Dislocation Arrays in the Interfaces between Substrates and Epitaxial Islands
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Dislocation Arrays in the Interfaces between Substrates and Epitaxial Islands Annamalai Lakshmanan1, Vidyut Gopal1, Alexander H. King and Eric P. Kvam School of Materials Engineering Purdue University, West Lafayette IN 47907-1289. 1 Now at Applied Materials, Inc., Santa Clara, CA. ABSTRACT We present a model for dislocation array image effects during epilayer island growth. Misfit dislocations often appear at an interface between phases, to accommodate a lattice mismatch. In many situations, such as early film growth, one of the phases may be discontinuous, leaving the interface region clearly bounded. The structure of such a finite interface differs from the normally-modeled infinite boundary because of end effects near the edges of the islands. We have modeled the dislocation structure of such a finite interface in MBE-grown InAs islands on GaP, and compare our results to high-resolution images of the same structure. The 11% misfit causes dislocation introduction from the outset of growth. Islands containing between 4 and 14 dislocations were examined, and dislocation spacings were found to be enlarged near the island perimeters. The model provides a clear understanding of this and other effects.
INTRODUCTION Hetero-epitaxial interfaces and semi-coherent phase boundaries form a class of interfaces defined by the meeting of two crystals with the same orientation, but different lattice parameters. Such interfaces have been widely studied, and are usually described in terms of a lattice-matched structure superimposed upon which is an array of dislocations that relieves the strain required to bring the two lattices together. In the simplest case, it is possible to accommodate the strain with an array of edge dislocations, with Burgers vectors lying in the plane of the interface, and the dislocation spacing is given by S=
b1 b2 (b2 − b1 )
(1)
where b1 and b2 are the plane spacings in lattice 1 and lattice 2, respectively, with lattice two having the larger lattice parameter. These correspond to the Burgers vectors of the dislocations. An alternative to this expression is given in units of the lattice spacings themselves, and is N2 =
b1 (b2 − b1 )
or N1 =
b2 (b2 − b1 )
(2)
where Ni is the number of bi lattice spacings between dislocations. For an infinite bicrystal, a uniform dislocation array with such a spacing fully accommodates the strain in the direction of O4.9.1
the Burgers vector, and minimizes the energy of the interface. The case of a finite interface, however, has not received any serious attention, although it is of some interest relative to the cases of quantum wells and dots, or the early stages of film growth in systems that adopt the Volmer-Weber growth morphology. In this paper, we address the equilibrium structure of a finite epitaxial interface in a lattice-mismatched system. We use a phenomenological computer model to interpret and understand the dislocation arrays observed in the interfaces between InAs islands and the GaP substrates upon which they are grown.
Figure 1: Typical image of
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