Numerical Boltzmann/Spherical Harmonic Device CAD Overview and Goals

1. 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

2. 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.).

3. 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

4. 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

5. 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 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

6. 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

7. 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

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

9. 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

10. Numerical Boltzmann/Spherical Harmonic Device CAD Results: Device Structure and I-V Characteristics Device Structure Doping Profile I-V Characteristics Leff=0.08mm G0 Curves, Vds=0.05 V

11. Ig vs Vg, Vd Ig vs Vg, Vd tox=25Å Gate Current Density log(Ig)(A/meV) tox=25Å Drain Source Energy(eV) Oxide Thickness(Å) Position along Gate(m) Ig vs Position and Energy Ig vs Oxide Thickness Numerical Boltzmann/Spherical Harmonic Device CAD Results: Gate Tunneling and Thermal Emission Current

12. Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm NMOSFET DeviceStructure DopingProfile DistributionFunction Y=0.0003 µm Y=0.1 µm

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

14. Numerical Boltzmann/Spherical Harmonic Device CAD Results: Lm=50nm PMOSFET DeviceStructure DopingProfile DistributionFunction Y=0.0003 µm Y=0.1 µm

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

16. Numerical Boltzmann/Spherical Harmonic Device CAD Results: SOI Fully Depleted SOI Structure Electron Distribution Function Electron Energy Impact Ionization Rate

17. Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Boltzmann/Wigner Results Doping profile Quantum Dist. Ftn. Carrier Con. Ratio: Clas/QM I~V Comparison

18. Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Schrodinger Results .. Potential of QM System Flow Chart Carrier Comparison Wave Functions

19. Numerical Boltzmann/Spherical Harmonic Device CAD Quantum Effects: Schrodinger Results .. Flow Chart Band Diagram Dispersion Relation of QM Well Quantum Domain

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

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

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

23. 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

24. 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.