(Top), schematic illustrating the wedge polishing method used to reveal the depth profile of the poling-inhibited domains. The slope of the wedge corresponds to a 5∘ angle. (a)–(c): SEM images of wedge-polished and briefly etched poling-inhibited domains showing their stretched depth profiles. Depending on the particular UV irradiation conditions there are three different surface qualities that can be identified: (a) solid continuous domains, (b) assembly of scattered nano-domains, and (c) solid, continuous domains but with laser-induced surface damage. The dashed line in each image indicates the position where the slope starts. The symbols on the bottom right of the (b) and (c) images indicate the domain quality. ( = spontaneous polarization.)
Plot of the depth and width of poling-inhibited domains in undoped CLN induced by different UV laser wavelengths and intensities as a function of the scanning speed. The data groups corresponding to the same intensity are contained within the individual grey bands. The symbols correspond to different surface qualities as defined in Fig. 1 .
The depth and width versus writing laser intensity of PI domains in undoped CLN, written with wavelength of 275, 300, 302, and 305 nm, writing speed of 1.0 mm s−1, and focused beam radius of ∼3 μm. The dashed line represents a linear fitting of the experimental data and the background symbols correspond to various surface qualities as defined in Figs. 1(b) and 1(c) .
The depth and width versus UV laser fluence for 302 nm written poling-inhibited line domains in undoped CLN for a specific writing speed ( , 1.0 mm s−1) with varying intensities and a specific writing intensity ( , 0.12 MW cm−2) with varying writing speed. The data are obtained from Fig. 2 . The background symbols correspond to various surface qualities as in Figs. 1(b) and 1(c) .
Comparison of poling-inhibited domain depth and width in undoped and 5 mol. % MgO doped CLN corresponding to the same UV irradiation conditions at a wavelength of 275 nm (0.13 MW cm−2 intensity, 0.1–1 mm s−1 writing speed). The symbols describe the surface quality as defined in Figs. 1(b) and 1(c) .
(a1) and (b1) SEM images of wedge-polished and HF-etched solid poling-inhibited domain tracks fabricated at two different UV laser intensity levels. (a2) and (b2) show the same domain patterns after annealing at 300 ∘C for 30 h followed by another 7 min HF etching. The dashed lines indicate the region where the slope changes as a result of wedge polishing.
SEM images of (a1,b1) poling-inhibited domains formed during slow poling at a low poling field of 20 kV mm−1 and (a2,b2) formed during fast poling at a high poling field of 22 kV mm−1. Wedged-polishing (with dashed line indicating the slope change) and briefly HF etching revealed the poling-inhibited domain stretched depth profile. Two levels of fluence were used to produce poling-inhibited domains (a) above and (b) below the threshold for surface damage. The detail of buried poling-inhibited domains in (a2) is revealed in high magnification SEM figure underneath as dense nano lines along the z-axis.
The simulated 2D space for the heat conduction. x- and z-axis represent lateral and depth dimension of the crystal respectively. The total investigated range is a X × Z area ( ). For numerical analysis, the X (and Z) length is divided into Nx (and Nz ) points with spatial division of (and ).
(a) Plot of the specific heat at constant pressure as a function of temperature. Square dots correspond to the measured value from Ref. 30 . The curve corresponds to the Einstein model for the heat capacity of solids. (b) Thermal diffusivity κ versus temperature. Square dots correspond to the measured value from Ref. 31 , while the curve corresponds to a double-exponential decay fitting.
The temperature simulations with conditions of: 3.5 μm beam radius, 10−4 s irradiation time, 30 μm−1 absorption coefficient and various powers. (a) and (b) Show the temperature distribution along the surface (x-axis) and the depth down the centre line (z-axis), respectively. (c) Shows the increase of peak temperature at surface centre (x, z = 0) with the irradiation time on linear (bottom) and on log (top) scale. (d) Indicates the peak temperature as a function of power. The straight line is the linear fitting.
