Ferroelectrics

A ferroelectric material in general is defined by the existence of a permanent spontaneous polarization P_s at temperatures below the Curie temperature whereby the direction of P_s can be reversed by the application of an electric field exceeding the coercive field E_c. The value of E_c is defined using the hysteresis loop which can be recorded during a poling cycle ramping up and down the applied electric field. Theoretical calculations of the value of E_c failed up to now. A ferroelectric material is by nature always piezoelectric and also pyroelectric.

Ferroelectric domains
A ferroelectric domain is an area of oriented spontaneous polarization. Local poling, i.e. the controlled formation of domains, makes of ferroelectrics very important materials for applications such as data storage devices or optical frequency converters. The controlled formation of domains is therefore of major importance. In general, local poling is performed by locally applying an electric field surpassing E_c using structured electrodes, named electric field poling (EFP). We investigated a new technique for controlled domain formation thereby defining the domain pattern by UV-laser light irradiation. Another technique under investigation for local poling consists in the application of an electric field with the help of a scanning probe microscope tip, named tip-based domain formation.

Domain formation by UV-laser irradiation
In close collaboration with Sakellaris Mailis from the ORC in Southampton, GB.
This method for domain revesal uses a tightly focused, strongly absorbed UV-laser beam to define the area of domain reversal. Scanning the laser beam across the LiNbO₃ surface results either in poling inhibition (+z) or in direct writing (-z and the non-polar x- and y-faces). This method for domain reversal allow for the formation of domain patterns irrespective of the crystallographic preferences (a domain growth along the y-axis) and further more avoids the cumbersome and expensive clean-room processing required for EFP.

The domain patterns obtained by UV-laser irradiation are seen in the opposed figure, recorded with piezoresponse force microscopy. (a) shows a PPLN structure (horizontal stripes) where three lines (perpendicular stripes) have been written across by scanning the UV-laser beam. The black area represents a -z face, the bright one a +z face. The crystal underwent no further processing. Obviously, direct domain inversion took place in on the -z face whereas the +z face remained unchanged. In (b) an example of poling inhibition is shown. Prior to large area EFP, the crystals +z face was irradiated with UV laser spots. In the EFP poling step, part of the crystal was poled (seen as dark area) - the spots however resisted poing. Finally (c) shows an example of direct writing on a x face of LiNbO₃surface. As it can be seen from the thermoinduced cracks, only half or the width of the laser-beam was domain inverted.

The domain patterns obtained by UV-laser irradiation are seen in the opposed figure, recorded with piezoresponse force microscopy. (a) shows a PPLN structure (horizontal stripes) where three lines (perpendicular stripes) have been written across by scanning the UV-laser beam. The black area represents a -z face, the bright one a +z face. The crystal underwent no further processing. Obviously, direct domain inversion took place in on the -z face whereas the +z face remained unchanged. In (b) an example of poling inhibition is shown. Prior to large area EFP, the crystals +z face was irradiated with UV laser spots. In the EFP poling step, part of the crystal was poled (seen as dark area) - the spots however resisted poing. Finally (c) shows an example of direct writing on a x face of LiNbO₃surface. As it can be seen from the thermoinduced cracks, only half or the width of the laser-beam was domain inverted.

Tip-based domain formation in He-implanted LiNbO₃
In close collaboration with Richard Osgood from Columbia University, USA.
Driven by the progess of smart-cut technology which allows to fabricate lithium niobate thin film single crystals we investigated the possibility of domain formation in He-implanted crystals. In view of their further applicability for photonic crystal devices, we focused on large-area nano-domain patterning.

	PFM-image of a cross-section of a He-implanted sample. (a) shows the schematics of the sample under investigation. In (b) the piezoresponse os displayed, and in (c) an according scanline. due to the sample geometry we recorded the lateral PFM signal, depicting the direction and magnitude of the d33 piezoelectric tensor element. In the non-affected area, far from the glue, the maximum signal is obtained. The glue-layer is not piezoelectric, and shows therefor no PFM signal at all, at the He-implanted layer, the piezoresponse is reduced to ~15% of its original value.

PFM-image of a cross-section of a He-implanted sample. (a) shows the schematics of the sample under investigation. In (b) the piezoresponse os displayed, and in (c) an according scanline. due to the sample geometry we recorded the lateral PFM signal, depicting the direction and magnitude of the d33 piezoelectric tensor element. In the non-affected area, far from the glue, the maximum signal is obtained. The glue-layer is not piezoelectric, and shows therefor no PFM signal at all, at the He-implanted layer, the piezoresponse is reduced to ~15% of its original value.

