Thermal-capillary analysis of the horizontal ribbon growth of silicon crystals

Parthiv Daggolu, Andrew Yeckel, Carl E. Bleil, Jeffrey J. Derby

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


A thermal-capillary, finite-element model is developed for the Horizontal Ribbon Growth (HRG) system to study the characteristics of the process and to assess its feasibility to grow silicon sheets. The mathematical model formulation rigorously accounts for mass, energy, and momentum conservation while simultaneously representing capillary physics of the menisci, tracking of the solidification front, and self-consistent determination of ribbon thickness. Model results show the potential, with suitable heat transfer design, for the HRG process to achieve the formation of an extended, wedge-shaped interface with latent heat dissipation primarily in a direction perpendicular to the pulling direction. These attributes allow the HRG system to achieve higher pull rates under lower thermal gradients than vertical ribbon growth systems. Crystal thickness is predicted to decrease with increasing pull rate; however, contrary to prior analyses, pull rate limits are identified as limit-point bifurcations to quasi-steady solutions. Multiple solution branches correspond to stable and unstable operating states, exhibiting dramatically different interfacial shapes that identify possible failure mechanisms.

Original languageEnglish (US)
Pages (from-to)129-139
Number of pages11
JournalJournal of Crystal Growth
Issue number1
StatePublished - Sep 15 2012

Bibliographical note

Funding Information:
This material is based on work supported in part by the Minnesota Supercomputer Institute and the National Science Foundation under CBET-0755030 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank the reviewers for several insights that improved this paper.

Copyright 2012 Elsevier B.V., All rights reserved.


  • A1. Computer simulation
  • A1. Fluid flows
  • A1. Heat transfer
  • A2. Edge defined film fed growth
  • B2. Semiconducting silicon
  • B3. Solar cells


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