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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 4 — Feb. 18, 2008
  • pp: 2336–2350
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Direct-writing of inverted domains in lithium niobate using a continuous wave ultra violet laser

A. C. Muir, C. L. Sones, S. Mailis, R. W. Eason, T. Jungk, Á. Hoffmann, and E. Soergel  »View Author Affiliations


Optics Express, Vol. 16, Issue 4, pp. 2336-2350 (2008)
http://dx.doi.org/10.1364/OE.16.002336


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Abstract

The inversion of ferroelectric domains in lithium niobate by a scanning focused ultra-violet laser beam (λ=244nm) is demonstrated. The resulting domain patterns are interrogated using piezoresponse force microscopy and by chemical etching in hydrofluoric acid. Direct ultra-violet laser poling was observed in un-doped congruent, iron doped congruent and titanium in-diffused congruent lithium niobate single crystals. A model is proposed to explain the mechanism of domain inversion.

© 2008 Optical Society of America

1. Introduction

Lithium niobate (LN) is a ubiquitous material within the optoelectronics industry due to its large electro-optic, acousto-optic and non linear optical properties [1

1. R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985). [CrossRef]

]. It is a ferroelectric crystal with a spontaneous polarisation caused by the displacement of Li+ and Nb5+ cations along the crystallographic c axis thus giving rise to 180° anti-parallel domains that can be switched by the application of a suitable external electric field. It is the orientation of these domains that determines the crystal response to many stimuli, for example the strain or refractive index change resulting from an applied electric field, and so precision scale engineering of domains has become a field of extensive research for application in a large number of areas ranging from harmonic generation through quasi-phase-matched parametric processes [2

2. A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti : indiffused lithium niobate waveguides ,” Appl. Phys. Lett. 84, 4430–4432 (2004). [CrossRef]

], signal modulation in telecomunications [3

3. F. S. Chen and W.W. Benson, “A lithium niobate light modulator for fiber optical communications,” Proceedings of the IEEE 62(1), 133–134 (1974). [CrossRef]

] to the creation of single-crystal microstructures by utilising differential etching [4

4. C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. Gawith, P. G. R. Smith, and R.W. Eason, “Fabrication of piezoelectric micro-cantilevers in domain-engineered LiNbO3 single crystals,” J. Micromech. Microeng. 12(1), 53–57 (2002). URL http://dx.doi.org/10.1088/0960-1317/12/1/308. [CrossRef]

]. The fabrication of well-defined domain patterns for this range of applications requires a robust method for domain inversion which can achieve the desired spatial ferroelectric domain distributions even on submicron scales and preferably in a flexible, repeatable and easy to apply manner.

Conventional domain engineering is achieved through the application of an external electric field greater than the coercive field of the crystal. The electric field strength is spatially modulated by applying a structured layer of photo-resist or metal across one surface to produce local screening. The electric field contrast provided by the photoresist layer is, however, relatively poor which limits the width of domain structures to greater than a few microns. Also the conventional method requires multiple fabrication steps and expensive cleanroom facilities.

Recent advances in domain engineering of LN have shown that laser light can be used to influence the domain reversal process and two methods have been identified; light assisted poling (LAP) [5

5. C. L. Sones, M. C Wengler, C. E. Valdivia, S. Mailis, R.W. Eason, and K. Buse, “Light-induced order-of-magnitude decrease in the electric field for domain nucleation in MgO-doped lithium niobate crystals,” Appl. Phys. Lett. 86, 212901 (2005). [CrossRef]

, 6

6. C. E. Valdivia, C. L. Sones, S. Mailis, J. D. Mills, and R. W. Eason, “Ultrashort-pulse optically-assisted domain engineering in lithium niobate,” Ferroelectrics 340, 75–82 (2006). URL http://dx.doi.org/10.1080/150190600888983. [CrossRef]

] and all optical poling (AOP) [7

7. C. L. Sones, C. E. Valdivia, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, and E. Soergel, “Ultraviolet laser-induced sub-micron periodic domain formation in congruent undoped lithium niobate crystals,” Appl. Phys. B 80(3), 341–344 (2005). URL http://dx.doi.org/10.1007/s00340-005-1731-7. [CrossRef]

, 8

8. C. E. Valdivia, C. L. Sones, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, E. Soergel, and I. Clark, “Nanoscale surface domain formation on the +z face of lithium niobate by pulsed ultraviolet laser illumination,” Appl. Phys. Lett. 86(2), 022906 (2005). URL http://dx.doi.org/10.1063/1.1849414. [CrossRef]

, 9

9. I. T. Wellington, C. E. Valdivia, T. J. Sono, C. L. Sones, S. Mailis, and R. W. Eason, “Ordered nano-scale domains in lithium niobate single crystals via phase-mask assisted all-optical poling,” Appl. Surf. Sci. 253(9), 4215–4219 (2007). URL http://dx.doi.org/10.1016/j.apsusc.2006.09.018. [CrossRef]

]. The LAP approach still uses an external electric field to invert the domains but localised domain reversal is achieved since the coercive field is lowered in the illuminated regions. The AOP approach creates domain inversion without an external electric field by illuminating the crystal with high energy laser pulses. These methods show much promise for domain engineering since the laser light patterns can be structured down to diffraction limited spot sizes and no photolithography is required.

In this paper we present AOP using focused continuous wave (c.w.) ultra-violet (UV) laser light and show that all-optical domain inversion is achievable under exposure conditions entirely different to those used in pulsed AOP and without the need for high peak powers of a pulsed source previously assumed essential. The domain structures created are analysed using piezoresponse force microscopy (PFM) and by chemical etching followed by both surface profiling and scanning electron microscopy.

In the following section the experimental methods used to create the domain patterns and those used to subsequently analyse them are described. In section 3 the experimental results are presented and analysed and a model of the formation mechanism is proposed whereby a poling field is produced by the drift of photo-excited charge carriers in the induced pyroelectric field.