Large area domain patterning was performed by automatized tip-based domain formation using a computer controlled scripting. An example with 20 x 20 domains, every individual domain being << 1µm in diameter, is shown in the figure opposed. A self-regulating domain size mechanism, beased on Coulomb repulsion, assures the identical size of the individual domains within the pattern. The voltage applied to te tip, together with the inter-domain spacing , defines the size of the individual domains. Using this technique we were able to fabricate large patterns with 16.000 domains, all of equal size. The depth of the domains was found to be of teh order of few microns.

Large area domain patterning was performed by automatized tip-based domain formation using a computer controlled scripting. An example with 20 x 20 domains, every individual domain being << 1µm in diameter, is shown in the figure opposed. A self-regulating domain size mechanism, beased on Coulomb repulsion, assures the identical size of the individual domains within the pattern. The voltage applied to te tip, together with the inter-domain spacing , defines the size of the individual domains. Using this technique we were able to fabricate large patterns with 16.000 domains, all of equal size. The depth of the domains was found to be of teh order of few microns.

He-large

Tip-based anomalous domain formation

Domain reversal with the help of the tip in ultra-thin single crystals was proven to allow for storage-devices of high density. This technique relies on the reproducible fomratin of domains, all of identical shape. However, it has been observed that in some cases tip-based domain formation yields doughnut-shaped domains, calles anomalous domain formation. This effect is caused by charge injection into the sample during the poling pulse. We optimized the parameters for domain formation in order to reliably allow for full-domains to be generated.

	The opposed figure shows a poling map obtained on a nearly stoichiometric magnesium doped LiNbO₃crystal. All domains were geneated with a fixed pulse amplitude of 100 V. We varied the pulse duration and the waiting time. The latter is given by the durating between the ending of the pulse before moving towards a new position. The domains in general exhibit a central hole which forms instantaneously after the pulse. The stability of the domains can be estimated by their ease of transforming into c-domains. For instance domains written with long pulses (right side) are more stable since they could relax during the pulse.

FD doughnut

The opposed figure shows a poling map obtained on a nearly stoichiometric magnesium doped LiNbO₃crystal. All domains were geneated with a fixed pulse amplitude of 100 V. We varied the pulse duration and the waiting time. The latter is given by the durating between the ending of the pulse before moving towards a new position. The domains in general exhibit a central hole which forms instantaneously after the pulse. The stability of the domains can be estimated by their ease of transforming into c-domains. For instance domains written with long pulses (right side) are more stable since they could relax during the pulse.

Tip-based determination of the coercive field

The determination of the coercive field requires in general the application of an electric field across a sample slab. This is technically realised by evaporating conductive electrodes or using a liquid-electrode setup. In particular for small samples, this technique fails. But also for slightly conducting materials, the coercive field can not be determined in this was. Scannig probe microscopy allows for a different method for determining E_c by analyzing the temporal evolution of the size of tip-based domains.

The figure shows the size of domains written with pulses of durations between 0.02 s and 1000 s. Obviously, the size is constant for short pulse durations (up to ~ 1 s) and increases logaritmically only for larged durations. The size of the domain that formes instantanesouly, the starter domain D_s, allows now for determining E_c. We therefore assumed that within the area of D_s, the electric field emerging from the tip at least as large as E_c. Together with the electric field distribution underneath the tip, a value for E_ccan be determined.

The figure shows the size of domains written with pulses of durations between 0.02 s and 1000 s. Obviously, the size is constant for short pulse durations (up to ~ 1 s) and increases logaritmically only for larged durations. The size of the domain that formes instantanesouly, the starter domain D_s, allows now for determining E_c. We therefore assumed that within the area of D_s, the electric field emerging from the tip at least as large as E_c. Together with the electric field distribution underneath the tip, a value for E_ccan be determined.

Fabrication of photonic microstructures
In close collaboration with Sakellaris Mailis from the ORC in Southampton, GB.
Microstructures of nonlinear optical crystalline material are in general fabricated by a cumbersome cutting and polishing procedure. Highly desirable for applications such as whispering mode galleryl resonatores the surface quality of sich components, however, is of major importance. A very different approach for the fabrication of topographical microstructures takes advantage of the domain selective etching. This allows to transfer a domain pattern into a topographical structure. In order to smoothen the surfaces which became rough during the etching process, the samples are submitted to a thermal annealing procedure. This technique yields ultra-smooth microstructures as it can be seen in the figure below.

FD ultra smooth

SEM images of a) the initial structure, comprising an undercut, produced by inhibition of poling followed by deep chemical etching using HF acid, b) corresponding annealed structure showing a quasi-oblate spheroid top. In both images the sample is tilted by 45°.

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Ferroelectrics

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