1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Phase field model of domain dynamics in micron scale, ultrathin ferroelectric films: Application for multiferroic bismuth ferrite
Rent:
Rent this article for
USD
10.1063/1.4754800
/content/aip/journal/jap/112/7/10.1063/1.4754800
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/7/10.1063/1.4754800
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Schematic of a representative device structure that is used as a test case for the developed method. Here, a thin film of ferroelectric material is grown on a substrate. Two electrodes are placed in order to apply an in-plane electric field. The electrostatic boundary condition on the material can be changed by using different materials on the ferroic thin film. The substrate strain can be varied by changing the substrate material with different lattice vectors. (b) The implemented numerical grid that contains both finite difference and finite element grids. The elements are a small block of linear brick element. The nodes of the block coincide with the FD grid. Both FEM and the FD grids are numbered in natural ordering.

Image of FIG. 2.
FIG. 2.

(a) FEM structure assembly by element. The newly added element (e8) nodes have matrix element contributions from the 7 elements (e1-7). Note that the contributing elements are only those that precede this element in the natural grid along the three directions. (b) FEM structure matrix assembly by node. The node in consideration is 26 (violet star). Due to the element connectivity the node has interaction with its in-plane surrounding nodes and also the layers above and below this node (green stars). Each node has a total of 26 connected nodes within the body of the structure. The number of connected element and nodes vary at the boundary. These boundary nodes and elements are assembled in a similar procedure with appropriate connectivity.

Image of FIG. 3.
FIG. 3.

(a) The FEM stiffness matrix assembly time as a function of the number of processors used with varying grid size. (b) The total cycle time for 6 iterations including the nonlocal electrostatic and elastic interactions as a function of the number of processors used with varying grid size. (c) Using a non-zero initial guess from the last time step solution, for the linear solver during the electrostatic and elastic interaction calculation improves the overall performance of the by a factor of 2 for all number of processors used. (d) Calculation of the long range interactions every 5 steps compared to every single step, improved the performance by about 4 times. This does not change the physical results since, the long range interactions usually act at low frequency compared to the short range interaction. For all the three structure sizes, we obtain linear scaling.

Image of FIG. 4.
FIG. 4.

Evolution of the polarization on the (001) surface under short circuit boundary condition. (a) The initial domain pattern with left (light blue) and up (red) polarization domains. (b) Nucleation of right polarization domain (yellow) through switching of up domains. (c) switched domain (yellow) grows. (d),(e) A new domain grows towards south (deep blue) and eventually switches the whole domain. The global polarization switches by in the process. (f) Experimental observation of switch of the domains under a short circuit boundary condition. Reprinted with permission from Phys. Rev. Lett. 107, 217202 (2011). Copyright 2011 American Physical Society.

Image of FIG. 5.
FIG. 5.

Evolution of the polarization on the (001) surface with an open boundary condition. (a) The initial domain pattern with left (light blue) and up (red) oriented polarization domains. (b) Anisotropic growth of right oriented domain (yellow) through a switch of the up (red) oriented polarization to right oriented domain (yellow). (c) The up (red) oriented domain grows simultaneously through domain wall switching of the left (light blue) domain. (d) Emergence of domain patterns (between red and yellow domains) aligned at to the initial domain pattern. (e),(f) PFM image showing the switch of domain pattern under open circuit boundary condition. Reprinted by permission from Macmillan Publishers Ltd: Nature Materials, 7, 478 (2008). Copyright 2008.

Image of FIG. 6.
FIG. 6.

Evolution of the polarization on the (001) surface with an open boundary condition without considering the domain wall charge. (a) The initial domain pattern. (b) Isotropic growth of right oriented polarization domain (yellow) through an switch of the up polarization (red). (c),(d) Gradual isotropic growth of the switched domain (yellow) due to the applied field. The emergent domains that do not have a specific stripe like pattern since the effect of charge was ignored.

Image of FIG. 7.
FIG. 7.

Evolution of the polarization on the (001) surface with an open boundary condition when a field is applied along the [100] direction. (a) The initial domain pattern with a defect introduced where the switching starts (dark blue and red dot). (b) Anisotropic growth of right oriented polarization domain (dark blue and red) through a switch of the left polarization (light blue and yellow) along the applied field direction. (c) The anisotropic growth continues and switches regions close to the electrode. Slow growth perpendicular to the applied field and retention of the domain size matches very well with the experimental observation. (d),(e) Experimental data showing the intermediate stage between switching. Reprinted with permission from Appl. Phys. Lett. 97, 062910 (2010). Copyright 2010 American Institute of Physics.

Image of FIG. 8.
FIG. 8.

Evolution of the polarization on the (001) surface with an open boundary condition when a field is applied along the [100] direction without considering the domain wall charge. (a) The initial domain pattern with a defect introduced where the switching starts. (b) Isotropic growth of right oriented polarization domain (dark blue) through a switch of the left polarization (light blue) along the applied field direction.

Loading

Article metrics loading...

/content/aip/journal/jap/112/7/10.1063/1.4754800
2012-10-01
2014-04-21
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Phase field model of domain dynamics in micron scale, ultrathin ferroelectric films: Application for multiferroic bismuth ferrite
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/7/10.1063/1.4754800
10.1063/1.4754800
SEARCH_EXPAND_ITEM