Non-Equilibrium Green's Function

Non-Equilibrium Green's Function (NEGF) is the fully quantum mechanical simulation formalism for carrier transport in nanoscale devices — capturing wave interference, tunneling, quantization, and coherent transport that semiclassical models cannot describe, making it essential for sub-5nm transistor and molecular device simulation.

What Is NEGF?

• Definition: A quantum field theory formalism that calculates the steady-state current through a nanoscale device by computing the single-particle Green's function of the open quantum system coupled to macroscopic contacts.
• Device Hamiltonian: The device region is represented by a tight-binding or DFT-derived Hamiltonian describing atomic-scale electronic structure.
• Self-Energy Matrices: The influence of macroscopic source and drain contacts is captured by self-energy matrices that inject and absorb carriers at all energies, representing the contacts as infinite reservoirs.
• Transmission Coefficient: The central output is T(E), the energy-resolved transmission probability for an electron to pass from source to drain, from which current is computed by integrating over the Fermi-window.

Why NEGF Matters

• Source-to-Drain Tunneling: NEGF naturally handles tunneling through the gate barrier in sub-5nm channel lengths — a leakage mechanism that limits how short transistors can be made and that semiclassical models completely miss.
• Quantum Confinement: Energy level quantization in nanowires and two-dimensional channels is captured self-consistently with the electrostatics, correctly predicting threshold voltage and subthreshold slope.
• Ballistic Transport: NEGF provides the rigorous quantum-mechanical description of ballistic current, including quantum contact resistance and mode quantization effects.
• 2D Materials: For graphene, MoS2, and other atomically thin channel materials, NEGF is the only simulation framework with the resolution to capture the relevant physics.
• Beyond-CMOS Devices: Tunnel FETs, single-electron transistors, and molecular junctions require NEGF for any quantitative analysis.

How It Is Used in Practice

• Atomistic TCAD: Tools such as Quantumwise ATK (now Synopsys QuantumATK) and NanoTCAD ViDES implement NEGF with DFT band structures for atomic-resolution device simulation.
• Calibration of Compact Models: NEGF results for short-channel transistors inform the tunneling and quantization corrections incorporated in industry compact models.
• Research Applications: Novel channel materials, gate stack designs, and beyond-CMOS concepts are evaluated at the atomic scale before fabrication using NEGF simulation.

Non-Equilibrium Green's Function is the quantum mechanical microscope for nanoscale transistor physics — when device dimensions fall below 5nm, NEGF is the only simulation approach that correctly captures tunneling, quantization, and coherent transport simultaneously.