Multiscale modeling of solar cells with interface phenomena

Abstract

We describe a mathematical model for heterojunctions in semiconductors which can be used, e.g., for modeling higher efficiency solar cells. The continuum model involves well-known drift-diffusion equations posed away from the interface. These are coupled with interface conditions with a nonhomogeneous jump for the potential, and Robin-like interface conditions for carrier transport. The interface conditions arise from approximating the interface region by a lower-dimensional manifold. The data for the interface conditions are calculated by a Density Functional Theory (DFT) model over a few atomic layers comprising the interface region. We propose a domain decomposition method (DDM) approach to decouple the continuum model on subdomains which is implemented in every step of the Gummel iteration. We show results for CIGS/CdS, Si/ZnS, and Si/GaAs heterojunctions.

Coupled optoelectronic simulation and optimization of thin-film photovoltaic solar cells

“…When there is a jump in either χ(z) or E g (z) or both, and thus in φ n (z) or φ p (z), then n(z) and p(z) may also have jumps. A heterojunction is formed at the discontinuity [36]. A commonly used way to model this discontinuity requires the assumption of continuous quasi-Fermi levels, whereas another commonly used way requires consideration of thermionic emission at the discontinuity [37].…”

Multiscale modeling of silicon heterojunction solar cells

“…In a multiscale formulation, the focus is on unifying models selfconsistently to facilitate a comprehensive and quantitative analysis of the problem. Recently, the multiscale methodology has been applied to address various issues in solar cells such as mechanical properties of materials [98], optical properties [99] and interface phenomena [100]. Using the principle of coupling macroscopic and microscopic models, the multiscale methodology has been used to study the effect of complex interface morphologies and bulk mechanisms in organic solar cells [101].…”

Domain Decomposition for Heterojunction Problems in Semiconductors

“…In (1)-(3) we use data: the net doping profile N T , a given expression for the electron-hole pair generation and recombination R, electrical permittivity , and electron and hole diffusivities D n , D p . Also, η is another scaling parameter [7]. The model (1)-(3) is completed with external boundary conditions; we impose Dirichlet conditions for the potential and recombination-velocity (Robin type) conditions for electron and hole densities.…”

“…The density sought in DFT is a function in R 3 , while the Schrödinger equation is solved for Ψ ∈ C 3N . Finding n is possible via application of the Right bottom: smoothed local pseudopotential from the DFT calculation (black), and valence band jump construction (red), which determines a n i , a p i , and ψ [7] theory of Hohenberg and Kohn to a minimization problem in n, and is equivalent to the solution of the Schrödinger equation for the ground state. However, an energy functional F [n] needed in the minimization principle in DFT is unknown, and DFT requires approximations to F [n].…”

“…The DDM approach we propose is non-standard because of the nonhomogeneous jumps arising from TEM. In [7] we presented the DDP algorithm for the potential equation. In this paper we report on the next nontrivial step which involves carrier transport equations.…”