# Simulation of Quantum Well Solar Cells with Non-Equilibrium Green's Functions

A number of the concepts for 3^{rd}-generation ultra-high efficiency solar cells are based on quantum effects in semiconductor nanostructures such as quantum wells, wires or points. In order to examine the optical and electronic properties of such structures, particularly in solar cells, a microscopic theory is required which is able to describe both the optical and also the transport characteristics of an open, interacting non-equilibrium system dominated by quantum effects. The non-equilibrium Green's function formalized theory in an atomistic basis – e.g. empirical tight binding – is a method that fulfils the requirements mentioned above and has already been used successfully to describe similar quantum-optoelectronic components such as quantum cascade lasers or infrared photodetectors.

In concrete terms, Dyson's equation for the retarded Green's function and Keldysh's equation for the electron-hole correlation functions are solved self-consistently with the equations for the self-energy of the perturbatively treated interactions between charge carriers with lattice vibrations (phonons) and light quanta (photons). In a second self-consistency loop, Poisson's equation is solved to determine the electric potential from the charge carrier densities calculated with Green's equations and the density of the dopants.

In addition to macroscopic variables such as charge carrier densities and currents, spectral microscopic characteristics can also be determined, e.g. the local density of states, the occupancy of quantized states and the spectrum of the photocurrent.