Intersections of two stacking faults in zincblende GaN
Introduction
Gallium nitride (GaN) is a wide-bandgap semiconductor that is frequently used in electronic and optoelectronic applications such as high electron mobility transistors, LEDs and laser diodes [1], [2], [3], [4], [5]. It crystallizes in the hexagonal wurtzite structure (B4, Pmc, No. 186), but a metastable cubic zincblende structure (B3, F3 m, No. 216) can be stabilized by epitaxial strain [6], [3], [5], [7], [4], [8] when growing GaN films on cubic substrates such as GaAs, SiC or Si . The absence of polarization fields and the lower band gap energy of zincblende GaN potentially enables for strong emission in the green part of the spectrum [2], [7], which makes this material an ideal candidate to solve the green gap problem [9], [2], [7], [10] and thus to manufacture green LEDs.
The stacking sequence of zincblende GaN in closed-packed directions is AaBbCc, where the capital and lower-case letters represent Ga and N, respectively. Each atom is tetrahedrally coordinated with four atoms of the other type. Similarly as in the diamond structure a planar stacking fault can be created by cutting the crystal along two different planes, which differ by the distance of atoms when viewed in the direction perpendicular to the normal of this plane. If the cut is made within a double-layer, i.e. between two atomic planes marked by the same letter such as A:aBbCc (colon shows the position of the cut), the resulting fault represents a shuffle set. On the other hand, a cut made between two consecutive double-layers, i.e. between two planes marked with different letters such as Aa:BbCc, produces a planar stacking fault in the glide set.
Hull and Bacon [11] reviewed stacking faults in the cubic diamond structure, which are common also to the zincblende structure. The intrinsic fault representing the glide set, AaBbCcAaBbCc , is formed by removing one double-layer (here Aa) or, equivalently by displacing a half of the crystal above the first Cc double-layer (after the colon) in the direction. The underlined and overlined sequences clearly represent two wurtzite stackings. Owing to lower energy of the wurtzite structure in GaN compared to the zincblende phase, the formation of this stacking fault will lead to the reduction of energy [2], [12], [13], [14], [6], [15], [16]. The extrinsic fault, AaBbCcAaBbCc , is formed by inserting an extra double-layer (here Bb) and contains again two wurtzite stacking sequences (underlined and overlined). Equivalently, this fault can be formed by cutting the crystal at the positions of the two colons and shearing it in between to bring the stacking into the sequence shown. The last stacking fault, a twin, is a three-layer (or more) stacking fault AaBbCcAaBbCc that again contains two wurtzite stacking sequences (underlined, overlined). Similarly as above, the twin is created by shearing a part of the crystal between the two colons shown. Using a simple Ising-like model, Wright [14] showed that all three faults have negative stacking fault energies (SFEs) in zincblende GaN, which suggests that planar stacking faults may form spontaneously to reduce the energy. The extrinsic fault was found to have the largest negative energy (i.e., it is most stable), followed by the intrinsic fault, and the twin that is the least stable of the three.
The stacking faults on all four planes in the zincblende structure are crystallographically equivalent and thus a growing zincblende GaN film will generally contain stacking faults on all these planes. This will inevitably lead to their intersections and, therefore, further film growth is expected to be controlled by the structures and energies of these intersections. The stacking faults are indeed frequently observed in GaN films grown epitaxially on cubic substrates such as -oriented 3C-SiC as shown in Fig. 1.
Atomistic calculations of the energies of generalized stacking faults and the associated surfaces [17] for diamond lattices have provided ample evidence that metastable stacking faults can form in the glide set [18]. On the other hand, no metastable stacking faults exist in the shuffle set. Since the atomic positions in the zincblende structure are the same as those in the cubic diamond structure, similar arguments are expected to hold in the case of zincblende GaN. However, these conclusions may break down when two stacking faults formed on non-coplanar planes intersect, which will lead to additional reconstructions of the crystal structure in the vicinity of the intersection of these planes.
The objective of this paper is to investigate the interactions of two different stacking faults in zincblende GaN by atomistic simulations. In the first step, we calculate the surface resulting from the formation of a single planar stacking fault in the glide and shuffle set. In the second step, we consider a situation, whereby the intrinsic stacking fault is created on one plane and another stacking fault is created on a different plane. The structures and energies of these intersections are investigated when the second fault is in the glide and shuffle set. Additionally, we investigate also the configuration, where one stacking fault is planar and the second fault on a different plane is non-planar, which was considered previously in a purely geometrical manner [19]. The results of these atomistic simulations are correlated with scanning transmission electron microscopy (STEM) investigations of the intersections of these faults in cubic zincblende GaN grown on 3C-SiC.
Section snippets
Isolated stacking faults
In all calculations made in this work, the interactions between atoms are described using the Tersoff-Brenner potential for GaN developed by Nord et al. [20] that captures correctly the angular dependence of the bond order. This description is purely covalent and the ionic contribution to bonds is included only indirectly by fitting the potential parameters to existing experimental data and DFT calculations. Since point charges are not considered as independent degrees of freedom and the
Intersections of two planar stacking faults
Epitaxial growth of zincblende GaN generally leads to nucleation of stacking faults on all four crystallographically equivalent planes. This gives rise to intersections of these faults and thus also to reconstructions of atomic positions along the line common to both fault planes. In order to investigate the structures and energies of these intersections, we use in the following a cylindrical simulation cell shown in Fig. 4(a), where the regions I and II have the same meaning as those
Intersections of one planar and one non-planar stacking fault
We have seen in the previous section that when the second stacking fault is at the position II or III in Fig. 4(b), one-half of the fault on the plane has the rocksalt structure, which is responsible for large . It would be more energetically favorable if the second stacking fault was created such that the atoms around this fault had locally wurtzite stacking. Such a configuration is indeed possible, but in this case the second fault cannot be planar. This was studied geometricaly by
Conclusions
Using atomistic simulations, we have investigated the structures and energies of three types of stacking fault configurations:
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Planar stacking faults on planes made in the glide and shuffle set. Only the stacking fault created in the glide set leads to stable stacking faults that are represented by the fault vector 1/6.
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Intersections of two planar stacking faults - an intrinsic fault on the plane and all possible planar stacking faults on the intersecting plane that lead
Data availability
The raw data required to reproduce these findings are available from authors upon request.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research was carried out under the project CEITEC 2020 (LQ1601) with financial support from the Ministry of Education, Youth and Sports of the Czech Republic under the National Sustainability Programme II. It was supported by CEITEC BUT, Brno University of Technology (Grant No. CEITEC VUT-J-19-5965). CzechNanoLab project LM2018110 funded by MEYS CR is gratefully acknowledged for the financial support of the measurements and sample fabrication at CEITEC Nano Research Infrastructure.
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