Computing Equilibrium Shapes of Wurtzite Crystals: The Example of GaN

TL;DR

This paper presents a method to predict equilibrium shapes of wurtzite crystals like GaN using an extended Wulff construction, accounting for polar and semipolar surfaces, and relates these shapes to experimental nanostructures.

Contribution

It extends the Wulff construction to polar and semipolar surfaces of wurtzite crystals, enabling prediction of equilibrium shapes from surface energies.

Findings

Different crystal shapes depend on chemical potential.

Predicted shapes explain observed GaN nanostructures.

Method improves understanding of crystal morphology in nanomaterials.

Abstract

Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. 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. By extending the concept of Wulff construction, we demonstrate that the ECSs can nevertheless be obtained for this class of materials. For the example of GaN, we identify different crystal shapes depending on the chemical potential, shedding light on experimentally observed GaN nanostructures.