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

Abstract

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.

Cu gettering by phosphorus-doped emitters in p-type silicon: Effect on light-induced degradation

“…6 This phenomenon is referred in literature to as copper-related light-induced degradation (Cu-LID) and recent root-cause investigations have proven that Cu-LID arises from the transformation of interstitial Cu atoms into highly recombination active precipitates in the bulk region of the wafer. [7][8][9][10] Gettering is a well-established technique, by which transition metal impurities are relocated to pre-defined substrate areas where they result less harmful for the device performance. In devices where the wafer bulk represents the region of major relevance for the device performance (e.g.…”

Low-T anneal as cure for LeTID in Mc-Si PERC cells

“…the possibility of formation and dissolution of recombination active metal precipitates and the simultaneous segregation of the mobile metals to the surface or the emitter. Modeling the metal precipitation and dissolution, as well as segregation and diffusion at different temperatures, is relatively straightforward based on the models found in literature [18]. In addition to modeling the impurity redistributions, we also simulate the recombination rate during the dark anneals reported above to see if they correlate with the experiments.…”

Vertically integrated modeling of light-induced defects: Process modeling, degradation kinetics and device impact

“…The central physical process of Cu-LID is the precipitation of benign interstitial copper point defects into recombination active Cu silicide precipitates under carrier injection [17]. The injection-dependent lifetime impact of these precipitates is modeled using a Schottky junction model for metallic precipitates [18].…”

“…The precursors for Cu-LID are thus Cu point defects, and our model inputs include the initial Cu point defect concentration [Cu] init as well as the stable lifetime that does not vary with illumination time τ . The LID-kinetics model used here is extensively described in [17] and experimentally validated in [19]. The impact of lifetime onto device efficiency is modeled by using the bulk lifetime and injection-dependent efficiencies modelled for a PERC-device with an architectural efficiency limit of 21.5% [20], i.e., the modeled efficiency of the device is 21.5% given an infinite bulk lifetime.…”

“…Specifically, we investigate whether LID-mechanisms could be identified via simulations based on the degradation behavior of complete devices and whether vertically integrating a LID-model and a process model could be used to develop process guidelines to mitigate the identified LID-defect in the same simulation environment. We use Cu-related LID (Cu-LID) as an example of a reasonably well-understood LID-mechanism [17].…”