Analysis of grain structure evolution via image processing based on optical measurements of mc Si wafers
A fast and thorough characterization of grain structure in multicrystalline silicon (mc-Si) is crucial to improve crystal growth and thus bulk lifetime in solar cells. The presented characterization techniques are based on simple optical measurements on as-cut mc-Si wafers. An insight into the entire brick is gained by connecting 2D-information, computed via advanced pattern recognition techniques, over brick height. We identify robust statistical key parameters. Their development within typical bricks of different cast-Si techniques is compared and it is found that the distinct behavior of different materials in the lower part of the brick subsides towards the brick top where grain size distribution is similar.
Seed-assisted growth of high-quality multi-crystalline silicon in directional solidification
Abstract An approach to grain control using seed-assisted growth in directional solidification (DS) is reported in this paper. Proper multi-crystalline silicon seeds at the bottom of the crucible provided numerous fine nucleation points for the controlled grain growth in an optimized hot-zone. Low dislocation density was observed with large numbers of uniform small grains in the silicon ingot, although the grain size increased with crystal growth. Crystals produced using seed-assisted growth showed a higher and more uniform minority carrier lifetime with a much lower dislocation multiplication rate. A higher average solar cell conversion efficiency of about 0.5% in absolute value was obtained in the seed-assisted grown silicon in comparison with that in the seedless silicon under the same cell fabrication process.
Stability results for the solutions of some third and fourth order differential equations
SummaryThe paper investigates conditions under which solutions of the equations (1) and (2) of § 1.1 tend to zero as t → ∞.