Towards a deeper fundamental understanding of (Al,Sc)N ferroelectric nitrides

Abstract

Density Functional Theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters being determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely the 4-fold-coordinated wurtzite (WZ) polar structure and a 5-times paraelectric hexagonal phase (to be denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest energy state within hexagonal symmetry as the Sc concentration increases from 0 to 40%. Furthermore, the model points out to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters, one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows to reproduce well their finite-temperature polar properties, and that a value of the axial ratio close to that of the ideal WZ structure does imply a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices operating at low voltages.