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Modeling of Crystal Growth and Devices

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ConsultingPVT GrowthAluminum Nitride

Due to its electrical and thermal properties, aluminum nitride is a promising material for fabrication of insulating substrates for high-temperature and high-frequency electronic devices. Bulk AlN crystals are normally grown by the sublimation technique (Physical Vapor Transport) involving evaporation of AlN powder in the hot zone of a reactor followed by crystallization the reactive species on the seed placed in a colder zone [1],[2]. Due to kinetic limitation of the molecular nitrogen adsorption/desorption rate (see, e.g., [3] ), the AlN growth requires temperatures higher than 1900 C. In our research, we study heat and mass transfer in AlN PVT growth, focusing on the effect of oxygen which is contained in the vapor.

Thermal Field Simulations

AlN crystal growth by PVT method is governed by the temperature distribution in the growth system. The heat transfer modeling involves consideration of the conductive and radiant heat transfer. Detailed modeling of the heat transfer in the overall growth system is necessary to predict and control the thermal field in the crucible.
2D Temperature distribution Theoretical and experimental 1D axial temperature distributions

Figure 1. Left: temperature distribution in the crucible zone of an AlN growth system. Right: Theoretical (lines) and experimental (dots) axial temperature distribution for different values of the heating power [4]

Heat Exchange in the Powder Source

One of the problems arising in modeling AlN sublimation growth is the lack of knowledge on the properties of the used materials, in particular, AlN powder. To evaluate the effective heat conductivity of the AlN powder, we employ a model that considers the powder as porous medium whose properties depend on the powder microstructure [5],[6].
2d-temperature distribution in the powder charge temperature dependence of the AlN powder thermal conductivity

Figure 2. Thermal conductivity of AlN powder: 2d-temperature distribution in the powder charge (left); temperature dependence of the AlN powder thermal conductivity for different mean granule sizes (right).

Mass Transport of the Reactive Species

When AlN is growing by the sublimation technique, its vapor usually consists of Al and N2. The reactive species are produced by the AlN powder evaporation and then transported to the seed where they contribute to the single AlN growth. The chemical model used to describe the heterogeneous processes involved in AlN growth are described in the section Models .
Al distribution in the growth chamber the AlN growth rate

Figure 3. Simulation of the species transport in an AlN growth system. Left: Al distribution in the growth chamber. Center: temperature dependence of the AlN growth rate [7].

The surface mechanisms related to AlN growth differ significantly from those of SiC. The principal difference comes from the kinetic limitation of the adsorption/desorption rate of molecular nitrogen [8] which is a major reactive vapor species along with atomic Al. To account for this effect, we use the temperature dependent N2 sticking coefficient extracted from the data on free evaporation of AlN in vacuum.
A specific feature of AlN sublimation growth is a dramatic growth acceleration when the vapor becomes nearly stoichiometric, i.e PAl ~ 2PN2 [9]. Then the species transport occurs entirely via convection with the gas velocity limited only by the evaporation kinetics. The stoichiometric composition can be achieved at a low vapor pressure close to a critical pressure Pc(T) which is associated with drastic changes in the gas flow pattern from a quasi-one-dimensional, corresponding to the directional species transport from the source to the seed, to essentially two-dimensional, due to the species emerging from the crucible to the ambient. At P < Pc, the AlN growth on the seed changes to etching, which can be also alternatively obtained by raising the temperature.

AlN Growth in Atmosphere Containing Oxygen

A special study was made to analyze the effect of oxygen present in the Al + N2 vapor. Considerable effect of the oxygen on the AlN growth rate was found at low temperatures. At growth temperatures, however, this species does not provide an additional supply of aluminum atoms to the crystal surface, in spite of a high Al2O concentration.
Thermodynamic calculations in Al-N-O system Growth rate vs. seed temperature

Figure 4. Simulation of the species transport in AlN growth system containing oxygen. Left: Thermodynamic calculations in Al-N-O system. Right: Growth rate vs. seed temperature. Operating conditions: Pressure = 400 Torr, Temperature gradient = 30 K, Gap = 15 mm, Oxygen molar fraction x = 0.05.


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[2] J.C. Rojo, G.A. Slack, K. Morgan, L.J. Schowalter, and M. Dudley, Mater. Res. Soc. Symp. Proc. 639, G1.10.1 (2001).
[3] M.V. Averyanova, S.Yu. Karpov, Yu.N. Makarov, I.N. Przhevalskii, M.S. Ramm, and R.A. Talalaev, MRS Internet J. Nitride Semicond. Res. 1, 31 (1996).
[4] M.V. Bogdanov, S.Yu. Karpov, A.V. Kulik, M.S. Ramm, Yu.N. Makarov, R. Schlesser, R.F. Dalmau, and Z. Sitar, Mater. Res. Soc. Symp. Proc. 743, L3.33 (2003).
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[8] L.H. Dreger, V.V. Dadape, and J.L. Margrave, J. Phys. Chem. 66 (1962) 1556
[9] P.M. Dryburgh, J. Cryst. Growth 125 (1992) 65.


[1] Averyanova M.V., Karpov S.Yu., Makarov Yu.N., Ramm M.S., Talalaev R.A. Theoretical model for analysis and optimization of group III-nitrides growth by molecular beam epitaxy. MRS Internet Journal of Nitride Semiconductor Research, Vol.1, Art.31, (1996)

[2] Averyanova M.V., Przhevalskii I.N., Karpov S.Yu., Makarov Yu.N., Ramm M.S., Talalaev R.A. Analysis of vaporization kinetics of group-III nitrides. Materials Science and Engineering, Vol.B43, p.167-171, (1997)

[3] Karpov S.Yu., Makarov Yu.N., Ramm M.S. The role of gaseous species in group-III nitride growth. MRS Internet Journal of Nitride Semiconductor Research, Vol.2, Art.45, (1997)

[4] Karpov S.Yu., Makarov Yu.N., Ramm M.S. Effect of elastic strain on growth of ternary group-III nitride compounds. Materials Science Forum, Vol.264-268, p.1189-1192 , (1998)

[5] Karpov S.Yu., Zimina D.V., Makarov Yu.N., Mokhov E.N., Roenkov A.D., Ramm M.G., Vodakov Yu.A. Sublimation growth of AlN in vacuum and in a gas atmosphere. Physica Status Solidi (a), Vol.176, p.435-438, (1999)

[6] Segal A.S., Karpov S.Yu., Makarov Yu.N., Mokhov E.N., Roenkov A.D., Ramm M.G., Vodakov Yu.A. On mechanisms of sublimation growth of AlN bulk crystals. Journal of Crystal Growth, Vol.211, p.68-72, (2000)

[7] Karpov S.Yu., Kulik A.V., Ramm M.S., Mokhov E.N., Roenkov A.D., Vodakov Yu.A., Makarov Yu.N. AlN crystal growth by sublimation technique. Materials Science Forum, Vol.353-356, p.779-782, (2001)

[8] Karpov S.Yu., Kulik A.V., Segal A.S., Ramm M.S., Makarov Yu.N. Effect of reactive ambient on AlN sublimation growth. Physica Status Solidi (a), Vol.2 188, p.763-767, (2001)

[9] Bogdanov M.V., Karpov S.Yu., Kulik A.V., Ramm M.S., Makarov Yu.N., Schlesser R., Dalmau R.F., Sitar Z. Experimental and theoretical analysis of heat and mass transport in the system for AlN bulk crystal growth. Materials Research Society Symposium Proceedings, Vol.743, p.L3.33, (2003)


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