Numerical Boltzmann/Spherical Harmonic Device CAD Overview and Goals Overview: Further develop and apply the Numerical Boltzmann/Spherical Harmonic method.

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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

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 Achieved harmonics: 5) Develop thin oxide gate leakage current model: Achieved

Numerical Boltzmann/Spherical Harmonic Device CAD Scheduled Deliverables: 2nd Year ( ) 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

Numerical Boltzmann/Spherical Harmonic Device CAD Scheduled Deliverables: 3nd Year ( ) 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 Intel’s 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

Start Input from SUPREM Sort Data Interpolate to Rectangular Grid Smoothen Doping Profile Simulator END Flow Chart Doping Profile After Interpolation Doping Profile after DD Simulation Numerical Boltzmann/Spherical Harmonic Device CAD

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Device Structure and Distribution Function Y=  mY=0.4  m Distribution Function Electron Concentration MOS Cross Section

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Benchmark I-V with Experiment Doping Profile Leff = 0.88  m Leff = 0.35  m Leff = 0.15  m

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Impact Ionization and Substrate Current Generation Rate Agreement with experiment: No fitting parameters! Leff = 0.88  m Leff = 0.35  m Leff = 0.15  m

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Device Structure and I-V Characteristics Device Structure I-V Characteristics L eff =0.  m Doping Profile G0 Curves, V ds =0.05 V

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Gate Tunneling and Thermal Emission Current I g vs V g, V d Oxide Thickness(Å) t ox =25Å I g vs Oxide Thickness I g vs V g, V d Position along Gate(  m) Source Drain Gate Current Density log(Ig)(A/  m  eV) Energy(eV) t ox =25Å I g vs Position and Energy

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm NMOSFET Device StructureDoping Profile Distribution Function Y= µmY=0.1 µm

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm NMOSFET Electron Concentration I-V Characteristics G0 CurveSubstrate Current

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm PMOSFET Device StructureDoping Profile Distribution Function Y= µmY=0.1 µm

Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm PMOSFET Hole Concentration I-V Characteristics G0 CurveSubstrate Current

Numerical Boltzmann/Spherical Harmonic Device CAD Results: SOI Fully Depleted SOI StructureElectron Distribution Function Electron EnergyImpact Ionization Rate

Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Boltzmann/Wigner Results Doping profile Quantum Dist. Ftn. Carrier Con. Ratio: Clas/QMI~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 Flow Chart Quantum Domain Dispersion Relation of QM Well..

Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Schrodinger Results Electron Distribution FunctionElectron Concentration 2-D Electron Concentration Effective and Classical Potential..

Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Schrodinger Results I-V Charactistics Current Vector(SHBTE)Current Vector(QM-SHBTE).. Subthreshold Characteristics

Numerical Boltzmann/Spherical Harmonic Device CAD Direct Tunneling Gate Currents Device Structure Wavefunction with lower energyWavefunction with higher energy.. Band Diagram

Numerical Boltzmann/Spherical Harmonic Device CAD Direct Tunneling Gate Currents Ig vs. Vg at Vd=1.0 V Distribution Function at Low Drain BiasDistribution Function at Hign Drain Bias.. Ig vs. Vg at Vd=0.05 V

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.