*3.1. Experimental Measurement*

Figure 2 shows the surface roughness measurement mechanism with a CLSM system: (a) is a schematic optical imaging system in which the laser beam as a probe has a wavelength of 405 nm, and the section of scanning is set 10 nm, and the spot size of the focused laser beam is defined by the full width at the half-maximum (FWHM) of the laser intensity distribution, (b) is an illustrative sample of the retrieved image in the CLSM measurement, and (c) is the standard definition of the peak-to-valley (P-V) roughness.

**Figure 2.** CLSM (confocal laser scanning microscopy) measurement and the definition for surface roughness: (**a**) The schematic optical imaging system, (**b**) the retrieved image of CLSM-measured result of an object, and (**c**) the definition for the fabricated surface roughness.

In the CLSM metrology, the roughness is defined as a root mean square (rms) *PSz* of all the P-V periods as [13,15]

$$PS\_z = (1/N)\sqrt{\left(\sum\_{i=1}^{N} R\_{ai}^2\right)}\tag{8}$$

where *Rai* is the average roughness at the *i* th scanned period in the CLSM measurement. In this definition of roughness, the *PSz* could be taken as a one-dimensional (1-D) roughness σ1*D*, then the 2-D average roughness σ2*<sup>D</sup>* and the 3-D average roughness σ3*<sup>D</sup>* are defined as

$$
\sigma\_{2D} = (1/m) \sum\_{j=1}^{m} P S\_z(aj) \tag{9a}
$$

$$
\sigma\_{3D} = (1/n) \sum\_{k=1}^{n} \sigma\_{2D}(ak) \tag{9b}
$$
