The domain shape invariant

Let us consider Equations (15) and (16) it can be seen that the ratio rU2/lm depends logarithmically on the applied voltage and the tip-sample system capacitance yielding  

The radius of string-like nanodomains observed under the fdb conditions is much smaller than its length, rm -C lm. Consequently, for the fdb phenomenon the shape invariant value should also be small. Equation (10.18) shows that the shape invariant has the lowest value if a ferroelectric material satisfies the following conditions  

In Table 10.2 below we summarize the calculated values of the shape invariant r 2//m and aspect ratio rm/lm of string-like domains in different fe crystals formed under the fdb conditions. The experimental parameters used for these calculations are U = 3kV (applied voltage), R = 50 nm (typical radius of curvature of the tip apex), d = 0.5 nm (distance between the tip apex and the sample surface). The calculated aspect ratios rm/lm are quite different for the chosen fe. 

10 Ferroelectric Domain Breakdown Application to Nanodomain Technology 

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