Proposal for an electrostrictive logic device with the epitaxial oxide heterostructure

The possible use of electrostrictive materials for information processing devices has been widely discussed because it could allow low-power logic operation by overcoming the fundamental limit of subthreshold swing greater than 60 mV/decade in conventional MOSFETs. However, existing proposals for electrostrictive FET applications typically adopt approaches that are entirely theoretical and simulative, thus lacking practical insights into how an electrostrictive material can be best interfaced with a channel material. Here we propose an electrostrictive FET device, involving the epitaxial oxide heterostructure as an ideal material platform for maximum strain transfer. The ON/OFF switching occurs due to a stress-induced concentration change of oxygen vacancies in the memristive oxide channel layer. Based on finite-element simulations, we show that the application of a minimal gate voltage bias can induce stress in the channel layer as high as 108 N/m2 owing to the epitaxial interface between the electrostrictive and memristive oxide layers. Conductive AFM experiments further support the feasibility of the proposed device by demonstrating the stress-induced conductivity modulation of a perovskite oxide thin film, SrTiO3, that is well known to serve as the substrate for epitaxial growth of other functional oxide layers.

. An electrical potential distribution throughout the piezoelectric material layer under an applied gate voltage bias of 1V.

Tensor Equations, Material Parameters, and Other Simulation Details
Fundamental electrostrictive physics utilizes a compliance matrix, (the tensor rank of 4), a coupling matrix, (the tensor rank of 3), and the relative permittivity ( ) at constant stress (the tensor rank of 2) [1]. Full tensor equations that correspond to Eq. (1) and (2) in the main manuscript are written as: ) ( ) The Voigt notation helps to represent symmetric tensors by reducing their order. The Voigt form of compliance, coupling, and relative permittivity matrices are illustrated below in Table S1.
The material parameters used in our simulation are summarized below in Table S2. In addition to a basic set of parameters such as density (ρ, in kg/m 3 ), Young's modulus (E, in Pa), and Poisson's ratio (ν, dimensionless) (see Table S2(a)), the use of an electrostrictive material requires us to enter the elements of the above matrices ( , and ) (see Table S2(b)). It is noted that since our simulation adopts an experimentally benchmarked model, the d33 parameter takes a range of values rather than a single, fixed value; depending on the thickness of the BTO layer, d33 changes from 3.13×10 -13 (C/N) to 7.38×10 -12 (C/N). These values are based on experimental measurements with the BTO thin films [2], which are quite different from the built-in value in the COMSOL material library (8.56×10 -11 C/N). For values that are not directly available from the experimental work, we used the extrapolation technique by implementing the line graph equation and using the graph reading software [3].  Regarding other simulation details, it is important to note that tetrahedral extra-fine meshing was applied only to the STO layer for computational efficiency. Because the focus of our simulative work is to investigate the maximum stress level induced at the STO layer, normal mesh conditions applied to the other layers (gate electrode, piezoelectric layer, and substrate) did not alter the main scope of our work or the simulation result.

C-AFM Experiments
In order to perform the electromechanical coupling experiments (i.e., stress-induced conductivity modulation) with the (Bruker Innova Series) C-AFM instrument, the control parameter of the experimental setup (Vsetpoint) needs to be precisely converted to the mechanical pressure (N/m 2 ). This conversion is based on the Hooke's law (i.e., Force is the product of spring constant and displacement). With the spring constant (N/m) and the deflection sensitivity (m/V) values separately obtained from the built-in calibration software, the amount of applied forces could be calculated for a given value of the setpoint voltage (displacement is the product of deflection sensitivity and setpoint voltage). The pressure is then calculated by dividing the force by the contact area where the force is applied. For each pressure applied, the resistance was measured using the conductive tip (Asyelec.01-R2), and the conductivity of the STO thin film was finally calculated. All relevant equations are summarized below.
The spring constant calibration was performed in the contact AFM mode, where a thermal tune spectrum was plotted to fit with a simple harmonic oscillator model with the resonance frequency and Q-factor parameters. The deflection sensitivity was calculated in the C-AFM mode, performing the point spectroscopy (photodetector signal vs. piezo-movement) measurements on the sample and extracting the slope of the repulsive portion in the resulting plot. Fig. S2 shows the measured current-voltage (I-V) characteristic of the STO-based two-terminal device, fabricated using the simple shadow mask technique (top electrode contact/STO/silicon/bottom electrode contact). A clear hysteresis is observed in the DC bias sweep, indicating that oxygen-vacancy controlled memristive switching can enable ON/OFF switching required for electrostrictive FET operations. In this demonstration, a relatively thin (9 nm-thick) film of single-crystalline STO was prepared by the MBE technique with a decent amount of oxygen vacancies introduced during the growth.