Surface patterns due to step flow anisotropy formed in crystal growth process

https://doi.org/10.1016/j.jnoncrysol.2010.05.029Get rights and content

Abstract

The growth of gallium nitride on a GaN(0001) surface was conducted in an N-rich state for both metal organic vapor phase epitaxy (MOVPE) and hydride vapor phase epitaxy (HVPE) methods and therefore it was controlled by surface diffusion of Ga adatoms. At these conditions two consecutive atomic steps on the GaN(0001) surface had one or two broken bonds. Consequently, their kinetic properties were different. According to the wurtzite symmetry, the step had a trigonal symmetry preserving the number of broken bonds for rotation by 2π/3 and exchanging the step type for rotation by π/3. The simplest model was introduced which allowed the growth of a GaN crystal to be simulated at this surface, preserving the lattice symmetry, and taking into account the presence of one or two broken bonds for the consecutive step order and orientation. The Monte Carlo simulations of the model showed that, depending on the terrace width, the steps either tended to group in a double step structure, or, for wider terraces, formed wave-like structures (step meandering). The results of the Monte Carlo simulations exactly recovered the structures that were observed in the Atomic Force Microscopy images of a GaN surface grown by MOVPE.

Introduction

Two principal sources of active nitrogen are used in the growth of GaN single crystals and epitaxial layers: first — nitrogen, either plasma activated in molecular beam epitaxy (MBE) [1], or high pressure activated in solution growth [2], and second — ammonia, used in a vast majority of methods, including metal organic vapor phase epitaxy (MOVPE) [3], hydrogen vapor phase epitaxy (HVPE) [4], [5] ammonothermal growth [6] The latter source is typical for vapor growth methods, such as MOVPE and HVPE, presently dominating in the nitride technology. These ammonia based methods differ by the use of gallium sources: trimethylgallium (TMG) in MOVPE and GaCl in HVPE. In both methods, a nonreactive carrier gas, hydrogen or nitrogen, is used to transport both reactive species. An overwhelming majority of GaN growth is carried out on a GaN(0001) surface [7]. This is due to two different reasons. The first factor is that at present virtually all available substrates have this orientation only. The second factor is advancement in the technology whereby most of the growth methods have been developed for this surface only. Therefore, all optoelectronic device structures, both light emitting diodes (LEDs) and laser diodes (LDs) are grown using this orientation. This surface is used in spite of the well know problems of existing and strain induced electric fields in multiquantum wells (MQW), separating electrons and holes, reducing the rates of radiative recombination, and overall the efficiency of LDs and LEDs [8], [9]. Such an electric field also shifts the energy levels of quantum states which is known as the quantum confined Stark effect (QCSE) [10], [11]. Recently, attempts have been undertaken to grow MQW structures on different orientations [12], [13]. These orientations have brought a significant increase in the device efficiency, confirming the immense detrimental influence of electric fields in structures grown on a GaN(0001) surface.

However, achievements in growth on other surface orientations do not reduce the importance of the GaN(0001) surface. The harmful effect of QCSE on LEDs and LDs is, on the contrary, beneficial for field effect transistors (FET). The electric field localizes electrons at the AlGaN–GaN interface allowing us to obtain a high mobility of the two-dimensional electron gas [14]. Therefore, in the long range development of nitride epitaxy, growth on a GaN(0001) surface will retain its importance. Altogether, the investigations of the surface structure and the properties of the GaN(0001) surface, and also growth of GaN in an environment typical for MOVPE or HVPE growth conditions, are interesting both from the fundamental point of view and also for applications.

The paper is organized as follows. The model used in simulations is described in 2 Model for simulations, 3 Results of simulations is devoted to the results obtained in the simulations; Section 4 presents an analytical 1D model of steps with double velocities. Section 5 contains conclusions.

Section snippets

Model for simulations

The surface fluxes of the reactive species are not equivalent in the MOVPE and HVPE growth of GaN on GaN(0001). The ammonia flux is typically two (HVPE) or three (MOVPE) orders of magnitude higher than the Ga flux. At the standard growth temperature which is close to 1000°C the Ga transporting agents TMG or GaCl are highly unstable, but they decompose easily at the surface only, leaving Ga atoms. Ammonia is unstable as well, but its decay occurs in the gas phase that creates highly nonreactive

Results of simulations

Simulations for different values of J, μ and for different mean widths of terraces were performed in order to find out how the shape of fast and slow steps depended on these three parameters. Three different regimes of the system behavior were found. The range of the interaction parameter values 4 < βJ < 6 was identified as the best to realize stationary crystal growth. All the examples shown were calculated for βJ = 5.5. For narrow terraces — initially set to be around 40a (a was a lattice constant)

Analytic model

The mechanism of creation of a double step structure in the system with the two types of anisotropic steps will be studied using the Burton–Carbera–Franck (BCF) formulation [22], [23], [24] of the surface diffusion controlled crystal growth. In the BCF model it is assumed that due to the step adsorption the local density ρ changes being the smallest at the steps. Accordingly, the particles diffuse towards the steps. In the simplest formulation one can consider a train of parallel steps, i.e.

Conclusions

Depending on the step orientation — two different crystallographically consecutive step structures can be created on a GaN(0001) surface: with a single broken bond and with two broken bonds. Rotation by π/3 exchanges these two step types. Monte Carlo simulations describe a 2D nucleation controlled growth mode for large adparticle supersaturations and a step flow mode for smaller supersaturations.

Three regimes of step flow are observed during growth on the GaN(0001) surface, namely: low

Acknowledgements

Research partially supported by grants from Poland's Ministry of Science and Higher Education (Grant Number N202 042 32/1171 — M.Z.K) and partially by the European Union within the European Regional Development Fund, through grant Innovative Economy (POIG.01.01.02-00-008/08 —S.K.).

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