm
Doping Profile
G0 Curves, Vds=0.05 V
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Gate Tunneling and Thermal Emission Current
Ig vs Vg, Vd
Ig vs Vg, Vd
tox=25Å
tox=25Å
Source
Drain
Oxide Thickness(Å)
Ig vs Position and Energy
Ig vs Oxide Thickness
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Lm=50nm NMOSFET
Device Structure
Doping Profile
Distribution Function
Y=0.0003 µm
Y=0.1 µm
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Lm=50nm NMOSFET
Electron Concentration
I-V Characteristics
G0 Curve
Substrate Current
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Lm=50nm PMOSFET
Device Structure
Doping Profile
Distribution Function
Y=0.0003 µm
Y=0.1 µm
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: Lm=50nm PMOSFET
Hole Concentration
I-V Characteristics
G0 Curve
Substrate Current
Numerical Boltzmann/Spherical Harmonic Device CAD
Results: SOI
Fully Depleted SOI Structure
Electron Energy
Electron Distribution Function
Impact Ionization Rate
Numerical Boltzmann/Spherical Harmonic Device CAD
Quantum Effects: Boltzmann/Wigner Results
Doping profile
Carrier Con. Ratio: Clas/QM
Quantum Dist. Ftn.
I~V Comparison
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Quantum Effects: Schrodinger Results
Flow Chart
Potential of QM System
Wave Functions
Carrier Comparison
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Quantum Effects: Schrodinger Results
Band Diagram
Quantum Domain
Flow Chart
Dispersion Relation of QM Well
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Quantum Effects: Schrodinger Results
Electron Distribution Function
2-D Electron Concentration
Electron Concentration
Effective and Classical Potential
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Quantum Effects: Schrodinger Results
Subthreshold Characteristics
Current Vector(SHBTE)
I-V Charactistics
Current Vector(QM-SHBTE)
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Direct Tunneling Gate Currents
Band Diagram
Device Structure
Wavefunction with lower energy
Wavefunction with higher energy
Numerical Boltzmann/Spherical Harmonic Device CAD
..
Direct Tunneling Gate Currents
Ig vs. Vg at Vd=0.05 V
Ig vs. Vg at Vd=1.0 V
Distribution Function at Low Drain Bias Distribution Function at Hign Drain Bias
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
(<0.10µm), 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 Intel’s TCAD platform.