Abstract
A two-dimensional, quasi-steady-state, thermal-capillary model is developed for a micro-pulling-down (μ-PD) system to study limitations to steady growth of sapphire. The model incorporates mass, energy, and momentum conservation equations, and also accounts for the physics of the melt meniscus, the solidification front, and the crystal radius. Limit points with respect to pull rate are found under higher-gradient thermal conditions but are shown to unfold with changes in die heating and ambient temperature. Limit points related to crystal size and capillary effects are also found with respect to static head (melt height); however, classical criteria of capillary instability are shown to be invalid. Thus, a more fundamental understanding is obtained for μ-PD operating limits, their origins, and their possible avoidance.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 148-159 |
| Number of pages | 12 |
| Journal | Journal of Crystal Growth |
| Volume | 335 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 15 2011 |
Bibliographical note
Funding Information:The work conducted at the University of Minnesota and was supported in part by the Minnesota Supercomputer Institute and the Department of Energy, National Nuclear Security Administration, under Awards DE-FG52-06NA27498 and DE-FG52-08NA28768. The content of the work does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred. The authors also wish to acknowledge the technical input of Dr. Z.W. Yan of LBL. A revised manuscript benefited from the comments of several reviewers.
Keywords
- A1. Computer simulation
- A1. Fluid flows
- A1. Heat transfer
- B1. Oxide
- B2. Scintillator materials