2. Experimental method

A UV laser beam of wavelength 244 nm is provided by a frequency-doubled argon ion laser. The beam is expanded, spatially filtered and collimated before being focused onto a LN sample by a 40mmfocal length lens. The focused spot has a calculated radius of approximately 1.5µm, however, from the size of damage features seen in a photo-resist covered slide we believe the actual spot radius to be approximately 2.5 µm. The LN samples are mounted upon a three axis computer-controlled stage system (Newport MM2000). The exposure was also controlled by a computer-controlled shutter such that the beam was present only when the stage velocity was constant to ensure uniform exposure along the written lines. The stages were translated to write lines along both the x and y axes at speeds between 50 to 300 µm s-1. Exposures of the above conditions were made at incident powers between 20 and 30 mW, which corresponds to an intensity range of 100–150 kW cm-2. At powers below ~ 20 mW no significant effect is seen and at powers higher than ~ 30 mW, although the effect is seen, it is accompanied by excessive surface damage associated with melting of the surface.The samples used were all 500 µm thick, z-cut, optical quality single-crystal wafers. Exposures were carried out on both the positive and negative z faces of iron-doped (0.1 mol % and 0.01 mol %) and un-doped crystals and in duplicate such that identical samples could be analysed by PFM and by etching. Exposures were carried out on the ‒z face only of titanium in-diffused crystals.

For PFM analysis an atomic force microscope with a conducting tip was used to measure the piezoresponse of the exposed surface by applying an electric field to the surface with the tip and measuring the induced strain by the tip deflection. An overview of the principles of PFM can be found in [10

10. T. Jungk, A. Hoffmann, and E. Soergel, “Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy,” Appl. Phys. Lett. 89(16), 163,507 - (2006). URL http://dx.doi.org/10.1063/1.2362984. [CrossRef]

, 11

11. E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–752 (2005). URL http://dx.doi.org/10.1007/s00340-005-1989-9. [CrossRef]

].

Chemical etching in hydrofluoric (HF) acid is a well-established method of domain visualisation in LN due to the fact that the negative z face etches readily whilst the positive z face does not etch at all [12

12. C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem 12, 295–298 (2002).

]. Thus if domains are inverted during UV laser irradiation they will present as either a raised ridge in the case of negative z face exposures or as an etched trench in positive z face exposures. A number of un-doped samples were etched at room temperature in HF acid of 48% aqueous solution for consecutive intervals of 5 minutes, between which they were imaged with an optical microscope and profiled using a KLA-Tencor stylus profilometer. After a cumulative etching time of 1 hr these samples were imaged with a scanning electron microscope (SEM). Other un-doped samples, and both the titanium in-diffused and iron doped samples, were etched for around 15 minutes only before being imaged with an SEM.

Further exposures were performed on a periodically poled LN (PPLN) sample which was analysed by PFM as the PPLN structure gave a benchmark against which to compare any UV laser induced PFM signal.

3. Results and discussion

Figure 1 shows SEM images after etching of exposed areas on the ‒z face of un-doped congruent LN with scan speeds of 50 and 200 µm s-1. It is clear to see that the behaviour is strongly dependent upon exposure conditions with an abrupt qualitative change occurring at the highest power, splitting the behaviour into two regimes. These two regimes will be referred to as the high power regime and the low power regime, with the understanding that the terms are relative to the somewhat narrow power window of the main investigation. As was mentioned earlier, the effect is seen to occur at higher powers above 30 mW, but is accompanied by undesirable melting and thermal damage, and is not seen at powers considerably below 20 mW. The width of the power window is believed to be due to the strong temperature dependence of the effect and the steep rate of change of temperature with power for these beam parameters as was seen in [13

13. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, “Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions,” Appl. Phys. A 83(3), 389–396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]

]. In the high power regime the surface is seen to be smooth and resists etching in the crystallographic z direction. The surface contains cracks, due to thermal damage, and is decorated with thin lines that extend along the x axes of the crystal. The features in this regime will be discussed in detail later.

In the low power regime it is seen that etching is also resisted in the exposed regions, resulting in a raised ridge structure. The upper surface of the ridges is seen to consist of densely packed discrete features that have dimensions of around 50–100 nm, an example of this is shown in high magnification in Fig. 2. These features are visible as they resist etching in the vertical direction whilst the ‒z face they are embedded within does not. Thus the surrounding material etches and the topography of the upper surface of the ridge is revealed.

The change in height with cumulative etching time of the ridges, with respect to the unexposed background –z face, is shown in Fig. 3. The slope of the curve gives the differential etch rate between exposed and unexposed regions. In the high power (solid) curve it can be seen that the gradient is constant and has a value which agrees with the etch rate of virgin LN [12

12. C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem 12, 295–298 (2002).

]. As the power decreases it is seen that the etch resistance lasts for a time dependent upon the power and scan speed, but this time decreases with with decreasing power or increasing velocity, until features etch at the same rate as unexposed regions. This may be understood by the mechanism with which the nano-topography of the upper surface of the ridges is revealed: As the surrounding material is etched the sides of these nano-features are revealed to the etchant and they begin to side-etch. The ease at which etchant can enter between the features and attack the sides will, of course, depend upon the packing density. When the side etched distance reaches the radius of the features they will begin to reduce in height and the differential etch rate between the ‒z crystal face and the exposed region will reduce. At the point at which the the entire depth of these nano-features is revealed side-etching will remove them completely and the differential etch rate will go to zero as the underlying material is revealed. At this point the height of the ridge is preserved.

The widths of the upper surface of the ridges after 15 mins etching is plotted in Fig. 4 as a function of scan speed for powers of 29, 27, 26 and 25 mW. It can be seen that the width is strongly dependent upon incident power and only weakly dependent upon the scan speed with the width increasing with increasing power and decreasing with increasing scan speed. Whilst, for a particular scan speed, it is seen that width of the upper layer decreases with decreasing power, the overall width of the ridge left after etching is essentially constant (not shown in Fig. 4). This indicates that this entire width was initially covered in a capping layer of the discrete features described above, but that either the density and/or depth of the features decreased with distance from the center of the beam path such that the outer features were removed by the time the measurements were taken. For higher power exposures the depth and density of features at the outer edges of the beam will be greater and hence more will remain and the width of the upper surface will be greater. Figure 4 then shows that the density and depth of the capping layer vary with power.

