Quantum-kinetic Theory of Defect-mediated Recombination in Nanostructure-based Photovoltaic Devices

In this paper, a quantum-kinetic equivalent of Shockley-Read-Hall recombination is derived within the non-equilibrium Green's function formalism for a photovoltaic system with selectively contacted extended-state absorbers and a localized deep defect state in the energy gap. The novel approach is tested on a homogeneous bulk absorber and then applied to a thin film photo-diode with large built-in field in the defect-rich absorber region. While the quantum-kinetic treatment reproduces the semi-classical characteristics for a bulk absorber in quasi-equilibrium conditions, for which the latter picture is valid, it reveals in the thin film case non-classical characteristics of recombination enhanced by tunneling into field-induced sub-gap states. INTRODUCTION Many novel concepts for high-efficiency photovoltaic devices rely on the utilization of the tunable optoelectronic properties of semiconductor nanostructures such as quantum wells, wires and dots. A consistent description of the fundamental physical mechanisms underlying the photovoltaic device operation, i.e., charge carrier photogeneration and extraction, needs to consider the local modification of the density of states, wave functions and associated interand subband rates, as well as the non-local transport processes, i.e., tunneling contributions, induced by the nanostructure components. An adequate approach can be found on the level of a quantum-kinetic theory, and has been developed recently, based on the non-equilibrium Green's function formalism (NEGF) [1]. However, so far, the theory was constrained to the radiative limit. In this paper, the framework is extended to cover defect-mediated non-radiative interband transitions, providing a quantum-kinetic equivalent to the standard semi-classical picture introduced by Shockley and Read [2] and by Hall [3] (SRH), and discussed in standard textbooks on recombination in semiconductors [4]. Starting from the general expression for the interband rate in the NEGF formalism [5], the latter is used to describe defect-mediated transitions by formulating the respective scattering self-energy terms that couple extended band states to localized defect states. The semi-classical limit of the theory is verified with a simple two-band quasi-0D model of a bulk absorber with carrier selective contacts, while a two-band quasi-1D model with spatial resolution is used to investigate the deviations from the semi-classical picture for strong built-in fields. THEORY In the general theory of interband transitions within the NEGF framework, the (local) interband rate for scattering from (to) a band state c to (from) state b is formulated in terms of the associated scattering self-energies and Green's functions for initial and final states of the scattering process as follows: