Higher Order Nonlinear Dielectric Microscopy
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Higher Order Nonlinear Dielectric Microscopy Yasuo Cho and Koya Ohara Research Institute of Electrical Communication, Tohoku University 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ABSTRACT A higher order nonlinear dielectric microscopy technique with higher lateral and depth resolution than conventional nonlinear dielectric imaging is investigated. The proposed technique involves the measurement of higher order nonlinear dielectric constants, with a depth resolution of down to 1.5 nm. The technique is demonstrated to be very useful for observing surface layers of the order of unit cell thickness on ferroelectric materials.
INTRODUCTION Recently, we proposed a new, purely electrical technique for imaging the state of ferroelectric polarization and the local crystal anisotropy of dielectric materials. This technique involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is called scanning nonlinear dielectric microscopy (SNDM)[1-4]. This is the first successful purely electrical method for observing ferroelectric polarization distributions that is unaffected by free-charge shielding. The resolution of the technique has thus far been improved down to the sub-nanometer scale [see APPENDIX]. In this technique, we detect capacitance variation under applied electric field mainly caused by nonlinear dielectric response. (Piezoresponse also affects the capacitance variation as it cancels the capacitance variation caused by the nonlinear dielectric effect, but its magnitude is usually much smaller.) In this study, we have developed a new SNDM technique with a much higher resolution, capable of detecting a higher order nonlinear dielectric constant. In the conventional SNDM technique, we measure the lowest order nonlinear dielectric constant ε(3), which is a 3rd rank tensor. To improve the performance and resolution of SNDM, we have modified the technique such that a higher order nonlinear dielectric constants ε(4) and ε(5) (4th and 5th rank tensor, respectively) are detected. It is expected that higher order nonlinear dielectric imaging will provide higher lateral and depth resolution. We confirmed this improvement over conventional SNDM imaging experimentally, and used the technique to observe the growth of a surficial paraelectric layer on periodically poled LiNbO3.
HIGHER ORDER NONLINEAR DIELECTRIC MICROSCOPY Equation (1) is a polynomial expansion of the electric displacement D as a function of electric field E. D = Ps + ε ( 2 ) E +
1 1 1 ε (3) E 2 + ε ( 4 ) E 3 + ε (5 ) E 4 2 6 24
C9.9.1
L
(1)
Here, ε(2), ε(3), ε(4) and ε(5) correspond to linear and nonlinear dielectric constants and are tensors of rank 2nd, 3rd, 4th and 5th, respectively. Even-ranked tensors including linear dielectric constant ε(2) do not change with polarization inversion, whereas the sign of the odd-ranked tensors reverses. Therefore, information regarding polarization can be elucidated by measuring odd-ranked nonlinear dielectric constants such as ε(3) and ε(5). Figure 1 is a schematic
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