Fig. 1. Variation with power of the UV laser-induced layer on the ‒z face. Lines scanned along the crystallographic y direction. SEM images of structures revealed by HF etching for 15 minutes. (a-d) Scan speed 50 µm s-1. (e-h) Scan speed 200 µm s-1.

In the low power regime, then, an upper layer of discrete features is seen to form that resist etching in the +z direction but do etch in the perpendicular direction. The depth and density of the features is seen to depend upon the position within the exposed region and upon the incident power, with only a weak dependence upon the scan speed.

In the high power regime exposures on the ‒z face [Fig. 1(a)] are seen to result in an etch resistant layer of quite different topography as compared to low power exposures. The surface of the layer is seen to be very flat, smooth, and rigid as compared to the low power regime where it consisted of discrete features. The edges of the layer are also seen to be sharp and well-defined. Some cracks are present due to thermal damage and these generally span the surface without particular alignment to crystal axes. New features are also revealed by etching that align to the x axes of the crystal and these will be further examined later. Figure 5 shows an SEM image of a high-power exposure after 1 hr etching where the affected layer can be seen to extend to a depth of around 1 µm, whilst the total height of the ridge is just over 2 µm. To investigate better the topography of the features the sample was tilted with respect to the electron beam, about the long axis of the line. The layer is seen to resist etching in the depth direction completely up to etching times of 1 hr as can be seen in Fig. 3, however Fig. 5 shows that the upper layer does etch in the vertical direction from underneath as can be seen from the voids where etchant has been permitted to enter through the thermal cracks. Furthermore it can be seen from the symmetric shape of the voids that the etch rate of the layer from underneath, toward the surface, is very similar to that of the unaffected crystal beneath.

Fig. 2. SEM image of the discrete features seen on the upper surface of the ‒z face in the low power regime.
Fig. 3. Change in feature height above ‒z face with etch time for different power exposures at a scan speed of 100 µm s-1. Flat gradient shows no etch resistance. Error bars obtained as standard deviations of repeated measurements. Insert shows how the height is defined.
Fig. 4. Variation in the width of the upper surface of the etched ridges with power and scan speed. Error bars obtained as standard deviations of repeated measurements.

It was stated in section 2 that the etch characteristics of the +z and ‒z faces are different [12

12. C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem 12, 295–298 (2002).

] and so this fact can be used to determine the ferroelectric polarity. LN also shows anisotropy in the etch characteristics of the y faces [14

14. T. J. Sono, J. G. Scott, C. L. Sones, C. E. Valdivia, S. Mailis, R. W. Eason, J. G. Frey, and L. Danos, “Reflection second harmonic generation on a z-cut congruent lithium niobate crystal,” Phys. Rev. B 74(20), 205424 (2006). URL http://dx.doi.org/10.1103/PhysRevB.74.205424. [CrossRef]

] and so this also can be used to determine the ferroelectric polarity. Although both y faces etch in HF the ‒y face etches at a greater rate allowing determination of the direction of the y axes. The etch behaviour of the layer in the y direction of the crystal when the beam is scanned along the perpendicular x axis can be seen in Fig. 6, which shows a high-power exposure after 1 hr etching. The image is taken with no sample tilt. It can clearly be seen that at the top of the figure the layer terminates abruptly whilst at the bottom of the figure the layer terminates with a slope. This indicates that, at the same time as the surrounding crystal has etched downwards in the crystallographic z direction, the layer has etched inwards but only on the lower edge. This asymmetry is not seen when the beam is scanned along the crystallographic y direction as can be seen in Fig. 1(a).

The distinction between a high and low power regime was seen to be made at the same incident powers on the +z face of the crystal. In the low power regime +z face exposures are seen to produce trenches after etching as can be seen in Fig. 7(b). The depths of these trenches, as measured by stylus profiling, was seen to be proportional to the scan speed with depth increasing as the scan speed decreases. The measured depths of the trenches reached some tens of nanometers however the true depth may be greater due to limitations of the profilometer tip to probe such narrow structures. The behaviour of the +z face in the high power regime is different. At high powers etching is not seen to occur over the entire exposed area. This can be seen in Fig. 7(a) that shows an exposure after 1 hr etching. Large cracks [seen horizontally in Fig. 7(a)] caused by thermal effects can be seen (also visible before etching) however new features have been revealed that are aligned with the x crystallographic direction (vertically in the figure).

No difference was seen in the etch behaviour of iron doped samples as compared to un-doped samples since the same corresponding surface topographywas present in both the high and low power regimes. This suggests that defects with energy levels within the band-gap play little role and that the effect is dominated by band-band transitions.

Fig. 5. SEM image of typical features on the ‒z face after high power UV exposure revealed after 1 hr etching. The x axis of the crystal runs horizontally in the figure. Sample tilted at 30° to the electron beam. The areas indicated by annotations form the upstanding ridge structure and are both in relief of the crystal surface.
Fig. 6. SEM image of a high-power exposure after 1 hr etching viewed from directly above. The polarity of the affected layer is seen through the differential y etching indicating that the affected layer is of the opposite polarity to the surrounding crystal. Insert shows axes of the underlying crystal.

Figure 8 shows an SEM image of a ‒z face exposure, in the high power regime, on a titanium in-diffused sample after etching in HF acid. It can be seen that the etch behaviour is again similar to that of the exposures on un-doped LN, with a raised ridge being formed. The cracks due to thermal damage can again be seen, however, the features that align to the x axes, that were seen earlier on iron-doped and un-doped LN, are seen with a much lower density. The quality of the edges is reduced due to remnant titanium on the surface.

Fig. 7. Typical behaviour of +z exposures in the high and low power regimes. Beams scanned along the crystallographic x direction.
Fig. 8. Typical behaviour of ‒z exposures in the high power regime on titanium in-diffused LN. Beam scanned along the crystallographic y direction.

