Daniel Brinkman

Extracting Cu diffusion parameters in polycrystalline CdTe

It is well known that Cu plays an important role in CdTe solar cell performance as a dopant. In this work, a finite-difference method is developed and used to simulate Cu diffusion in CdTe solar cells. In the simulations, which are done on a two-dimensional (2D) domain, the CdTe is assumed to be polycrystal-line, with the individual grains separated by grain boundaries. When used to fit experimental Cu concentration data, bulk and grain boundary diffusion coefficients and activation energies for CdTe can be extracted. In the past, diffusion coefficients have been typically obtained by fitting data to simple functional forms of limited validity. By doing full simulations, the simplifying assumptions used in those analytical models are avoided and diffusion parameters can thus be determined more accurately.

Cu migration and its impact on the metastable behavior of CdTe solar cells

In this work we report on development of a 1D reaction-diffusion simulator of Cu kinetics in CdTe solar cells to investigate its role in the observed device performance changes. Evolution of intrinsic and Cu-related defects in CdTe solar cell has been studied in time-space domain self-consistently with free carrier transport. The simulation successfully predicts decelerating reductions of device performance for open-circuit stress and steadier reductions for short-circuit stress under elevated temperature, in agreement with experimental findings. The simulation results indicate that the movement of Cu interstitials could be responsible for such changes. Although 1D simulation has intrinsic limitations when applied to polycrystalline films, the results presented here imply that the 1D approach is still suitable in better understanding of the performance and metastabilities of CdTe photovoltaic device.

Self-consistent simulation of CdTe solar cells with active defects

We demonstrate a self-consistent numerical scheme for simulating an electronic device which contains active defects. As a specific case, we consider copper defects in cadmium telluride solar cells. The presence of copper has been shown experimentally to play a crucial role in predicting device performance. The primary source of this copper is migration away from the back contact during annealing, which likely occurs predominantly along grain boundaries. We introduce a mathematical scheme for simulating this effect in 2D and explain the numerical implementation of the system. Finally, we will give numerical results comparing our results to known 1D simulations to demonstrate the accuracy of the solver and then show results unique to the 2D case.

Numerical Simulation of Copper Migration in Single Crystal CdTe

Absorber material with high and stable p-type doping that does not impede free carrier lifetime is the key component enabling efficiency and stability improvements in thin-film CdTe technology. To better understand the compensation mechanism and the metastable effects related to Cu acceptors, the most common p-type dopant in CdTe, i.e., a detailed kinetic model describing the behavior of intrinsic and Cu-related defects in this material, has been developed and applied for the first time. Migration and reactions of these point defects in single crystal CdTe have been investigated by solving diffusion-reaction equations in the time-space domain self-consistently with free carrier transport. The simulation results supported by reasonable match to experimental data have shed light on the nature of limited Cu incorporation (also known as the Cu solubility limits) and Cu self-compensation during the annealing and cooling processes.

Simulating Cl diffusion in polycrystalline CdTe

Most theoretical treatments of grain boundary (GB) diffusion start with the model developed by Fisher over sixty years ago, where a bulk material with a low diffusion constant is bisected by a narrow slab with high diffusivity (the GB). For this system, Fisher derived two coupled differential equations, the second involving a first order derivative. While Fishers model can be applied to more general situations, it can be very cumbersome to implement in cases where the GBs are only piecewise linear and/or intersect at arbitrary angles. In this work, we develop an alternate model involving only second order derivatives that is more conducive to simulating arbitrary GB geometries, but yields results that are equivalent to those one would obtain from Fishers. We apply our model to the problem of Cl diffusion in CdTe, using it to obtain Cl concentration profile data that is similar to those obtained in recent experiments.

One-dimensional reaction-diffusion simulation of Cu migration in polycrystalline CdTe solar cells

In this work, we report on developing 1D reaction-diffusion solver to understand the kinetics of p-type doping formation in CdTe absorbers and to shine some light on underlying causes of metastabilities observed in CdTe PV devices. Evolution of intrinsic and Cu-related defects in CdTe solar cell has been studied in time-space domain self-consistently with free carrier transport and Poisson equation. Resulting device performance was simulated as a function of Cu diffusion anneal time showing pronounced effect the evolution of associated acceptor and donor states can cause on device characteristics. Although 1D simulation has intrinsic limitations when applied to poly-crystalline films, the results suggest strong potential of the approach in better understanding of the performance and metastabilities of CdTe photovoltaic device.

Using diffusion-reaction simulation to study the formation and self-compensation mechanism of Cu doping in CdTe

An improved model of copper p-type doping in CdTe absorbers is proposed that accounts for the mechanisms related to tightly bound Cu(i)-Cu(Cd) and Cd(i)-Cu(Cd) complexes that both limit diffusion and cause self-compensation of Cu species. The new model explains apparent discrepancy between DFT-calculated and fitted diffusion parameters of Cu reported in our previous work, and allows for better understanding of performance and metastabilities in CdTe PV devices.

Modeling and numerics for two partial differential equation systems arising from nanoscale physics

This work was supported in part by King Abdullah University of Science and Technology (KAUST) Award Number: KUK-I1-007-43.

A 2D diffusion-reaction CdTe solar cell simulator that includes active defects and grain boundaries

We have developed a 2D diffusion-reaction simulator suitable for modeling CdTe solar cells that contain active defects. It utilizes a self-consistent numerical scheme in which the device is mapped onto a finite element mesh. To demonstrate its versatility, we apply the simulator to the problems of defect migration during the annealing process and the extraction of current-voltage characteristics and quantum efficiencies. Our simulator also includes grain boundaries which are known to play an important role in CdTe devices as they strongly affect the migration of defects such as chlorine (Cl).

Preditive simulation of defect migration and metastabilities in CdTe solar cells

In this work, a diffusion-reaction model was implemented and used to study Cu migration during the annealing process and stress test. Its impact on the metastable behavior of CdTe solar cells was also investigated. The preliminary results support our theoretical model presented here that explains rapid changes in atomic concentration of Cu in CdTe as a function of stress conditions.