Quantum Device Simulation 30A MOS CV Curve Quantum Currents and - PowerPoint PPT Presentation

Quantum Device Simulation 30A MOS CV Curve – Quantum Currents – and PHEMTs

Introduction ß Why a Quantum Mechanical based simulator is necessary ß Introduction to QM issues and theory ß Implementation and syntax ß Practicalities of use ß Examples (MOS, PHEMT, Diode) Quantum Device Simulation - 2 -

Introduction (con’t) ß Why Use a QM simulator ß Reduction in device size => coherence length of electrons ß Thin gate oxides => CV shift ß Channel sheet carrier shift => MOS/HEMT ß Heterojunction tunneling ß Pulse doping ‘smear’ Quantum Device Simulation - 3 -

Quantum Issues ß Quantization “carrier confinement” ß 1D/2D/3D => Quantum Well/Wire/Dot ß Schrodinger's Equation h 2 h 2 d 2 d 2 - - + V(y) + V(y) z i (y) = (y) = E E i i z i (y) (y) z i z i 2m * * dx 2 2 2m dx ß Eigen Value Problem Quantum Device Simulation - 4 -

Quantum Issues (con’t) ß Results appear as a sequence of ß Eigen energies => Discrete energies where electrons may reside ß Eigen functions => Probability distribution of electrons along each slice ß Schrodinger -Poisson => Spacial distribution of electrons to replace classical one Quantum Device Simulation - 5 -

Quantum Issues (con’t) ß Transport ß Transmission, Deflection ß Concentration ß Quantum corrections to standard transport equations ß Provided by Quantum moments equation n 2 2 n 2 Ln 2 ∆ Ln(n) (n) Uq = - = - ∆ Uq * 8m 8m * ß Based on second moments of the Wigner distribution function ß Quantum Temperature => Quantum diffusion term ß Bohm Quantum Potential Quantum Device Simulation - 6 -

Implementation and Syntax ß Schrodinger-Poisson Solver ß models Schrodinger Eigens =15 ß Quantum Moments ß models quantum ß solve qx.damp=1.0 ß Bohm Quantum Potential ß BQP Quantum Device Simulation - 7 -

Electrostatic Potential, Classical and Quantum Electron Concentrations Figure 1. Quantum Device Simulation - 8 -

Eigen Wave Functions and Energy Levels Figure 2. Quantum Device Simulation - 9 -

MOS 30A Gate – CV Curve Figure 3. Quantum Device Simulation - 10 -

Figure 4. Quantum Device Simulation - 11 -

Classical and Quantum Electron Concentrations Figure 5. Quantum Device Simulation - 12 -

HDiode Figure 6. Quantum Device Simulation - 13 -

Classical and Quantum Electron Concentrations Figure 7. Quantum Device Simulation - 14 -

Classical and Quantum Currents Figure 8. Quantum Device Simulation - 15 -

PHEMT – Zero Bias Case Figure 9. Quantum Device Simulation - 16 -

PHMET Figure 10. Quantum Device Simulation - 17 -

Model Comparison Quantum Device Simulation - 18 -

Conclusion ß As a device dimenstions shrink, qunatum effects become more significant ß Schrodinger-Poisson solve provides calculations of bound state energies, carrier wave functions and carrier concentrations ß Quantum effects included in carrier transport by using quantum moments models Quantum Device Simulation - 19 -