The temperature simulations with conditions of: 3.5 μm beam radius, 10−4 s irradiation time, 20 mW and various absorption coefficients. (a) and (b) Show the temperature distribution along the surface (x-axis) and the depth down the centre line (z-axis), respectively. (c) Shows the increase of peak temperature at surface centre (x, z = 0) with the irradiation time on linear (bottom) and on log (top) scale. (d) Indicates the peak temperature as a function of absorption coefficients.
The dependence of peak temperature at surface centre as a function of intensity for 10−4 s irradiation time. The changing of intensity is achieved either by (i) a fixed power of 20 mW with various beam radii (red dashed lines) or by (ii) a fixed beam radius of 3.5 μm with various writing power (grey solid lines).
Pre-exponential diffusion constant D 0 versus composition of LN crystals derived from Refs. 41 and 42 , assuming a composition independent activation energy. Both scales of Li mol. % (bottom) and normalized concentration c (top) are shown. c = 1 corresponds to the composition of congruent LN with 48.45 mol. % (Li). The dashed black curve represents the derived results from the references, while the solid grey curve is the fitting and the extension.
(a) Temperature distribution used for migration simulations, obtained with condition of: 3.5 μm beam radius, 10−4 s irradiation time, 30 μm−1 absorption coefficient and 20 mW. (b) Initial (t = 0) diffusivity D and (c) diffusion potential under the temperature distribution in (a). (d) and (e) The fluxes of Li ions along x and z-axis, respectively. (f) The normalized Li ion concentration after diffusion time of 5 × 10−3 s. (g) and (h) The normalized Li ion concentration along x and z-axis, respectively, for various diffusion times.
(a) Spontaneous polarization of congruent LN versus temperature, replotted from Ref. 44 . Above the Curie point ∼1470 K, the LN crystal become paraelectric with zero polarization. (b) The inverse of relative permittivity of congruent LN versus temperature, replotted from Ref. 45 . The data extracted from the reference is plotted as the black dashed curve while the fitted exponential growth is the solid grey curve.
(a) The distribution of polarization magnitude for the same temperature distribution in Fig. 14(a) . The direction of polarization is indicated by the arrow towards –z direction. (b) The bound charge distribution . (c) The inverse of relative permittivity along z-axis . (d) The pyroelectric potential . (e) and (f) The distribution of x and z components of the flux ( and , respectively). The negative value means the flow towards –x and –z directions (crystal surface) as indicated by the arrows. (g) The normalized Li ion concentration for a typical migration time of 5 × 10−3 s. The red curve corresponds to the c = 1 which separates the Li rich region above and the deficient region below. (h) The normalized Li ion concentration along z-axis for various migration times.
Simulation results for migration under both diffusion and pyroelectric field. (a) The total electric potential. (b) The z components of the initial total flux at t = 0. Positive and negative refers to the flux towards +z and –z direction, respectively, which is also indicated by the two arrows. (c) The normalized concentration at migration time of 5 × 10−3 s. The two red curves refer to the c = 1 contour lines which separate Li deficient and rich regions. (d) Normalized Li ion concentration along z-axis for various migration times.
(a) Coercive field versus the normalized Li ion concentration c and the Li ion mol% concentration, replotted from Ref. 47 . The dashed line indicates the CLN composition. (b) The calculated coercive field distribution corresponding to the Li ion distribution in Fig. 17(c) formed by diffusion and pyroelectric drift. The red curve refers to the coercive field of the initial congruent composition (c = 1).
Schematic of poling inhibited domain wall (red solid curves) formed during (a) slow poling and (b) fast poling. The arrow indicates the spontaneous polarization . The regions enclosed by white dashed curves refer to the Li deficient regions. The red dashed curve in (b) indicates the lateral expansion of domain wall at high poling voltage with high domain wall energy. In (a) slow poling, the poling inhibited domain dimension is mainly determined by the outer lithium deficient volume, while in (b) fast poling, the fast domain wall velocity reveals the more complex lithium concentration distribution reflected in the poling inhibited domain structure (inset). The white arrows indicate the final domain structure.
The absorption coefficients α, and absorption depths of undoped CLN for the UV wavelengths of 244, 300, 302, 305 nm at room temperature.
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