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Modeling of Crystal Growth and Devices

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ConsultingPVT GrowthGallium Nitride

    Homoepitaxy on GaN substrates, which is beneficial to fabricate device-quality nitride-based heterostructures, requires bulk GaN crystals of an appropriate size. Today, Sublimation Sandwich Technique [1] is considered as a promising method to obtain GaN bulk crystals, along with High Pressure Crystal Growth and Chloride Hydride Vapor Phase Epitaxy. This method has been initially developed for growth of high-quality SiC crystals and then applied to group-III nitrides[2].
    Due to extremely low chemical reactivity of N2 on GaN surfaces, growth of GaN in nitrogen atmosphere does not occur, which erequires external flow of nitrogen-containing reactive species to initiate the growth process. The best choice of such species in all respects is ammonia.

Modeling of bulk GaN growth

    To analyze in detail the gas-flow dynamics in the reactor and the concentration distribution of the main gaseous species, we use numerical simulation of the growth [3].
Figure 1 shows typical geometries of the growth reactor of vertical configuration and the distribution of the ammonia concentration over the reactor, as well as the temperature distribution in the reactor.
Scheme Temperature distribution

Figure 1. Left: Simplified scheme of GaN growth by Sublimation Sandwich Technique. Right: Temperature distribution in a reactor in GaN growth (the substrate temperature is 1150C, and temperature difference is 50C).

Species Transport in GaN growth

     A specific feature of the sublimation process is accumulation of molecular hydrogen inside the growth cell. Generation of H2 is related entirely to heterogeneous reactions proceeding on the surfaces of the substrate and the source. The mole fraction of H2 in the growth cell exceeds 93% so that it displaces the other species. This effect prevents in lateral uniformity of the V/III ratio and GaN growth rate.
Figure 2 illustrtaes the 2D distribution of concentrations of ammonia in the whole reactor and the distributuion of the all main gaseous species (Ga, NH3 and H2) in the growth cell.
Scheme Temperature distribution

Figure 2. Left: Ammonia concentration in the reactor. Right: Distributions of the gaseous species in the growth cell. The color transition from blue to red indicates increasing species mass fraction.

Transport of gallium between source and substrate

To analyze the Ga transport between the source and the substrate we consider the following effects: i) Ga diffusion ii) gas convection in the growth cell enhanced by hydrogen generation at the surface of the source, iii) multiple channel desorption of Ga (via gaseous compounds with hydrogen and other possible species), and iv) generation of Ga droplets at the surface of the source followed by their transport to the substrate. It is found that the largest contribution into high Ga transport rate is related to droplet generation, which is related to the liquid surface instability. The specific mechanism of Ga transport is illustrated by Figure 3 (left) where the dependence of GaN growth rate on the clearance d between the source and substrate is plotted.

Physical limitation of GaN growth rate in Sublimation Sandwich Technique

Of a special interest is the question of the maximum growth rate achievable by PVT. The effectiveness of the ammonia supply into the growth cell can be accounted by a coefficient that can be defined as the product of the ammonia sticking coefficient on GaN surface [4] and the ratio of NH3 partial pressure inside the growth cell to its partial pressure at the inlet of the reactor. To calculate the GaN growth rate, we use the quasi-thermodynamic approach [5]. Figure 3 (right) shows the temperature dependence of the growth rate. Under ideal conditions, all the ammonia arriving at the inlet of the reactor is transported to the substrate. In this case is equal to the NH3 sticking coefficient, i.e. 0.04 [4], and the growth rate can be as high as 15-20 mm/h.
Scheme Temperature distribution

Figure 3. Left: Growth rate versus clearance between the source and substrate. Right: GaN growth rate versus temperature. The red arrow indicates the maximum growth rate achievable for the chosen temperature gradient and reactor pressure, limited only by Ga transport.

Growth window for the Sublimation Sandwich Technique

The estimation of the GaN growth rate made above takes into account only limitations related to the rate of Ga transport to the growing surface. At the same time other factors can be important introducing additional limitations on the growth process. Among these factors are formation of liquid Ga on the growth surface, failure of epitaxial growth resulting in polycrystal formation, surface morphology degradation, etc. Analyzing a large number of experimental data we can conclude that there exists some "growth window" in coordinates dT - T where single GaN crystals can be obtained. Beyond this window various factors interfere with growth.


[1] Yu.A. Vodakov, E.N. Mokhov, A.D. Roenkov, M.E. Boiko, P.G. Baranov, J.Cryst.Growth 183, 10 (1997).
[2] Yu.A. Vodakov, M.I. Karklina, E.N. Mokhov, A.D. Roenkov, Inorg. Mat. 16 , 537 (1980).
[3] P.G. Baranov, E.N. Mokhov, A.O. Ostroumov, M.G. Ramm, M.S. Ramm, V.V. Ratnikov, A.D. Roenkov, Yu.A. Vodakov, A.A. Wolfson, G.V. Saparin, S.Yu. Karpov, D.V. Zimina, Yu.N. Makarov, H. Juergensen, MRS Int. J. of Nitr. Sem. Res. 3, 50 (1998).
[4]M.V. Averyanova, S.Yu. Karpov, Yu.N. Makarov, M.S. Ramm, R.A. Talalaev, MRS Int. J. of Nitr. Sem. Res. 1, 31 (1996).
[5]M. Mesrine, N. Grandjean, J. Massies, Appl. Phys. Lett. 72 , 350 (1998).


[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] Baranov P.G., Mokhov E.N., Ostroumov A.O., Ramm M.G., Ramm M.S., Ratnikov V.V., Roenkov A.D., Vodakov Yu.A., Wolfson A.A., Saparin G.V., Karpov S.Yu., Zimina D.V., Makarov Yu.N., Juergensen H. Current status of GaN crystal growth by sublimation sandwich technique. MRS Internet Journal of Nitride Semiconductor Research, Vol.3, Art.50, (1998).

[5] Karpov S.Yu., Makarov Yu.N., Ramm M.S., Talalaev R.A. Analysis of gallium nitride growth by gas-source molecular beam epitaxy. Journal of Crystal Growth, Vol.187, p.397-401, (1998).


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