Machine learning-based interatomic potential development and phase transition analysis of ferroelectric hafnium dioxide

The ferroelectric phase ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>P</a:mi> <a:mi>c</a:mi> <a:mi>a</a:mi> <a:msub> <a:mn>2</a:mn> <a:mn>1</a:mn> </a:msub> </a:mrow> </a:math> , which is in orthorhombic symmetry) of hafnium dioxide <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mo>(</b:mo> <b:msub> <b:mi>HfO</b:mi> <b:mn>2</b:mn> </b:msub> <b:mo>)</b:mo> </b:math> has gained much attention due to its potential applications in nanoelectronics and advanced memory devices. However, its complex phase behavior under external stimuli, such as pressure and temperature, remains a subject of intense investigation. This study focuses on developing a machine learning-based interatomic potential (MLIP) that is trained with data from density-functional theory (DFT) calculations to simulate phase transitions and mechanical properties of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>HfO</c:mi> <c:mn>2</c:mn> </c:msub> </c:math> . The developed MLIP predicts lattice parameters, equations of state, bulk and shear moduli, and elastic constants that closely align with DFT predictions for several phases and at various pressures. Once validated, the MLIP is used to investigate the phase transitions of ferroelectric <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>HfO</d:mi> <d:mn>2</d:mn> </d:msub> </d:math> <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mo>(</e:mo> <e:mi>P</e:mi> <e:mi>c</e:mi> <e:mi>a</e:mi> <e:msub> <e:mn>2</e:mn> <e:mn>1</e:mn> </e:msub> <e:mo>)</e:mo> </e:mrow> </e:math> under both isobaric and constant stress conditions at elevated temperatures ranging from 200 to 2500 K. We used several complementary methods, including local symmetry identification, radial distribution function, and x-ray diffraction characterization, to identify interesting phase transitions among several competitive hafnia phases predicted from our simulations. The suggested methods uniformly reveal that under pure deviatoric condition, the system favors a transition from the orthorhombic <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>P</f:mi> <f:mi>c</f:mi> <f:mi>a</f:mi> <f:msub> <f:mn>2</f:mn> <f:mn>1</f:mn> </f:msub> </f:mrow> </f:math> phase to a tetragonal ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>P</g:mi> <g:msub> <g:mn>4</g:mn> <g:mn>2</g:mn> </g:msub> <g:mo>/</g:mo> <g:mi>n</g:mi> <g:mi>m</g:mi> <g:mi>c</g:mi> </g:mrow> </g:math> ) phase, whereas a zero stress condition drives the system from the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>P</h:mi> <h:mi>c</h:mi> <h:mi>a</h:mi> <h:msub> <h:mn>2</h:mn> <h:mn>1</h:mn> </h:msub> </h:mrow> </h:math> phase to another orthorhombic <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mo>(</i:mo> <i:mi>P</i:mi> <i:mi>b</i:mi> <i:mi>c</i:mi> <i:mi>n</i:mi> <i:mo>)</i:mo> </i:mrow> </i:math> phase. These findings provide crucial insights into stress and temperature-induced phase behavior of hafnia, guiding future experimental and theoretical studies for optimizing hafnia-based ferroelectric devices.