Non-Equilibrium Green's Functions (NEGF) are mathematical tools used to study quantum transport in mesoscopic and nanoscale systems. They provide a powerful framework to analyze how quantum particles, such as electrons, propagate through a system that is not in thermal equilibrium. This is particularly important in the context of nanotechnology where devices often operate far from equilibrium conditions.
As device dimensions shrink into the nanometer scale, classical methods of analyzing transport phenomena become inadequate. Quantum effects, such as tunneling and interference, become significant. NEGF allows for a rigorous quantum mechanical treatment of transport properties, providing insights into the behavior of electrons in nanoscale materials and devices. This understanding is crucial for designing and optimizing next-generation electronic components, such as transistors and sensors.
NEGF is based on the concept of Green's functions, which describe the response of a system to an external perturbation. In the context of quantum transport, Green's functions are used to describe the propagation of electrons through a device. The NEGF formalism involves solving a set of coupled integral equations that relate the Green's functions to the system's Hamiltonian and the self-energies representing interactions with contacts or other environments.
The main components of the NEGF formalism include:
1. Retarded Green's Function (Gr): Describes the propagation of an electron from one point to another within the system. 2. Advanced Green's Function (Ga): The Hermitian conjugate of the retarded Green's function, describing the time-reversed process. 3. Lesser Green's Function (G
