Effect of mechanical loads on stability of nanodomains in ferroelectric ultrathin films: towards flexible erasing of the non-volatile memories

Abstract

Intensive investigations have been drawn on nanoscale ferroelectrics for their prospective applications such as developing memory devices. In contrast with the commonly used electrical means to process (i.e., read, write or erase) the information carried by ferroelectric domains, at present, mechanisms of non-electrical processing ferroelectric domains are relatively lacking. Here we make a systematical investigation on the stability of 180° cylindrical domains in ferroelectric nanofilms subjected to macroscopic mechanical loads, and explore the possibility of mechanical erasing. Effects of domain size, film thickness, temperature and different mechanical loads, including uniform strain, cylindrical bending and wavy bending, have been revealed. It is found that the stability of a cylindrical domain depends on its radius, temperature and film thickness. More importantly, mechanical loads have great controllability on the stability of cylindrical domains, with the critical radius nonlinearly sensitive to both strain and strain gradient. This indicates that erasing cylindrical domain can be achieved by changing the strain state of nanofilm. Based on the calculated phase diagrams, we successfully simulate several mechanical erasing processes on 4 × 4 bits memory devices. Our study sheds light on prospective device applications of ferroelectrics involving mechanical loads, such as flexible memory devices and other micro-electromechanical systems.

Figure 1. Schematic illustration of mechanical loads on stability of cylindrical domains in ferroelectric ultrathin films.

(a) The model system. The left panel depicts the investigated subject, a ferroelectric nanofilm divided into rectangular memory units. Some of the memory units of the initially poled nanofilm are written with 180° cylindrical domains, to carry bit information. The right panel depicts the top view of a basic memory unit with a cylindrical domain of radius r. (b) Application of common mechanical loads to the nanofilm with written pattern to explore domain stability and the possibility of mechanical erasing. (i) Uniform strain, (ii) cylindrical bending, and (iii) wavy bending.

Figure 2. Phase diagram of equilibrium domain pattern.

In-plane distributions of (a) polarization and (b) strain field at the top surface of a 128 nm × 128 nm × 8 nm simulation cell written with a cylindrical domain (r = 16 nm) at room temperature. Phase diagrams of equilibrium domain pattern in (c) 128 nm × 128 nm × h cells as a function of thickness h and domain size r at room temperature, and in (d) 128 nm × 128 nm × 8 nm cells as a function of temperature and domain size r. The cells are initially written with cylindrical domains with size r ranging from 1 nm to 64 nm. (e) and (f) the critical size of stable cylindrical domain as a function of thickness and temperature, respectively.

Figure 3. Equilibrium domain patterns under different external biaxial strains.

Equilibrium domain patterns of a 128 nm × 128 nm × 8 nm simulation cell under different external biaxial strains, i.e., , −0.005, 0 and 0.005. The cell is with an initial random polarization distribution. The green arrows indicate some small domains that are stable at .

Figure 4. Control of domain stability by uniform strain.

Control of domain stability by uniform strain on 128 nm × 128 nm × 8 nm simulation cells at room temperature. The cells are initially written with cylindrical domains with size r from 1 nm to 64 nm. (a) Schematics of a cell under biaxial strain () and uniaxial strain (). Domain evolution in a cell with cylindrical domain (r = 16 nm) under (b) and (c) . Phase diagrams of equilibrium domain pattern in cells under (d) uniaxial stain and (e) biaxial strain. (f) and (g) The average polarization of the equilibrium domain patterns in z-direction, i.e., <P₃>, in the initial cylindrical domain region, for the two loading cases.

Figure 5. Control of domain stability by cylindrical bending.

Control of domain stability by cylindrical bending on 128 nm × 128 nm × 8 nm simulation cells at room temperature. The cells are initially written with cylindrical domains with size r from 1 nm to 64 nm. (a) Schematics of a cell under cylindrical bending, i.e., . Distribution of as a function of ε_top in the x-z plane of a cell under (b) pure bending (ε_top = −ε_bot) and (c) mixed bending-strain (ε_top ≠ 0, ε_bot = 0). Phase diagrams of equilibrium domain pattern in cells under (d) pure bending and (e) mixed bending strain conditions. (f) and (g) The average polarization of the equilibrium domain patterns in z-direction, i.e., <P₃>, in the initial cylindrical domain region, for the two bending cases.

Figure 6. Control of domain stability by wavy bending.

Control of domain stability by wavy bending on 128 nm × 128 nm × 8 nm simulation cells at room temperature. The cells are initially written with cylindrical domains with size r from 1 nm to 64 nm. (a) Schematics of a cell under wavy bending, i.e., , with λ = 128 nm. Distribution of (b) and (c) flexoelectric field as a function of A_b in the x-z plane of a cell under wavy bending. Phase diagrams of equilibrium domain pattern in cells under wavy bending with flexoelectric field (d) switched off and (e) on. (f) and (g) The average polarization of the equilibrium domain patterns in z-direction, i.e., <P₃>, in the initial cylindrical domain region, for the two bending cases.

Figure 7. Mechanical erasing of the information in nano-ferroelectric memories.

Mechanical erasing of the information in 4 × 4 bits memory systems. (a) A 256 nm × 256 nm × 8 nm memory system written with 4 × 4 bits of information carried by cylindrical domains of r = 16 nm. Total erasing of the information of this system is demonstrated by applying (b) uniform biaxial strain () or (c) cylindrical bending (ε_top = −ε_bot = 0.006). (d) Making use of nontrivial flexoelectric effect, partial erasing can be achieved by applying wavy bending (A_b = 1.0 nm and λ = 128 nm) to the system. By changing the bending wave phase by π, the remaining information is also erased. (e) A 256 nm × 256 nm × 6 nm memory system written stable information at the valleys under wavy bending (A_b = 0.2 nm and λ = 128 nm). (f) The information is erased after removing the wavy bending.