The etch results of the ‒z face exposures indicate that the layer formed on the ‒z face may be crystalline LN with an inverted ferroelectric domain polarity for the following reasons. A domain inverted layer on the ‒z face would present a +z face to the etchant and so would resist etching in the inward surface normal direction. If the etchant was permitted within or below this inverted layer it would see in the outward surface normal direction a ‒z face and would so etch accordingly, which is what we see. The etchant which is present at the head-to-head domain boundary between a positive surface domain and an underlying negative bulk domain would be presented with two negative z faces and so would etch in the directions both away from and toward the surface, at the same time as etching sideways, and so a void would be formed. The void would be diamond-shaped in cross-section with opposite vertices on the line parallel to the surface indicating the depth of the surface domain. This is seen in Fig. 5 and gives the approximate depth of the surface domains as ~1µm. Also, once a domain inverted layer is revealed by the etching of the surrounding crystal, thus forming a ridge structure, it would present either y or x faces to the etchant depending upon the scanning direction and hence geometry of the newly formed ridge. In the case that x faces are presented there would be no asymmetry of the etching since the x axis of LN does not etch differentially. This is the behaviour seen in Fig. 1(a). In the case that the y faces of the crystal are presented to the etchant however an asymmetry is expected since the y axis etches differentially, with the crystal etching at a far greater rate in the ‒y direction than in the +y direction [14

14. T. J. Sono, J. G. Scott, C. L. Sones, C. E. Valdivia, S. Mailis, R. W. Eason, J. G. Frey, and L. Danos, “Reflection second harmonic generation on a z-cut congruent lithium niobate crystal,” Phys. Rev. B 74(20), 205424 (2006). URL http://dx.doi.org/10.1103/PhysRevB.74.205424. [CrossRef]

]. The direction of the y axis is of course coupled to the direction of the z axis such that when the z axis is inverted the y axis inverts also [14

14. T. J. Sono, J. G. Scott, C. L. Sones, C. E. Valdivia, S. Mailis, R. W. Eason, J. G. Frey, and L. Danos, “Reflection second harmonic generation on a z-cut congruent lithium niobate crystal,” Phys. Rev. B 74(20), 205424 (2006). URL http://dx.doi.org/10.1103/PhysRevB.74.205424. [CrossRef]

]. This asymmetry of the etching in the y direction was seen in Fig. 6 which, through the argument above, identifies the y axis of the ridge structure as pointing upward in the figure. The direction of the y axis of the underlying and unexposed LN points downward in the figure. The asymmetries of the etch behaviour thus show that the exposed region is still crystalline and that the direction of the z and y axes is opposite to that of the virgin crystal.

In the case of illuminations on the +z face the etch results suggest that, at low powers, a layer of crystal with a depth of a few tens of nanometers may reverse its polarization. When this occurs a ‒z face is presented to the etchant which then etches readily, leaving a trench. The etching would stop at the bottom of the domain inverted layer when again a +z face was present. At high powers the entire area is not seen to etch which implies that domain inversion has not taken place across the full beam width.

Piezoresponse force microscopy utilises the converse piezoelectric effect to determine the polarity of ferroelectric domains [10

10. T. Jungk, A. Hoffmann, and E. Soergel, “Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy,” Appl. Phys. Lett. 89(16), 163,507 - (2006). URL http://dx.doi.org/10.1063/1.2362984. [CrossRef]

]. An electric field is applied to the sample through a conducting atomic force microscopy tip which limits the depth resolution of the technique since the field within the crystal extends to approximately three times the radius of curvature of the tip. In our case this corresponds to a depth of around 100 nm. Any domain features with depth greater than this will be seen as bulk domains and give the full piezoresponse amplitude contrast of plus or minus one for positive or negative domains respectively. Domain features with depth less than 100 nm, however, will give the integrated piezoresponse of the sampling volume. This makes identification of shallow domains difficult since both shallow inverted domains and regions of non-piezoelectric material can give the same net PFM response. Figure 10 shows the topography (a) and PFM amplitude (b) of a scanned exposure over a PPLN sample. The PPLN domains run horizontally over the image whilst the UV scanned lines run vertically. The full PFM contrast is clearly visible due to the PPLN structure with black areas indicating a ‒z face and white areas indicating a +z face. It can be seen that the UV exposed areas show the same contrast as the +z areas of the PPLN. This indicates that in the areas of the PPLN that had a ‒z face, the polarity of the crystal has inverted to a depth greater than the sampling depth of PFM. Where the beam has passed over +z areas of the PPLN no change in the PFM contrast is seen implying that no domain reversal has occurred. This agrees well with the results seen with chemical etching in which a positive domain was seen to be formed on the ‒z face, and so resisted etching, whilst no large negative domains were seen to form on the +z face since the exposed area did not etch. The PFM results thus corroborate the evidence, given previously by the etch behaviour of the exposed crystals, that inverted domains are formed, in the high power regime, on the ‒z face but not on the +z face. The minimum depth of the domain formed is given by PFM as ~ 100 nm and a greater estimate of the depth, which may be taken as an upper limit, has been given earlier as ~ 1µm. Although methods exist to measure the depth of domains, such as side-polishing and etching [15

15. V. Y. Shur, “Kinetics of ferroelectric domains: Application of general approach to LiNbO3 and LiTaO3,” J. Mater. Sci. 41(1), 199–210 (2006). URL http://dx.doi.org/10.1007/s10853-005-6065-7. [CrossRef]

], we do not believe that these are suitable in this instance due to the presumed shallow depth of the structures and the damage of the edge which is caused by mechanical polishing.

Fig. 9. SEM images showing alignment to the x axes of features exposed by etching on the positive and negative z faces after UV exposure in the high power regime.
Fig. 10. Topography and PFM amplitude of a scanned UV exposure over PPLN. PPLN domains run horizontally in the images and UV written lines run vertically. In the PFM image ‒z domains appear black and +z domains appear white. UV scans are seen to invert ‒z areas of PPLN.

