Tip-based proximity ferroelectric switching and piezoelectric response in wurtzite multilayers

Proximity ferroelectricity is a paradigm for inducing ferroelectricity when a nonferroelectric polar material (such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>Al</a:mi> <a:mi mathvariant="normal">N</a:mi> </a:mrow> </a:math> ), which is unswitchable with an external field below the dielectric breakdown field, becomes a practically switchable ferroelectric in direct contact with a thin switchable ferroelectric layer (such as <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>Al</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mo>−</d:mo> <d:mi>x</d:mi> </d:mrow> </d:msub> <d:msub> <d:mi>Sc</d:mi> <d:mi>x</d:mi> </d:msub> <d:mrow> <d:mrow> <d:mi mathvariant="normal">N</d:mi> </d:mrow> </d:mrow> </d:math> ). Here, we develop a Landau-Ginzburg-Devonshire approach to study the proximity effect of local piezoelectric response and polarization reversal in wurtzite ferroelectric multilayers under a sharp electrically biased tip. Using finite-element modeling, we analyze the probe-induced nucleation of nanodomains, the features of local polarization hysteresis loops and coercive fields in the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>Al</g:mi> <g:mrow> <g:mn>1</g:mn> <g:mo>−</g:mo> <g:mi>x</g:mi> </g:mrow> </g:msub> <g:msub> <g:mi>Sc</g:mi> <g:mi>x</g:mi> </g:msub> <g:mrow> <g:mrow> <g:mi mathvariant="normal">N</g:mi> </g:mrow> </g:mrow> <g:mo>/</g:mo> <g:mrow> <g:mi>Al</g:mi> <g:mi mathvariant="normal">N</g:mi> </g:mrow> </g:math> bilayers and three-layers. Similar to the wurtzite multilayers sandwiched between two parallel electrodes, the regimes of “proximity switching” (when all layers collectively switch) and the regime of “proximity suppression” (when they collectively do not switch) are the only two possible regimes in the probe-electrode geometry. However, the parameters and asymmetry of the local piezoresponse and polarization hysteresis loops depend significantly on the sequence of the layers with respect to the probe. The physical mechanism of proximity ferroelectricity in the local probe geometry is a depolarizing electric field determined by the polarization of the layers and their relative thickness. The field, whose direction is opposite to the polarization vector in the layer(s) with the larger spontaneous polarization (such as <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>Al</k:mi> <k:mi mathvariant="normal">N</k:mi> </k:mrow> </k:math> ), renormalizes the double-well ferroelectric potential to lower the steepness of the switching barrier in the “otherwise unswitchable” polar layers. Tip-based control of domains in otherwise nonferroelectric layers using proximity ferroelectricity can provide nanoscale control of domain reversal in memory, actuation, sensing, and optical applications. The ability of the tip-induced proximity switching to differentially switch multilayers, based on the order of the layers, provides a powerful tool for selective domain engineering.