A Phenomenological Thermodynamic Energy Density Function for Ferroelectric Wurtzite Al_1-xSc_xN Single Crystals

In this work, we develop a composition-dependent Landau-Devonshire free energy density function for aluminum scandium nitride (Al_1-xSc_xN) using the layered hexagonal structure as the high-symmetry centrosymmetric reference state. By assuming a linear dependence of the second-order Landau coefficient on Sc concentration, the energy function accounts for compositional effects on the total free energy. The parameters of the thermodynamic energy function are fitted to existing experimental and theoretical data. With composition-dependent stiffness constants and electrostrictive coefficients, the free energy density accurately reproduces key ferroelectric properties such as spontaneous polarization, relative permittivity, and piezoelectric coefficients. A notable divergence in relative permittivity is observed at the critical composition where the ferroelectric transition occurs. We further analyze Al_1-xSc_xN thin films under biaxial substrate strain and find that the strain has minimal impact on the critical composition or the phase boundary between ferroelectric and non-ferroelectric wurtzite phases. These results demonstrate the feasibility of applying this composition-dependent Landau-Devonshire energy function to describe novel wurtzite-type ferroelectric solid solutions. The developed energy function serves as a foundational tool for quantitatively modeling Al_1-xSc_xN and can be extended to more complex models such as phase-field. This advancement enables potential quantitative studies of inhomogeneous ferroelectric switching and finite-size effects, thereby promoting the integration of these promising materials into microelectronic devices.