Computing equilibrium shapes of wurtzite crystals: the example of GaN

Low-dimensional semiconductor nanostructures have attracted a lot of interest in the past decades, largely due to their applications in low-energy consumption and energy-harvesting devices. Owing to surface effects, the performance of such devices strongly depends on the nanocrystal morphology. To achieve comprehensive understanding and control of the preferred growth morphology, one must know the material’s natural shape that results from its crystallographic anisotropy. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are hard to access experimentally but can generally be well predicted by first-principles methods. Unfortunately, this is not necessarily so for polar and semipolar surfaces of wurtzite crystals.

Figure 1: GaN crystals under thermodynamic equilibrium conditions. The shape varies continuously from Ga-rich conditions(left) to N-rich conditions (right). The labels—pyramid I,truncated pyramid, and pyramid II—refer to the top shape.

By extending the concept of Wulff construction, we demonstrate that ECSs can nevertheless be obtained for this class of materials. It is found that for each semipolar plane, the relative energy with respect to its neighboring polar plane can be unambiguously computed as a function of chemical potential. This energy difference, corresponding to the crystal radius along the polar axis, is the important quantity that governs the crystal shape.


We have exemplified our approach with wurzite GaN. Taking into account several bulk-truncated surfaces, ECSs have been constructed. These crystals exhibit a rodlike shape along the polar c axis, with top and bottom geometries depending on the chemical potential, while the side walls are formed by both types of nonpolar surfaces. Our results can well explain the experimentally observed nanowire shapes. They also open a perspective to gaining insight into morphologies of the entire class of polar materials, concerning point groups of 6, 6 mm, 4, 4 mm, 3, 3 mm, 2, and 2 mm, where such polar axes exist.

1 Author H. Li , L. Geelhaar , H. Riechert , C. Draxl

Computing Equilibrium Shapes of Wurtzite Crystals: The Example of GaN

Source Phys. Rev. Lett. , 115 , 085503 ( 2015 )
DOI : 10.1103/PhysRevLett.115.085503 | Download: PDF | 2651 Cite : Bibtex RIS
H. Li, L. Geelhaar, H. Riechert, and C. Draxl