PFM has also been used to examine the stability of the domains formed by measuring the piezoresponse of an exposure in the high power regime before and after heating at the crystal 200 °C for four hours. No significant change in the response was seen.

From the results presented above we believe that inverted ferroelectric domains are being formed during UV illumination. The precise mechanism for domain inversion has yet to be discovered however we can justify the UV laser induced ferroelectric domain inversion by considering an electric field formed by the separation of photo excited charges under the following reasoning.

LN is ferroelectric and so possesses a spontaneous electric polarization Ps which has associated with it an electric depolarisation field Edep. At room temperature the unexposed crystal is in equilibrium and Edep is screened by free charges and defects within the crystal [17

17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

] which create a compensation field, Escr, with equal magnitude to Edep and aligned parallel to Ps. This is shown schematically in Fig. 11(a). When the UV beam enters the crystal the energy is absorbed within the upper 50 nm (1/e2 intensity absorption depth ≈ 30 nm) [18

18. A. M. Mamedov, “Optical properties (VUV region) of LiNbO3,” Opt. Spectrosc. 56(6), 645–649 (1984).

] and is mostly converted into heat, creating temperature distributions with spatial extents of the order of the beam width [13

13. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, “Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions,” Appl. Phys. A 83(3), 389–396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]

]. When the crystal is heated, Ps and, consequently, Edep are decreased as the Li and Nb cations move toward the para-electric positions. Escr is very slow to react [17

17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

] to changes in Ps and so a net field is left as Escr now overcompensates Edep, as shown in Fig. 11(b). At the same time, since the photon energy of the UV beam (5.1 eV) is greater than the LN band gap (≈ 4 eV), photo-excitation occurs creating electron-hole pairs. Most will re-combine and release their energy as heat. However, a fraction will survive and be free to travel within the crystal under the influence of both electric fields and concentration gradients. These photo-excited charges will see the net electric field, Enet, and will drift under its influence with holes moving toward the +z face and electrons moving toward the ‒z face, as shown in Fig. 11(c). It is worth noting here that charges excited between intrinsic energy bands in LN are not accelerated in the same way as those from defect levels and do not contribute to the bulk photovoltaic currents [19

19. K. Buse, “Light-induced charge transport processes in photorefractive crystals. I. Models and experimental methods,” Appl. Phys. B 64(3), 273–291 (1997). URL http://dx.doi.org/10.1007/s003400050175. [CrossRef]

] as do impurity defects with energies within the band gap. The separated photo-excited charges will thus create a photo-induced space-charge field, E sc-ph, anti-parallel to Escr. If drift were the only driving force a maximum steady state photo-induced field would be created that was equal to the vector sum of the Edep and Escr however charges also move by diffusion under the influence of concentration, and possibly thermal [13

13. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, “Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions,” Appl. Phys. A 83(3), 389–396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]

], gradients which may increase the magnitude of the photo-induced field. The field may also be increased by thermal [20

20. E. M. Bourim, C. W. Moon, S. W. Lee, and I. K. Yoo, “Investigation of pyroelectric electron emission from monodomain lithium niobate single crystals,” Physica B 383(2), 171–182 (2006). URL http://dx.doi.org/10.1016/j.physb.2006.02.034. [CrossRef]

] or photo-induced emission [21

21. G. I. Rozenman, “Photoinduced exoemission from lithium niobate,” Sov. Phys. Solid State 30(8), 1340–1342 (1988).

] of electrons from the surface. As the beam moves on, the crystal cools and Ps and, consequently, Edep again increase. Edep and Escr now cancel leaving the net field in the crystal equal to Esc-ph. If Esc-ph is greater than the coercive field of LN it is energetically favorable for the spontaneous polarisation to align with the photo-induced field and the polarisation will be reversed.With reference to Fig. 11(e) domain inversion should occur only for Esc-ph >Escr such that alignment of Ps with Esc-ph would lower the total energy of the system. This threshold field for inversion is the coercive field of the crystal, Ec [17

17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

]. In the model above where Escr remains constant, with magnitude equal to the room temperature depolarisation field, the estimate of the coercive field is the magnitude of Edep and is given by

Ec=Psε
(1)

where ε is the permittivity along the z axis. The estimate of the coercive field above evaluates to 28,235 kV cm-1 using ε=30ε 0 and Ps=0.75 C m-2. This is clearly greater than the experimentally determined coercive field of 210 kV cm-1 [17

17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

]. However, this overestimate of the coercive field by orders of magnitude is also found in more rigorous derivations [22

22. S. Kim, V. Gopalan, and A. Gruverman, “Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalate,” Appl. Phys. Lett. 80(15), 2740–2742 (2002). URL http://dx.doi.org/10.1063/1.1470247. [CrossRef]

] and the lowering of the coercive field in ferroelectrics from the theoretical value for perfect crystals has been attributed to charged defects [23

23. A. N. Morozovska, “Theoretical description of coercive field decrease in ferroelectric-semiconductors with charged defects,” Ferroelectrics 317, 37–42 (2005). [CrossRef]

] or to mobility of pre-existing domain walls [22

22. S. Kim, V. Gopalan, and A. Gruverman, “Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalate,” Appl. Phys. Lett. 80(15), 2740–2742 (2002). URL http://dx.doi.org/10.1063/1.1470247. [CrossRef]

]. Regardless of the origin of the reduction in coercive fields it is clear that Esc-ph need not be greater than Escr for domain reversal to be achieved and if Esc-ph>Ec the Ps will invert [Fig. 11(f)].

This model agrees well with the previously seen dependence of the domain width on speed and power as was shown in Fig. 4. It was seen that the width of the domain inverted region had only a weak dependence upon scan speed but a very strong dependence upon power, which indicates that the effect is not simply a function of exposure. Although the model requires photo-excited charges, the number density of which will be a function of exposure, the driving force for charge movement originates from the temperature distribution created by the heating laser. The temperature distribution has been shown to be independent of scan speed for speeds below around 20 cm s-1 [13

13. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, “Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions,” Appl. Phys. A 83(3), 389–396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]

] and hence independent of exposure. The strong temperature dependence and the requirement seen to be reasonably near the melting point can be understood with the model above by considering the steep change of Ps with temperature near the Curie point since Ps ∝ (T cT)1/2, as shown in reference [17

17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

], where Tc is the curie temperature.

