The calculated maximum Ga amount using the Langmuir equation during distillation at 1360 K and growth at 1160 K was 67.9 g. This calculated value was much higher than 25 g of Ga loss observed. This disagreement was corrected by using the transmission probability by Clausing theory which includes the consideration of the condensation of Ga particles back into melt due to collision between Ga particles inside the crucible. The evaporated amount of Ga assuming the presence of collisions was obtained by applying a receding length of melts over time to the evaporation rate within a cylindrical crucible. Using the correction, the evaporated amount of Ga, 28.9 g was closed to the observed amount of loss, 25 g.
Acknowledgements Support for this research from the W.M. Keck Foundation is gratefully acknowledged. The authors also would like to thank ultra-pure GaAs Keck Project team members at Purdue University.
- 1. M. J. Manfra, “Molecular Beam Epitaxy of Ultra-High-Quality AlGaAs/GaAs Heterostructures: Enabling Physics in Low-Dimensional Electronic Systems,” Annu. Rev. Condens. Matter Phys, 5 (2014), 347-73
- 2. G. C. Gardner et al., “Modified MBE Hardware and Techniques and Role of Gallium Purity for Attainment of Two Dimensional Electron Gas Mobility >35 x AlGaAs/GaAs Quantum Wells Grown by MBE,” Journal of Crystal Growth, 441 (2016), 71-77
- 3. Kyungjean Min, “Analysis of High-Purity of Ga by ICP-MS,” (MS thesis, Purdue University, 2014)
- 4. M. A. Herman and H. Sitter, “Molecular Beam Epitaxy, Fundamentals and Current Status,” Springer (1996)
- 5. I. Langmuir, “The Vapor Pressure of Metallic Tungsten,” Phys. Rev., 2 (11) (1913), 329-342
- 6. M. Knudsen, “Der molekulare Gaswiderstand gegen eine sich bewegende Platte,” Ann. Phys. 351(5) (1915), 641-656
- 7. P. Clausing, “Uber die Stromung sehr verdhnnter Gase durch Rohren von beliebiger Lange,” Ann. Phys. 404(8) (1932), 961-989
- 8. P. Krasuski, “Angular distribution of flux at the exit of cylindrical tubes,” J. Vac. Sci. Technol. A 5, (1987), 2488-2492
- 9. C. B. Alcock, VP. Itkin, MK. Horrigan, “Vapour pressure equations for the metallic elements: 298-2500 K,” 23 (1984) 309-313
- 10. O. Kubaschewski and CB. Alcock, “Metallurgical Thermochemistry, 5th ed,” Pergamon Press, (1979)