OP: COLLABORATIVE RESEARCH: Integrated Simulation of Non-homogeneous Thin-film Photovoltaic Devices

Solar cells are desirable as energy sources that neither use fossil fuels nor produce greenhouse gases. They must be designed to efficiently absorb sunlight and convert it to electricity. The solar cell needs to be sufficiently thick to absorb light across the solar spectrum. To reduce this thickness, and so reduce manufacturing cost, several layers of materials are used: first, to help light penetrate the solar cell, and then to trap it inside. Some of these layers are semiconductors in which electricity is generated, while others (for example, a periodically corrugated metallic back layer) may help absorption by trapping light near their surface. However, the amount of electricity generated by a solar cell does not just depend on absorption, but also on the transport of electrons within the layers of the solar cell. If the density of electrons decreases during transport, thereby trumping any gain in sunlight absorption, then a chosen light-management strategy will not be fruitful. The project team will develop an integrated pair of computer models that simultaneously predict the absorption of sunlight and the consequent electrical performance of the solar cell using modern techniques from numerical analysis. The codes will extend current simulation technology to allow for semiconductor layers with properties that vary from place to place and allow fully three-dimensional models of the device. Using their codes, the PIs will optimize device designs for best electricity generation. Definitive predictions will be provided about thin-film photovoltaic solar cells, thereby providing significant progress towards inexpensive and sustainable production of electricity. These codes will be made available to other photovoltaic researchers.

The overall model of the thin-film photovoltaic solar cell will have a photonic submodel and an electrical submodel. In the photonic model, the quasi-periodic Maxwell's equations will be solved using edge finite elements. To improve flexibility, the PIs will analyze and implement a non-standard mortaring technique to take care of quasi-periodicity. Compatible electrical models will be analyzed and implemented using the Hybridizable Discontinuous Galerkin (HDG) method on hexahedral elements for the non-linear convection and diffusion problem governing drift and diffusion of electrical charge carriers. The HDG scheme will require a novel analysis to understand this non-linear convection-diffusion problem. Stability and convergence will be explored first for linear convection-diffusion problems, and the methodology will then be extended to an implicit-explicit time-stepping scheme for the drift-diffusion system. Besides a full 3D model, the PIs will develop a 2D model assuming translation invariance of the photovoltaic device in one transverse direction. The second step of the proposed research is to use the new simulation capability to design optimal nonhomogeneous thin-film photovoltaic solar cells via the Differential Evolution Algorithm. This will optimize for maximal photovoltaic electricity-generation efficiency. Additionally, domain and coefficient derivatives will be characterized and implemented to allow the computation of sensitivities and the use of gradient-based optimization. Detailed photonic-and-electrical modeling with doubly periodic back-reflectors and non-homogeneous light-absorbing layers will permit a major expansion of solar-cell design methodologies, besides yielding optimal designs for maximal photovoltaic electricity-generation efficiency.