Anisotropy between the behaviour on the two faces is expected under the following reasoning. The optical absorption depth is around 30 nm at the writing wavelength and so photo-excited charges can only be created within this depth. Thus the source of free charges able to create Esc-ph is essentially two dimensional and located at the surface in a plane parallel to the surface. As can be seen in Fig. 11(c) the field Enet in which the photo-excited charges move is directed parallel to Ps regardless of which face is heated. Thus when heating the +z face photo-excited holes will be trapped at the surface whilst photo-excited electrons will drift into the bulk of the crystal and, conversely, when the ‒z face is heated photo-excited holes will drift into the bulk whilst photo-excited electrons will be trapped at the surface. If the mobilities of both electrons and holes were equal then the two situations would be similar and the same Esc-ph would result. However, electron and hole mobilities are in general different with electrons being more mobile than holes with typical semiconductor mobility ratios of 3 (Si) to 23 (GaAs). Thus even from relatively simple consideration an anisotropy between the behaviour on the two z faces is expected.

Fig. 11. Schematic of the proposed mechanism for domain inversion. Solid arrows represent electric field vectors. Other vectors represented by broken arrows for clarity.

In the experimental work and modeling described above, a laser wavelength of 244 nm has either been used or assumed for the incident light. As previously mentioned this wavelength has an optical absorption depth of 30 nm [18

18. A. M. Mamedov, “Optical properties (VUV region) of LiNbO3,” Opt. Spectrosc. 56(6), 645–649 (1984).

], which has two pertinent consequences with regard to the model described above. The first of these is that the length scale of the temperature distributions created by the beam are given by the beam radius, since the absorption depth is much less than the beam radius. The second is that the region in which photo-excited charges can be created is, of course, limited to the absorption depth. Since the ratio of the absorption depth to the beam radius is ≈80 the source of charges that can create the field Esc-ph is essentially two dimensional and located at the surface. The limited depth of the charge source limits the distance over which charge separation can occur and hence the depth over which E sc-ph extends. This then, ultimately, result in a limit to the depth of the domain formed. If a laser wavelength at which the optical absorption depth within the crystal is greater than the 30 nm optical absorption depth at λ=244 nm, and that still has a photon energy greater than the band-gap, then the charge source will become extended in the depth direction and deeper domains may be able to be formed. The optical absorption coefficient increases rapidly with decreasing wavelength near λ=244 nm, so increasing the wavelength will increase the depth of the charge source. The temperature distributions within the crystal, and hence charge driving forces, would remain unchanged until the absorption depth was of equal magnitude to the beam radius.

The full dynamical behaviour of this nonlinear system is complex and subtle and a full numerical investigation of the charge dynamics under UV illumination is currently underway and will be presented in a future communication.

In short we believe that domain formation is due to a space-charge field created by the combined effects of photo-excitation of charge and drift within an electric field, caused by the decrease of spontaneous polarisation at elevated temperatures, and that the different behaviour of the two faces is due to the difference in mobilities of electrons and holes.

4. Conclusion

In conclusion, we have demonstrated domain inversion in congruent lithium niobate, iron-doped congruent lithium niobate and titanium in-diffused lithium niobate by a scanning continuous wave ultra-violet laser operating at a wavelength of 244 nm. The domain structures obtained have been analysed using piezoresponse force microscopy and by chemical etching in hydrofluoric acid, followed by surface profiling and scanning electron microscopy. The positive domains formed on the ‒z face are also seen to contain self aligned nano-domains of negative polarity which are aligned along the x axes of the crystal. On the +z face domain inversion can be seen at low powers, over the width of the exposed area, by etching. At higher powers domain inversion is not seen over the entire width of the exposure however aligned nano-domains are seen within the exposed area. The domains formed on the ‒z face at high powers have also been observed by piezoresponse force microscopy. A model is proposed to explain the mechanism of domain inversion whereby the domain inversion is obtained through the action of a space-charge field of photo-excited charges and the differences of behaviour on the positive and negative faces can be explained by different electron and hole mobilities. We believe that by varying the illuminating laser wavelength to tune the optical absorption depth to a greater value the depth of the domains will be increased. Additionally to the numerous technological uses of directly-written domain structures the demonstration of etched ridge structures on titanium in-diffused planar waveguides also makes possible the fabrication of strip loaded waveguides with no photolithography [24

24. N. Uchida, “Optical waveguide loaded with high refractive-index strip film,” Appl. Opt. 15, 179–182 (1976). [CrossRef] [PubMed]

].

The authors would like to thank Rutherford Appleton Laboratories Laser Loan Pool for the generous loan of the frequency doubled argon ion laser.We would also like to acknowledge the Engineering Physical Sciences Research Council (EPSRC) for the PhD funding of A. Muir and the EPSRC Portfolio Partnership in Photonics grant (reference EP/C515668/1).

1.

R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical Properties and Crystal Structure,” Appl. Phys. A 37, 191–203 (1985). [CrossRef]

2.

A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, “First-order quasi-phase-matched blue light generation in surface-poled Ti : indiffused lithium niobate waveguides ,” Appl. Phys. Lett. 84, 4430–4432 (2004). [CrossRef]

3.

F. S. Chen and W.W. Benson, “A lithium niobate light modulator for fiber optical communications,” Proceedings of the IEEE 62(1), 133–134 (1974). [CrossRef]

4.

C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. Gawith, P. G. R. Smith, and R.W. Eason, “Fabrication of piezoelectric micro-cantilevers in domain-engineered LiNbO3 single crystals,” J. Micromech. Microeng. 12(1), 53–57 (2002). URL http://dx.doi.org/10.1088/0960-1317/12/1/308. [CrossRef]

5.

