MOS-AK ESSCIRC Leuven (Belgium) 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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Outline Introduction Introduction Simulation Strategy Simulation Strategy Summary Summary Introduction

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Scaling into mesoscopic regime Scaling into mesoscopic regime –Increasing influence of qm-effects –Changing of device behavior Question: Question: –Validity of device models –Influence in classical circuits

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Quantum Interference Classical Circuit Includingqm-Effects

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Outline Introduction Introduction Simulation Strategy Simulation Strategy Summary Summary

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 QM-Effects in MOS Devices Tunneling currents Tunneling currents Charge quantization Charge quantization

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 MOSFET MOSFET –Tunneling Currents (channel – gate, edge direct tunneling) –Charge quantization MOS Capacitor MOS Capacitor –Channel – gate tunneling –Charge quantization

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Quantum-mechanical Modeling and Numerical Simulation Quantum mechanical descriptions Quantum mechanical descriptions –Transmission formalism –Scattering matrix –Non-equilibrium Green‘s function formalism (NEGF)

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Selfconsistent potential Tunneling current

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

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

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Circuit Simulation (Choi et al, Transaction on Electron Devices ´01)

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 V out V in

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Clock Va Vb Vx Vout

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 (Nii et al, IEEE Journal of Solid States ´04)

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Leakage Currents I off IgIg

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Outline Introduction Introduction Simulation Strategy Simulation Strategy Summary Summary

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Summary Numerical simulation Numerical simulation Spice models Spice models Circuit simulation Circuit simulation Circuit functionality – quantum effects Circuit functionality – quantum effects

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Classical description Classical description –Drift-Diffusion –Hydrodynamic transport equation –Boltzmann transport equation Semi-classical description (QM-corrections) Semi-classical description (QM-corrections) –Density Gradient –Quantum hydrodynamic equation

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Poisson equation Schrödinger equation Electron density n Potential U

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 Schrödinger equation Schrödinger equation Density matrix Density matrix Electron density Electron density Poisson equation Poisson equation

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

Felgenhauer Uni Hannover MOS-AK ESSCIRC 2004 QM transport process Integral values I,U I,U Circuit modeling Physical Layer