Theoretical Lower Limit of Coercive Field in Ferroelectric Hafnia
Jiyuan Yang, Jing Wu, Jingxuan Li, Chao Zhou, Yang Sun, Zuhuang Chen, Shi Liu
Abstract
The high coercive field ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi mathvariant="script">E</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> ) of hafnia-based ferroelectrics presents a major obstacle to their applications. The ferroelectric switching mechanisms in hafnia that dictate <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi mathvariant="script">E</d:mi> <d:mi>c</d:mi> </d:msub> </d:math> , especially those related to domain nucleation in the nucleation-limited-switching (NLS) model and domain-wall motion in the Kolmogorov-Avrami-Ishibashi (KAI) model, have remained elusive. We develop a deep-learning-assisted multiscale approach, incorporating atomistic insights into the critical nucleus, to predict both NLS- and KAI-type coercive fields. The theoretical NLS-type <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi mathvariant="script">E</g:mi> <g:mi>c</g:mi> </g:msub> </g:math> values agree with previous experimental results as well as our own measurements and also exhibit the correct thickness scaling for films between 3 and 20 nm. Combined theoretical and experimental investigations reveal that the giant <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi mathvariant="script">E</j:mi> <j:mi>c</j:mi> </j:msub> </j:math> in hafnia-based ferroelectrics arises from the ultrathin geometry, which confines switching to the NLS mechanism. We predict that the theoretical lower limit for KAI-type <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi mathvariant="script">E</m:mi> <m:mi>c</m:mi> </m:msub> </m:math> is <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:mn>0.1</p:mn> <p:mtext> </p:mtext> <p:mtext> </p:mtext> <p:mi>MV</p:mi> <p:mo>/</p:mo> <p:mi>cm</p:mi> </p:mrow> </p:math> arising from mobile domain walls. The activation of KAI-type switching to achieve lower <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi mathvariant="script">E</r:mi> <r:mi>c</r:mi> </r:msub> </r:math> is supported by our experimental demonstration of a low coercive field of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:mn>1</u:mn> <u:mtext> </u:mtext> <u:mtext> </u:mtext> <u:mi>MV</u:mi> <u:mo>/</u:mo> <u:mi>cm</u:mi> </u:mrow> </u:math> in 60 nm ferroelectric <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mo stretchy="false">(</w:mo> <w:mrow> <w:msub> <w:mrow> <w:mi>HfO</w:mi> </w:mrow> <w:mrow> <w:mn>2</w:mn> </w:mrow> </w:msub> </w:mrow> <w:msub> <w:mrow> <w:mo stretchy="false">)</w:mo> </w:mrow> <w:mrow> <w:mi>n</w:mi> </w:mrow> </w:msub> <w:mo>/</w:mo> <w:mo stretchy="false">(</w:mo> <w:mrow> <w:msub> <w:mrow> <w:mi>ZrO</w:mi> </w:mrow> <w:mrow> <w:mn>2</w:mn> </w:mrow> </w:msub> </w:mrow> <w:msub> <w:mrow> <w:mo stretchy="false">)</w:mo> </w:mrow> <w:mrow> <w:mi>n</w:mi> </w:mrow> </w:msub> </w:mrow> </w:math> ( <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>n</cb:mi> <cb:mo>=</cb:mo> <cb:mn>3</cb:mn> </cb:math> unit cells) superlattices. These findings establish a comprehensive framework for understanding ferroelectric switching in hafnia and highlight the potential of geometry and domain-wall engineering to achieve low- <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi mathvariant="script">E</eb:mi> <eb:mi>c</eb:mi> </eb:msub> </eb:math> devices.