C. L. Sones, M. C Wengler, C. E. Valdivia, S. Mailis, R.W. Eason, and K. Buse, “Light-induced order-of-magnitude decrease in the electric field for domain nucleation in MgO-doped lithium niobate crystals,” Appl. Phys. Lett. 86, 212901 (2005). [CrossRef]

6.

C. E. Valdivia, C. L. Sones, S. Mailis, J. D. Mills, and R. W. Eason, “Ultrashort-pulse optically-assisted domain engineering in lithium niobate,” Ferroelectrics 340, 75–82 (2006). URL http://dx.doi.org/10.1080/150190600888983. [CrossRef]

7.

C. L. Sones, C. E. Valdivia, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, and E. Soergel, “Ultraviolet laser-induced sub-micron periodic domain formation in congruent undoped lithium niobate crystals,” Appl. Phys. B 80(3), 341–344 (2005). URL http://dx.doi.org/10.1007/s00340-005-1731-7. [CrossRef]

8.

C. E. Valdivia, C. L. Sones, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, E. Soergel, and I. Clark, “Nanoscale surface domain formation on the +z face of lithium niobate by pulsed ultraviolet laser illumination,” Appl. Phys. Lett. 86(2), 022906 (2005). URL http://dx.doi.org/10.1063/1.1849414. [CrossRef]

9.

I. T. Wellington, C. E. Valdivia, T. J. Sono, C. L. Sones, S. Mailis, and R. W. Eason, “Ordered nano-scale domains in lithium niobate single crystals via phase-mask assisted all-optical poling,” Appl. Surf. Sci. 253(9), 4215–4219 (2007). URL http://dx.doi.org/10.1016/j.apsusc.2006.09.018. [CrossRef]

10.

T. Jungk, A. Hoffmann, and E. Soergel, “Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy,” Appl. Phys. Lett. 89(16), 163,507 - (2006). URL http://dx.doi.org/10.1063/1.2362984. [CrossRef]

11.

E. Soergel, “Visualization of ferroelectric domains in bulk single crystals,” Appl. Phys. B 81(6), 729–752 (2005). URL http://dx.doi.org/10.1007/s00340-005-1989-9. [CrossRef]

12.

C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem 12, 295–298 (2002).

13.

A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, “Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions,” Appl. Phys. A 83(3), 389–396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]

14.

T. J. Sono, J. G. Scott, C. L. Sones, C. E. Valdivia, S. Mailis, R. W. Eason, J. G. Frey, and L. Danos, “Reflection second harmonic generation on a z-cut congruent lithium niobate crystal,” Phys. Rev. B 74(20), 205424 (2006). URL http://dx.doi.org/10.1103/PhysRevB.74.205424. [CrossRef]

15.

V. Y. Shur, “Kinetics of ferroelectric domains: Application of general approach to LiNbO3 and LiTaO3,” J. Mater. Sci. 41(1), 199–210 (2006). URL http://dx.doi.org/10.1007/s10853-005-6065-7. [CrossRef]

16.

V. Y. Shur, D. K. Kuznetsov, A. I. Lobov, E. V. Nikolaeva, M. A. Dolbilov, A. N. Orlov, and V. V. Osipov, “Formation of self-similar surface nano-domain structures in lithium niobate under highly nonequilibrium conditions,” Ferroelectrics 341, 85–93 (2006). URL http://dx.doi.org/10.1080/00150190600897075. [CrossRef]

17.

M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).

18.

A. M. Mamedov, “Optical properties (VUV region) of LiNbO3,” Opt. Spectrosc. 56(6), 645–649 (1984).

19.

K. Buse, “Light-induced charge transport processes in photorefractive crystals. I. Models and experimental methods,” Appl. Phys. B 64(3), 273–291 (1997). URL http://dx.doi.org/10.1007/s003400050175. [CrossRef]

20.

E. M. Bourim, C. W. Moon, S. W. Lee, and I. K. Yoo, “Investigation of pyroelectric electron emission from monodomain lithium niobate single crystals,” Physica B 383(2), 171–182 (2006). URL http://dx.doi.org/10.1016/j.physb.2006.02.034. [CrossRef]

21.

G. I. Rozenman, “Photoinduced exoemission from lithium niobate,” Sov. Phys. Solid State 30(8), 1340–1342 (1988).

22.

S. Kim, V. Gopalan, and A. Gruverman, “Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalate,” Appl. Phys. Lett. 80(15), 2740–2742 (2002). URL http://dx.doi.org/10.1063/1.1470247. [CrossRef]

23.

A. N. Morozovska, “Theoretical description of coercive field decrease in ferroelectric-semiconductors with charged defects,” Ferroelectrics 317, 37–42 (2005). [CrossRef]

24.

N. Uchida, “Optical waveguide loaded with high refractive-index strip film,” Appl. Opt. 15, 179–182 (1976). [CrossRef] [PubMed]

OCIS Codes
(140.3610) Lasers and laser optics : Lasers, ultraviolet
(160.2260) Materials : Ferroelectrics
(160.3730) Materials : Lithium niobate
(160.4670) Materials : Optical materials

ToC Category:
Materials

History
Original Manuscript: November 30, 2007
Revised Manuscript: January 26, 2008
Manuscript Accepted: January 27, 2008
Published: February 4, 2008

Citation
A. C. Muir, C. L. Sones, S. Mailis, R. W. Eason, T. Jungk, A. Hoffman, and E. Soergel, "Direct-writing of inverted domains in lithium niobate using a continuous wave ultra violet laser," Opt. Express 16, 2336-2350 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2336


