Accurate modeling of copper precipitation kinetics including Fermi level dependence

Copper contamination causes minority carrier lifetime degradation in p-type silicon bulk under illumination, leading to considerable efficiency losses in affected solar cells. Although the existence of this phenomenon has been known for almost two decades, ambiguity prevails about the underlying defect mechanism. In Paper I of this two-part contribution, we propose the first comprehensive mathematical model for Cu-related light-induced degradation in p-type silicon (Cu-LID). The model is based on the precipitation of interstitial Cu ions, which is assumed to be kinetically limited by electrostatic repulsion from the growing Cu precipitates. Hence, growth and dissolution rates of individual Cu precipitates are derived from the drift-diffusion equation of interstitial Cu and used in a kinetic precipitation model that is based on chemical rate equations. The kinetic model is interlinked to a Schottky junction model of metallic precipitates in silicon, enabling accurate calculation of the injection-dependent electric field enclosing the precipitates, as well as the precipitate-limited minority carrier lifetime. It is found that a transition from darkness to illuminated conditions can cause an increase in the kinetics of precipitation by five orders of magnitude. Since our approach enables a direct connection between the time evolution of precipitate size-density distribution and minority carrier lifetime degradation under illumination, a procedure for calculating the Cu-LID-related lifetime as a function of illumination time is included at the end of this article. The model verification with experiments is carried out in Paper II of this contribution along with a discussion of the kinetic and energetic aspects of Cu-LID. Published by AIP Publishing.

supporting

confidence: 48%

Modeling of light-induced degradation due to Cu precipitation in p-type silicon. I. General theory of precipitation under carrier injection

Vahlman

Haarahiltunen

Kwapil

et al. 2017

“…Still, interactions between the precipitating species appear important in explaining the smaller measured as-grown distribution. Copper has a large energy barrier to nucleation in silicon, 45 but with co-precipitation a reduction in this barrier may explain the more widespread precipitation seen here in the CuþFe sample relative to the Fe only samples.…”

Section: B Co-contamination Effects (Fe1cu)mentioning

confidence: 89%

Improved iron gettering of contaminated multicrystalline silicon by high-temperature phosphorus diffusion

Fenning

Zuschlag

Bertoni

et al. 2013

The efficacy of higher-temperature gettering processes in reducing precipitated iron concentrations is assessed by synchrotron-based micro-X-ray fluorescence. By measuring the same grain boundary before and after phosphorus diffusion in a set of wafers from adjacent ingot heights, the reduction in size of individual precipitates is measured as a function of gettering temperature in samples from the top of an ingot intentionally contaminated with iron in the melt. Compared to a baseline 820 C phosphorus diffusion, 870 C and 920 C diffusions result in a larger reduction in iron-silicide precipitate size. Minority carrier lifetimes measured on wafers from the same ingot heights processed with the same treatments show that the greater reduction in precipitated metals is associated with a strong increase in lifetime. In a sample contaminated with both copper and iron in the melt, significant iron gettering and complete dissolution of detectable copper precipitates is observed despite the higher total metal concentration. Finally, a homogenization pre-anneal in N 2 at 920 C followed by an 820 C phosphorus diffusion produces precipitate size reductions and lifetimes similar to an 870 C phosphorus diffusion without lowering the emitter sheet resistance. V C 2013 AIP Publishing LLC. [http://dx.

“…Possible reasons include either a considerable deviation of the actual precipitate shape from spheres or a sufficient amount of heterogeneous nucleation sites in the studied materials, such as vacancies, dislocations, and/or oxygen precipitate/Si phase boundaries, which minimize the effects of lattice strain. However, with the given total Cu concentration, assuming a strain-minimizing shape such as very thin plates [35][36][37][38] would result in a great increase in precipitate radius and/or density. This would cause a substantial increase in the available recombination surface, decreasing the precipitate-limited lifetime up to several orders of magnitude.…”

Section: E Energetic Parameters and Nucleation Modementioning

confidence: 99%

Modeling of light-induced degradation due to Cu precipitation in p-type silicon. II. Comparison of simulations and experiments

Vahlman

Haarahiltunen

Kwapil

et al. 2017

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