5 DISCUSIÓN
5.5 Técnicas de la MTC como mayor número de evidencia:
AOP domain patterns all display several characteristics which lead to an understanding of the kinetics governing their formation. Nano-domain lines were initiated at domain nucleation sites, which could be UV-induced nucleations or pre-existing domains. The nano-domain lines grew along three directions aligned with the y axes of the crystal. When approaching neighboring domain lines or other surface and bulk domains, lines never joined or crossed, but rather electro-static interaction caused deflection along an alternative growth direction. A line was terminated when no direction existed in which it could maintain a separation greater than this characteristic deflection distance. These pattern characteristics were also observed in light-induced frustrated etching (LIFE) experiments, and their growth has been simulated using the rules above [Scott05]. A similar simulation approach was also employed in [Shur06c] for AOP patterns produced byλ= 308 nm ns-pulsed light, reproducing the results presented throughout this chap- ter. These simulations, however, were phenomenological models and required several adjustable parameters, such as nucleation density, deflection distance, and branching probability. Nevertheless, they demonstrated close agreement to experimentally ob- served patterns.
In all cases, the AOP domain lines appeared to grow outward from starting nucleation sites randomly scattered throughout the illuminated region. In some cases, these nucle- ation sites were pre-existing hexagonal domains, as shown in Figure 5.7. In most cases, however, these nucleation sites were induced at crystal defects by UV illumination, just as regular EFP initiated at crystal defect sites. These sites may be composed of lattice defects which present a smaller energy barrier to domain inversion, or pre-existing nano- domains. In this scenario, the nucleation site was not visible as a hexagonal domain, but instead was visible only as the convergence of three lines, as shown within the encircled area of Figure 5.4(b).
Growth from these nucleation sites proceeded along the −y directions of the crystal only. Again, this behavior was identical to the growth of hexagonal domains inverted by EFP, except in this case 2D nucleation was dominant over 1D nucleation. Branching, an instance of 2D nucleation, is the growth of a new domain line outward from an existing domain line, which acts as a nucleation site. While not strictly forbidden, typical AOP did not result in branching, although it has been reported using high fluences [Shur06c]. Instead, typical domain lines grew along a single −y direction until they approached other UV-induced lines or other domains.
Figure 5.21: SEM micrograph showing the reproducible distances over which the
domain lines are deflected. The shape of each bend is also reliably reproduced on a sub-micron scale.
Rather than merging with adjacent domains, nano-domain lines deflected along an al- ternative path rotated±120◦ relative to its original growth direction. This process was repeated very reliably, with a consistent distance between deflections and very simi- lar bend shapes, as shown in detail in Figure 5.21. Using the dye laser operating at
λ = 298 nm in undoped CLN, the deflection distance was 1.825±0.11 µm. Using the KrF excimer laser operating at λ = 248 nm in Mg:CLN, the deflection distance was 2.234±0.10 µm. The uncertainties in the measurements were dominated by blurring in the SEM imaging caused by charge accumulation at the edges of the etched trenches, rather than variability in the deflection distance itself. This deflection distance was likely a function of material parameters and the cross-sectional shape of the domain lines.
AOP lines are needle-like domains with angled-walls composed of finite steps of: (1) ver- tical wall segments parallel to the spontaneous polarization (θ= 0◦), and (2) horizontal wall segments perpendicular to the spontaneous polarization (θ = 90◦) [Gopalan98]. The horizontal wall segments form head-to-head charged domain walls [Shur00] which are likely the source of the electro-static interaction between the AOP domain lines. Regular bulk domains are composed of only vertical domain walls which are without charge, and hence tend to merge rather than deflect their growth. Deep surface domains also tend to merge because they are dominated by vertical domain walls. As the depth of the surface domain diminishes, however, the averaged domain wall angleθincreases, in- creasing the proportion of horizontal wall segments and increasing the force of repulsion, as observed with AOP domain lines. These three scenarios are depicted in Figure 5.22. The domain wall angle is inversely related to the domain aspect ratio (depth/width).
The minimum deflection distance also impacted the results of UV illumination through a phase mask. While individual nucleation sites were observed along each high intensity line produced by the phase mask with Λ = 726 nm, neither domain lines nor domain chains formed in adjacent periods. The minimum distance between these domain lines
-z
+z
(a)
(b)
(c)
q
q
- - - - - - - - - - - - - - - - - - - - - - - - - -- -- -- -Figure 5.22: Vertical domain walls (θ = 0◦) show no charging (a), while increasing
θ increases the density of charge on the domain walls (b–c). The negative signs (−) indicate charge compensation at the head-to-head domain interface.
was three periods, or∼2.2µm. This is in good agreement with the deflection distances measured above, as lines within two periods would be separated by less than the deflec- tion distance observed in self-organized patterns formed by unstructured illumination. Therefore illumination with a period greater than the deflection distance would likely achieve a periodic pattern with domain lines aligned along every adjacent high intensity peak. However, larger periods would also decrease the confinement of the UV-induced domains to the high intensity lines. Periods much greater than the widths of the domain lines would approach the situation of large-area unstructured illumination, resulting in self-organized patterns rather than lines aligned along a single y axis.
Since the deflection distance is believed to be a result of electro-static interaction due to the charge compensation on the head-to-head domain boundaries, a reduction in the spontaneous polarization of the material would be expected to reduce this charge and hence reduce the deflection distance. An increase in crystal temperature is one method of reducing the spontaneous polarization. However, UV illumination with crystal tempera- tures above 100◦C by Iain Wellington (University of Southampton) showed the opposite trend ofincreasing the distance between adjacent domain lines formed via illumination through a phase mask. Currently this effect is unexplained, and is complicated by the temperature range in which LN undergoes a large change in conductivity and several other material properties [Gopalan01].
