Atomistic modeling and HRTEM analysis of misfit dislocations in InN/GaN heterostructures

Abstract

The enhanced structural mismatch of InN and GaN binary alloys leads in almost spontaneous formation of misfit dislocations (MDs) at the corresponding interfaces, thereby accommodating plastic relaxation. The open issue of the MD array in-plane configuration is addressed through a combination of high resolution transmission electron microscopy (HRTEM) observations with energetic mapping and HRTEM image simulation of InN/GaN interfaces extracted by atomistic modeling. Energetic mapping on the interfacial area of InN/GaN supercells relaxed by the Tersoff interatomic potential, designates that the MD arrays adopt $〈11\overline{2}0〉$ line directions and their Burgers vectors are $\text{b}=1/3〈2\overline{1}\overline{1}0〉$. HRTEM image simulations further reveal that the local arrangement of Moiré fringes observed in these interfaces depends strongly on the thickness of the TEM foil, thus resolving contradictory experimental reports. Geometric Phase Analysis on the simulated images justifies the results obtained by energetic mapping.

Introduction

A milestone in the advancement of III-Nitride-based technology was the identification of the InN band gap value being equal to ∼0.7 eV [1]. Extension of the III-Nitride device operational wavelength range from the deep ultraviolet to the infrared became thus feasible, at least in principle, through alloying of the binary compounds. Laser diodes and photovoltaics based on InGaN and high frequency field effect transistors based on AlInN/GaN heterostructures were recently fabricated while binary InN presents high potential for solar cells as well as chemical and biological sensors (e.g. [2], [3]).

Optimization of III-Nitride devices necessitates identification and thorough understanding of the relaxation mechanisms in employed heterostructures and the atomic arrangement at corresponding interfaces. This need is exemplified in the case of InN/GaN heterostructures since they form a high mismatch system (∼11%) [4] with a critical thickness of ∼2 monolayers [5], which indicates an almost spontaneous generation of misfit dislocations (MDs). Even if low-dimensional systems are exploited in order to enhance carrier confinement and avoid non-radiative recombinations, MDs shall be formed at these interfaces and affect optoelectronic properties (e.g. [6]). Moreover, modeling of interfaces in high misfit heteroepitaxial systems is an elaborate issue, accentuated when the interface comprises more than two MD arrays as in the high symmetry (0 0 0 1) polar interface in wurtzite heterostructures and the proximity of MD lines, in the case of high misfit, becomes so small that MD intersections come very close together.

Following elasticity theory, MDs in (0 0 0 1) III-N heterointerfaces could lie along the $〈11\overline{2}0〉$ or $〈10\overline{1}0〉$ directions. In either case, MDs could intersect in pairs leading to a “Star of David” distribution comprising hexagonal and triangular areas of “good” and “bad” fit respectively, separated by MDs (Fig. 1(a)). Alternatively, the MD lines may intersect in triads forming triple dislocations nodes and exhibiting a hexagonal texture as illustrated in Fig. 1(b).

High resolution transmission electron microscopy (HRTEM) experiments on (0 0 0 1) InN/GaN heterostructures grown by plasma assisted molecular beam epitaxy (PAMBE) revealed that the structural mismatch is effectively accommodated through the formation of a MD network at the interface. This comprises three equally spaced arrays of 60° mixed-type MDs, the projected edge component of which can be resolved as $\left\{1\overline{1}00\right\}$ GaN extra half-planes in HRTEM images taken along the $〈11\overline{2}0〉$ axis [4], [7]. The 60° MD network of $\text{b}=1/3〈1\overline{2}10〉$ was evidenced by Kehagias et al. [8] in both compact InN thin films, as well as non-coalesced three dimensional islands grown by PAMBE on (0 0 0 1) GaN/Al₂O₃ substrates.

Introduction of MDs, with line directions parallel to $〈2\overline{1}\overline{1}0〉$ directions, has been proposed as an efficient scheme for plastic relaxation at the initial stages of InN/GaN growth [9]. A set of three 60° $〈1\overline{2}10〉$ dislocations was also acknowledged as the origin of plastic relaxation in InN QDs in GaN matrix grown by metal-organic vapor phase epitaxy (MOVPE). Hexagonal and triangular areas separated by MDs were observed at the InN/GaN interface, which gave the overall impression of a “Star of David” distribution instead of a hexagonal reconstruction [10]. Interestingly scanning tunneling microscopy (STM) experiments by Liu et al. [11] showed a network of three sets of 90° partial MDs at the InN/GaN (0 0 0 1) heterointerface, which were parallel to $〈1\overline{2}10〉$ but formed a hexagonal network. In contrast to the above, cathodoluminescence experiments at the interface of InGaN/GaN heterostructures grown by MOVPE indicated the formation of a MD network along $〈1\overline{1}00〉$ [12].

Towards resolving the discrepancy of experimental results, atomistic simulations through well established interatomic potentials and the III-species environment approach [13], [14] are essential, since they have proven invaluable in the analysis of structural mechanisms, extended defects and dislocations in III-N semiconductors [15], [16], and can provide the relaxed interface for direct comparison with the HRTEM observations.

In our present study, energetic mapping of the InN/GaN interfacial area, as obtained by atomistic simulations through the III-species environment approach, is performed in order to determine the characteristics of the InN/GaN MD network. Moreover, a detailed analysis of HRTEM simulated images is undertaken, and strain maps along the 〈0 0 0 1〉 direction are obtained in order to establish the local arrangement of Moiré fringes and clarify experimental controversies.