Green’s Functions versus Density Matrices: Aspects of Free-Carrier Screening in Highly Excited Semiconductors

Abstract

The question of how to treat free-carrier screening in the description of highly nonequilibrium carrier plasmas is still widely disputed. To further inquire into this problem we compare different techniques to derive generalized Boltzmann Bloch equations (BBEs) for optically excited semiconductor systems which account for both the coherent and incoherent dynamics. Mostly such BBEs have been obtained either within the framework of non-equilibrium Green’s functions (NEGFs) or by using the density matrix approach (DMA). A loose end of the latter approach has been the lack of a consistent way to treat free-carrier screening, and the conventional procedure has been to replace the bare Coulomb potential in the basic Hamiltonian by an appropriately screened one. We show that from the equation of motion (EoM) for the two-particle NEG F one can derive a simple prescription of how to treat free-carrier screening within the DMA. As an example we obtain the semiconductor Bloch equations for a homogeneous bulk semiconductor and we show that the ad-hoc implementation of screening within the DMA introduces errors.