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On the Analysis of Parasitic Quantum Effects in Classical MOS Circuits

On the Analysis of Parasitic Quantum Effects in Classical MOS Circuits. Frank Felgenhauer , Simon Fabel, Wolfgang Mathis Institute of Electromagnetic Theory and Microwave Technique University of Hannover, Germany. Outline. Introduction Simulation Strategy Summary. Introduction.

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On the Analysis of Parasitic Quantum Effects in Classical MOS Circuits

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  1. On the Analysis of Parasitic QuantumEffects in Classical MOS Circuits Frank Felgenhauer, Simon Fabel, Wolfgang Mathis Institute of Electromagnetic Theory and Microwave TechniqueUniversity of Hannover, Germany

  2. Outline • Introduction • Simulation Strategy • Summary Introduction MOS-AK ESSCIRC 2004

  3. Introduction • Exponential increase in gate leakage • increased power consumption • degraded device performance • Charge carrier quantization in the channel • loss of inversion charge • loss of transconductance • Polysilicon-gate depletion effects MOS-AK ESSCIRC 2004

  4. Scaling into mesoscopic regime • Increasing influence of qm-effects • Changing of device behavior • Question: • Validity of device models • Influence in classical circuits MOS-AK ESSCIRC 2004

  5. Including qm-Effects Quantum Interference Classical Circuit MOS-AK ESSCIRC 2004

  6. Outline • Introduction • Simulation Strategy • Summary MOS-AK ESSCIRC 2004

  7. Simulation Strategy Qm-Effects in MOS devices Qm-Effects in MOS devices Quantum-mechanical modeling and numerical simulation Spice circuit models Circuit Simulation MOS-AK ESSCIRC 2004

  8. QM-Effects in MOS Devices • Tunneling currents • Charge quantization MOS-AK ESSCIRC 2004

  9. MOSFET • Tunneling Currents (channel – gate, edge direct tunneling) • Charge quantization • MOS Capacitor • Channel – gate tunneling • Charge quantization MOS-AK ESSCIRC 2004

  10. Simulation Strategy Qm-Effects in MOS devices Quantum-mechanical modeling and numerical simulation Spice circuit models Circuit Simulation MOS-AK ESSCIRC 2004

  11. Quantum-mechanical Modelingand Numerical Simulation • Quantum mechanical descriptions • Transmission formalism • Scattering matrix • Non-equilibrium Green‘s function formalism (NEGF) MOS-AK ESSCIRC 2004

  12. Non-equilibrium, open boundary conditions • 1-d MOS-structure • Time invariant system • Spatial dependent effective mass and permittivity • Scattering • Poisson self-consistency MOS-AK ESSCIRC 2004

  13. Tunneling current Selfconsistent potential MOS-AK ESSCIRC 2004

  14. Simulation Strategy Qm-Effects in MOS devices Quantum-mechanical modeling and numerical simulation Spice circuit models Circuit Simulation MOS-AK ESSCIRC 2004

  15. Spice Circuit Models • 1-d qm simulation • look-up table model • non-linear elements (black box) • non-linear current source  tunneling • non-linear capacitor  MOS C-V, charge quantization MOS-AK ESSCIRC 2004

  16. Simulation Strategy Parasitic effect identification Quantum-mechanical modeling and numerical simulation Spice circuit model Circuit Simulation MOS-AK ESSCIRC 2004

  17. Circuit Simulation (Choi et al, Transaction on Electron Devices ´01) MOS-AK ESSCIRC 2004

  18. Vout Vin MOS-AK ESSCIRC 2004

  19. Vx Clock Vout Va Vb (Choi et al, Transaction on Electron Devices ´01) MOS-AK ESSCIRC 2004

  20. Clock Va Vb Vx Vout MOS-AK ESSCIRC 2004

  21. (Nii et al, IEEE Journal of Solid States ´04) MOS-AK ESSCIRC 2004

  22. Leakage Currents Ig Ioff MOS-AK ESSCIRC 2004

  23. Outline • Introduction • Simulation Strategy • Summary MOS-AK ESSCIRC 2004

  24. Summary • Numerical simulation • Spice models • Circuit simulation • Circuit functionality – quantum effects MOS-AK ESSCIRC 2004

  25. MOS-AK ESSCIRC 2004

  26. Classical description • Drift-Diffusion • Hydrodynamic transport equation • Boltzmann transport equation • Semi-classical description (QM-corrections) • Density Gradient • Quantum hydrodynamic equation MOS-AK ESSCIRC 2004

  27. Poisson equation Electron density n Potential U Schrödinger equation MOS-AK ESSCIRC 2004

  28. Schrödinger equation • Density matrix • Electron density • Poisson equation MOS-AK ESSCIRC 2004

  29. Impact in Circuits • Static CMOS • Off-state power dissipation • Dynamic CMOS • Off-state power dissipation • Discharge breakdown, parasitic currents • Analog – mixed Signal • Discharge breakdown, parasitic currents • Magnitude variation MOS-AK ESSCIRC 2004

  30. Integral values I,U Integral values I,U QM transport process Circuit modeling Circuit modeling Physical Layer MOS-AK ESSCIRC 2004

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