The AOP process is an instance of non-equilibrium domain reversal conditions. With the incidence of nanosecond-duration UV pulses, the surrounding material heats up rapidly. While heating and cooling does not occur on the short time scale of the pulse, it does occur much faster than the typical switching time used during regular EFP of LN (τscr ' 50 ms) or LT (τscr ' 1 s). As a result, the necessary screening fields
were not realized, producing a higher rate of nucleus step generation (2D nucleation) than growth (1D nucleation) [Chernykh05; Shur06b]. In the limit of much greater 2D nucleation than 1D nucleation [R 1, as defined in (3.11)], star-like patterns formed and aligned along the y axes, as observed and simulated in [Lobov06]. These patterns
appeared identical to the AOP domain lines when viewed at a nucleation point [circled region of Figure 5.4(b)].
From this analysis, the kinetics of AOP domain line growth becomes clear. Starting at a nucleation point, a domain line grows outward along a−y direction by 2D nucleation. The suppression of 1D nucleation prevents the lateral growth of the domain. Therefore the width of the domain remains fixed at the size of nano-scale domain steps which invert simultaneously from 2D nucleation, as observed during hexagonal domain growth by EFP in Figure 3.10. Growth along a single−y axis is preferred to bending or branch- ing due to the greater electro-static self-interaction inherent in these cases. Therefore bending occurs only when the electro-static interaction with a neighboring domain line exceeds the self-interaction of the bend.
The competition between switching time and screening time also impacted the compo- sition of the domain line itself due to the phenomenon of correlated nucleation. Here, the continuous domain lines were broken into colinear line segments, as observed above upon illumination through a phase mask (Section 5.2.3). However, this has also occurred for unpatterned illumination. The formation of these domain chains began at a random nucleation site, depicted in Figure 5.23(a). This initial nucleation induced further nu- cleation at the distance called thecorrelation length,Lc, as depicted in (b). During this
time the initial nucleation site grew along the −y direction. The newly formed corre- lated nucleation induced another nucleation at a second distance of Lc, as depicted in
(c). Previous nucleations also reach a maximum length due to the electro-static inter- action between adjacent line segments of the domain chain, separated by a minimum distance,Ls, also depicted in (c). However,Lc andLs can vary across a crystal, result-
ing in domain chains which display only quasi-periodicity. WhenLc approachesLs, the
correlated nucleation sites are no longer able to grow, forming a chain of small nucleation dots rather than line segments Figure 5.23(d–f).
Experimentally, a range of line segment lengths was observed. Figure 5.24(a) shows correlated nucleation where short line segments construct the self-organized domain lines, corresponding to the case of Lc > Ls. Figure 5.24(b), instead, shows correlated
nucleation in which domain dots construct the self-organized lines, corresponding to the case ofLc 'Ls.
One method of controlling the correlation length is by controlling the thickness of the dielectric surface layer. This has been demonstrated by the introduction of an artifi- cial dielectric surface layer, increasing the layer thickness and thereby increasing the correlation length [Shur06a]. An alternative method may be to reduce the thickness of the intrinsic dielectric surface layer, thereby reducing the correlation length. This is a natural consequence of the AOP process due to the ablation. Therefore, more pulses or higher fluences should remove a greater amount of the intrinsic dielectric surface layer, thus reducing the correlation length. This effect has been observed above where 2 pulses
(a)
(b)
(c)
y
(d)
(e)
(f)
L
c1L
c2L
sFigure 5.23: The effect of different correlation lengths,Lc1> Lc2, is shown schemat-
ically, where a small Lc can inhibit nucleation growth due to the electro-static repul- sion between adjacent correlated nucleation sites. Triangles represent initial nucleation, while the pentagons represent growth along the domain line. These shapes are schematic
representations only and are not meant to depict actual domain shapes.
Figure 5.24: Correlated nucleation lines formed from individual (a) line segments or
(b) round dots. These undoped CLN samples were illuminated by (a) several pulses of λ= 248 nm and∼1 J/cm2, and (b) 100 pulses ofλ= 266 nm and∼1 J/cm2.
resulted in the line segments of Figure 5.24(a), but 100 pulses resulted in nucleation dots without growth (b).
Crystals from different manufacturers appeared to have different dielectric surface layer thicknesses, which would explain the occurrence of correlated nucleation in some crys- tals and not in others. In undoped and Mg-doped CLN supplied by Crystal Technology Ltd., AOP predominantly formedcontinuous self-organized domain lines devoid of cor- related nucleation. In undoped CLN supplied by Yamaju Ceramics Ltd., however, AOP consistently formed domain chains of correlated nucleation only. The differences in the surfaces of crystals from these suppliers was confirmed by the varying experimental results of UV illumination forming frustrated etching and hydrophilicity.
Mg-doped CLN supplied by Yamaju Ceramics Ltd. provided a further complication, where AOP formed isolated star-like patterns, as shown above in Figure 5.9, rather than
the typical intertwined self-organized patterns. This material was of higher quality and had a doping concentration above the ODT, whereas the material supplied by Crystal Technology Ltd. had a higher defect concentration (larger internal field, Table 3.2) and was doped below the ODT. The lower defect density of the Yamaju crystal resulted in the lower nucleation density observed. However this does not explain the short line length growing outward from these nucleations, as other materials exhibited domain lines which appeared limited in length only by the lateral extent of the illumination region and interaction with other lines. It is possible that the velocity of domain growth is much slower in this material, hence producing short lines that are not long enough to interact with the distant neighboring lines. This is supported by observations of EFP, where domain inversion is much smoother and slower in this material as compared to undoped CLN.