Modeling the size distribution of iron silicide precipitates in multicrystalline silicon
Precipitation of iron in multicrystalline (mc) silicon during typical solar cell processing is investigated with an advanced model that has been previously demonstrated to be able to simulate the iron distribution in two dimensions. The improving detection limits of precipitate measurements with x-ray fluorescence microscopy (μ XRF) allow a first comparison of measured and simulated precipitate densities in mc solar cell material. We focused on simulating the size distribution of iron-silicide precipitates at a grain boundary for a better comparison with experimental data. The simulated line densities of detectable iron precipitates as well as the size distribution along a grain boundary are in good agreement with experiments. These results verify the iron kinetics model, independent of the interstitial iron concentration. The dependency of the assumed total iron concentration and the model structure is investigated by varying these input parameters. The model predicts a fast dissolution of small and medium iron precipitates during inline phosphorus diffusion, resulting in an increase of the mean size of precipitates. Low-temperature anneals effectively reduce the interstitial iron concentration, but influence only the density of small precipitates, which are below experimental detection limits. The simulations demonstrate that iron precipitates become more important for the charge-carrier lifetime during solar cell processing.
Analyses of the Evolution of Iron-Silicide Precipitates in Multicrystalline Silicon During Solar Cell Processing
We simulate the precipitation of iron during the multicrystalline ingot crystallization process and the redistribution of iron during subsequent phosphorus diffusion gettering with a 2-D model. We compare the simulated size distribution of the precipitates with the X-ray fluorescence microscopy measurements of iron precipitates along a grain boundary. We find that the simulated and measured densities of precipitates larger than the experimental detection limit are in good agreement after the crystallization process. Additionally, we demonstrate that the measured decrease of the line density and the increase of the mean size of the iron precipitates after phosphorus diffusion gettering can be reproduced with the simulations. The size and spatial distribution of iron precipitates affect the kinetics of iron redistribution during the solar cell process and, ultimately, the recombination activity of the precipitated iron. Variations of the cooling rate after solidification and short temperature peaks before phosphorus diffusion strongly influence the precipitate size distribution. The lowest overall density of iron precipitates after phosphorus diffusion is obtained in the simulations with a temperature peak before phosphorus diffusion, followed by moderate cooling rates.
Role of the coronoid process in varus osteoarticular stability of the elbow.
The role of the coronoid process in varus osteoarticular stability of the elbow was investigated in 10 cadaveric elbows. Testing was performed at multiple flexion angles after incremental removal of the coronoid. At each flexion angle, removal of more than 50% of the coronoid produced a statistically significant decrease in the load resisting varus displacement compared with all lesser resection levels (P < .003). There was a trend for decreasing load after removal of 50% of the coronoid. The mean decrease in load across all flexion angles was 10.1%, 50.4%, and 75.4% after removal of 50%, 75%, and 100% of the coronoid, respectively. Resistance to varus displacement tended to decrease more as a percent of control at lower flexion angles than at higher flexion angles after removal of more than 50% of the coronoid. The coronoid process was found to be a key varus stabilizer in the elbow and may contribute more to elbow stability in extension than in flexion.