Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T04:50:45.205Z Has data issue: false hasContentIssue false
  • English
  • Français

A simplified analytical model of diamond growth in direct current arcjet reactors

Published online by Cambridge University Press:  03 March 2011

David S. Dandy  and
Michael E. Coltrin
David S. Dandy
Affiliation:
Department of Chemical Engineering, Colorado State University, Fort Collins, Colorado 80523
Michael E. Coltrin
Affiliation:
Chemical Processing Sciences Department, Sandia National Laboratories, Albuquerque, New Mexico 87185
Get access

Abstract

A simplified model of a direct current arcjet-assisted diamond chemical vapor deposition reactor is presented. The model is based upon detailed theoretical analysis of the transport and chemical processes occurring during diamond deposition, and is formulated to yield closed-form solutions for diamond growth rate, defect density, and heat flux to the substrate. In a direct current arcjet reactor there is a natural division of the physical system into four characteristic domains: plasma torch, free stream, boundary layer, and surface, leading to the development of simplified thermodynamic, transport, and chemical kinetic models for each of the four regions. The models for these four regions are linked to form a single unified model. For a relatively wide range of reactor operating conditions, this simplified model yields results that are in good quantitative agreement with stagnation flow models containing detailed multicomponent transport and chemical kinetics. However, in contrast to the detailed reactor models, the model presented here executes in near real-time on a computer of modest size, and can therefore be readily incorporated into process control models or global dynamic loop simulations.

Type
Articles
Information
Journal of Materials Research , Volume 10 , Issue 8 , August 1995 , pp. 1993 - 2010
Copyright
Copyright © Materials Research Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Cerio, F. M. and Weimer, W. A., Rev. Sci. Instrum. 63, 2065 (1992).CrossRefGoogle Scholar
2Woodin, R. L., Bigelow, L. K., and Cann, G.L., Proceedings of Applications of Diamond Films and Related Materials (Auburn, AL, 1991), p. 439.Google Scholar
3Rongzhi, L., Hailiang, S., Zhen, Y., Sen, T., and Hesun, Z., Proceedings of Applications of Diamond Films and Related Materials (Auburn, AL, 1991), p. 207.Google Scholar
4Goodwin, D. G., Appl. Phys. Lett. 59, 277 (1991).CrossRefGoogle Scholar
5Coltrin, M. E. and Dandy, D. S., J. Appl. Phys. 74, 5803 (1993).CrossRefGoogle Scholar
6Yu, B. W. and Girshick, S. L., J. Appl. Phys. 75, 3914 (1994).CrossRefGoogle Scholar
7Goodwin, D. G., J. Appl. Phys. 74, 6888 (1993).CrossRefGoogle Scholar
8Godwin, D. G., J. Appl. Phys. 74, 6895 (1993).CrossRefGoogle Scholar
9Young, R. M., Surf. Coat. Technol. 68/69, 384 (1994).CrossRefGoogle Scholar
10Sandier, S. I., Chemical and Engineering Thermodynamics, 2nd ed. (John Wiley & Sons, New York, 1989).Google Scholar
11Miller, J. A. and Melius, C. F., Combust. Flame 91, 21 (1992).CrossRefGoogle Scholar
12Coltrin, M. E., Kee, R. J., Evans, G. H., Meeks, E., Dandy, D. S., Rupley, F., and Grcar, J. F., “SPIN: a Fortran program for modeling one-dimensional rotating-disk/stagnation-flow chemical vapor deposition reactors,” Report No. SAND91-8OO3 (1991).CrossRefGoogle Scholar
13Frenklach, M., Wang, H., Bowman, C. T., Hanson, R. K., Smith, G. P., Golden, D. M., Gardiner, W. C., and Lissianski, V., Proceedings of 25th International Symposium on Combustion (Irvine, CA, 1994), poster presentation.Google Scholar
14Rosner, D. E., Transport Processes in Chemically Reacting Flow Systems. (Butterworths, Boston, MA, 1986).Google Scholar
15Harris, S. J., Appl. Phys. Lett. 56, 2298 (1990).CrossRefGoogle Scholar
16Westbrook, C. K., Warnatz, J., and Pitz, W.J., Proceedings of Twenty-second Symposium (International) on Combustion.(Seattle, WA, 1988), p. 893.Google Scholar
17Kondoh, E., Ohta, T., Mitomo, T., and Ohtsuka, K., Appl. Phys. Lett. 59, 488 (1991).CrossRefGoogle Scholar
18Kondoh, E., Ohta, T., Mitomo, T., and Ohtsuka, K., J. Appl. Phys. 73, 3041 (1993).CrossRefGoogle Scholar
19Harris, S. J. and Weiner, A. M., J. Appl. Phys. 75, 5026 (1994).CrossRefGoogle Scholar
20Butler, J. E. and Woodin, R. L., Philos. Trans. R. Soc. 342, 209 (1993).Google Scholar
21Newton, M. E., Cox, A., and Baker, J.M., personal communication (1994).Google Scholar
22Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B., Molecular Theory of Gases and Liquids, 1st ed. (John Wiley and Sons, New York, 1954), Vol. 1.Google Scholar
23Grew, K. E. and Ibbs, T. L., Thermal Diffusion in Gases. (Cambridge University Press, Cambridge, 1952).Google Scholar
24Warnatz, J., in Numerical Methods in Flame Propagation, edited by Peters, N. and Warnatz, J. (Friedr. Vieweg and Sohn, Wiesbaden, 1982).Google Scholar
25Brau, C. C. and Jonkman, R. M., J. Chem. Phys. 52, 477 (1970).CrossRefGoogle Scholar
26Mathur, S., Tondon, P.K., and Saxena, S. C., Molec. Phys. 12, 569 (1967).CrossRefGoogle Scholar
27Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E., and Miller, J.A., “A Fortran computer code package for the evaluation of gas-phase multicomponent transport properties,” Report No. SAND86-8246 (1986).Google Scholar