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References

  1. R. S. Weis and T. K. Gaylord, "Lithium Niobate: Summary of Physical Properties and Crystal Structure," Appl. Phys. A 37, 191 - 203 (1985). [CrossRef]
  2. A. C. Busacca, C. L. Sones, R. W. Eason, and S. Mailis, "First-order quasi-phase-matched blue light generation in surface-poled Ti : indiffused lithium niobate waveguides," Appl. Phys. Lett. 84, 4430 - 4432 (2004). [CrossRef]
  3. F. S. Chen andW.W. Benson, "A lithium niobate light modulator for fiber optical communications," Proceedings of the IEEE 62(1), 133 - 134 (1974). [CrossRef]
  4. C. L. Sones, S. Mailis, V. Apostolopoulos, I. E. Barry, C. Gawith, P. G. R. Smith, and R.W. Eason, "Fabrication of piezoelectric micro-cantilevers in domain-engineered LiNbO3 single crystals," J. Micromech. Microeng. 12(1), 53 - 57 (2002). URL http://dx.doi.org/10.1088/0960-1317/12/1/308. [CrossRef]
  5. C. L. Sones, M. C. Wengler, C. E. Valdivia, S. Mailis, R.W. Eason, K. Buse, "Light-induced order-of-magnitude decrease in the electric field for domain nucleation in MgO-doped lithium niobate crystals," Appl. Phys. Lett. 86, 212901 (2005). [CrossRef]
  6. C. E. Valdivia, C. L. Sones, S. Mailis, J. D. Mills, and R. W. Eason, "Ultrashort-pulse optically-assisted domain engineering in lithium niobate," Ferroelectrics 340, 75 - 82 (2006). URL http://dx.doi.org/10.1080/150190600888983. [CrossRef]
  7. C. L. Sones, C. E. Valdivia, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, and E. Soergel, "Ultraviolet laser-induced sub-micron periodic domain formation in congruent undoped lithium niobate crystals," Appl. Phys. B 80(3), 341 - 344 (2005). URL http://dx.doi.org/10.1007/s00340-005-1731-7. [CrossRef]
  8. C. E. Valdivia, C. L. Sones, J. G. Scott, S. Mailis, R. W. Eason, D. A. Scrymgeour, V. Gopalan, T. Jungk, E. Soergel, and I. Clark, "Nanoscale surface domain formation on the +z face of lithium niobate by pulse d ultraviolet laser illumination," Appl. Phys. Lett. 86(2), 022906 (2005). URL http://dx.doi.org/10.1063/1.1849414. [CrossRef]
  9. I. T. Wellington, C. E. Valdivia, T. J. Sono, C. L. Sones, S. Mailis, and R. W. Eason, "Ordered nano-scale domains in lithium niobate single crystals via phase-mask assisted all-optical poling," Appl. Surf. Sci. 253(9), 4215 - 4219 (2007). URL http://dx.doi.org/10.1016/j.apsusc.2006.09.018. [CrossRef]
  10. T. Jungk, A. Hoffmann, and E. Soergel, "Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy," Appl. Phys. Lett. 89(16), 163,507 - (2006). URL http://dx.doi.org/10.1063/1.2362984. [CrossRef]
  11. E. Soergel, "Visualization of ferroelectric domains in bulk single crystals," Appl. Phys. B 81(6), 729 - 752 (2005). URL http://dx.doi.org/10.1007/s00340-005-1989-9. [CrossRef]
  12. C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, "Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations," J. Mater. Chem 12, 295 - 298 (2002).
  13. A. C. Muir, G. J. Daniell, C. P. Please, I. T. Wellington, S. Mailis, and R. W. Eason, "Modelling the formation of optical waveguides produced in LiNbO3 by laser induced thermal diffusion of lithium ions," Appl. Phys. A83(3), 389 - 396 (2006). URL http://dx.doi.org/10.1007/s00339-006-3493-4. [CrossRef]
  14. T. J. Sono, J. G. Scott, C. L. Sones, C. E. Valdivia, S. Mailis, R. W. Eason, J. G. Frey, and L. Danos, "Reflection second harmonic generation on a z-cut congruent lithium niobate crystal," Phys. Rev. B 74(20), 205424 (2006). URL. [CrossRef]
  15. V. Y. Shur, "Kinetics of ferroelectric domains: Application of general approach to LiNbO3 and LiTaO3," J. Mater. Sci. 41(1), 199 - 210 (2006). URL http://dx.doi.org/10.1007/s10853-005-6065-7 [CrossRef]
  16. V. Y. Shur, D. K. Kuznetsov, A. I. Lobov, E. V. Nikolaeva, M. A. Dolbilov, A. N. Orlov, and V. V. Osipov, "Formation of self-similar surface nano-domain structures in lithium niobate under highly nonequilibrium conditions," Ferroelectrics 341, 85 - 93 (2006). URL http://dx.doi.org/10.1080/00150190600897075. [CrossRef]
  17. M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarenon Press, 1977).
  18. A. M. Mamedov, "Optical properties (VUV region) of LiNbO3," Opt. Spectrosc. 56(6), 645 - 9 (1984).
  19. K. Buse, "Light-induced charge transport processes in photorefractive crystals. I. Models and experimental methods," Appl. Phys. B 64(3), 273 - 291 (1997). URL http://dx.doi.org/10.1007/s003400050175. [CrossRef]
  20. E. M. Bourim, C. W. Moon, S. W. Lee, and I. K. Yoo, "Investigation of pyroelectric electron emission from monodomain lithium niobate single crystals," Physica B 383(2), 171 - 182 (2006). URL http://dx.doi.org/10.1016/j.physb.2006.02.034. [CrossRef]
  21. G. I. Rozenman, "Photoinduced exoemission from lithium niobate," Sov. Phys. Solid State 30(8), 1340 - 1342 (1988).
  22. S. Kim, V. Gopalan, and A. Gruverman, "Coercive fields in ferroelectrics: A case study in lithium niobate and lithium tantalate," Appl. Phys. Lett. 80(15), 2740 - 2742 (2002). URL http://dx.doi.org/10.1063/1.1470247. [CrossRef]
  23. A. N. Morozovska, "Theoretical description of coercive field decrease in ferroelectric-semiconductors with charged defects," Ferroelectrics 317, 37 - 42 (2005). [CrossRef]
  24. N. Uchida, "Optical waveguide loaded with high refractive-index strip film," Appl. Opt. 15, 179 - 182 (1976). [CrossRef] [PubMed]

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