## 2 The Excimer Laser Micromachining System and the Optical Diffraction Effect  
The micromachining trials were conducted using the excimer laser system shown in Figure 1. (For full details, refer to [14; 15; 16].) The system was implemented using a KrF laser source (COMPex Pro 210, Lambda Physik, Goettingen, Germany) with a wavelength of 248 nm. The laser was passed through a telescope lens system and an optical homogenizer to form a uniform flat-top laser energy distribution over a cross-sectional area of 1.5 \(\times\) 1.5 cm\({}^{2}\) on the photo-mask surface. The light passing through the photo-mask was projected onto the sample surface with a 10X de-magnification factor using a high-resolution projection lens system (P-Lens 4-10X/4-xxx, P/N_M290009, Lambda Physik,Goettingen, Germany). The sample was placed on a 4-axis (x-y-z-\(\theta\)) servo-controlled automatic stage. During the machining process, the stage motion and laser firing sequence were controlled by a personal computer. Figure 2a presents a schematic illustration of the hole-array mask pattern used to perform the micromachining process. As shown, the mask contains a rectangular array of square elements, with each element having a hole-opening aperture located at its center. For convenience, the side-length dimension of the square elements is denoted as d, while the hole radius is denoted as r. In designing the mask, the element size (d) was assigned a constant value, while the hole-radius (r) was varied so as to achieve a local variation in the optical transmission. Figure 2b,d provides qualitative illustrations of the laser-machined cross-sectional profiles obtained using the elements located along Section A-A of the photo-mask shown in Figure 2a given optical diffraction effects with different intensities. Figure 2b shows the machined profile for the case of negligible optical diffraction. It is observed that the micromachined features have a perfect binary characteristic, i.e., sharp edges and corners. However, while this situation represents the ideal case for 2D machining, it cannot be achieved in practice since the optical diffraction effect can never be entirely eliminated. As the intensity of the optical diffraction effect increases (i.e., the feature size in the photo-mask pattern decreases), a noticeable rounding of the edges and corners occurs. In the case of Figure 2c, the diffraction effect is relatively mild, so the machined profiles are still dominated by the hole-array mask pattern. However, as the feature size of the hole-array mask pattern reduces, the diffraction effect increases to such an extent that the machined depth and machined profiles are determined by an analog distribution of the diffracted laser energy. Thus, as shown in Figure 2d, individual hole features are no longer apparent in the machined surface profile. Rather, the neighboring hole features merge into one another, through optical diffraction of the image projection system, and with the machined depth determined by the projected laser energy at the corresponding position on the sample surface. It is noted that this result is typical of that achieved by 3D micromachining systems using a grey-tone or half-tone mask. Figure 2: \(Cont.\)  
The schematic presented in Figure 2 show that the optical diffraction effect must be quantitatively determined before an excimer laser machining system can be used in real-world 3D micromachining applications. Accordingly, 5\" Cr/soda-lime-glass masks were prepared containing various hole-arrayed patterns. To characterize the optical diffraction effect, the hole-arrayed patterns were designed in such a way that the hole radius (r) remained constant within each mask pattern. Consequently, the average transmission coefficient of the incident laser light, both globally and locally, was expressed as the ratio of the hole-opening area to the element area, i.e., \(\pi\)\(\mathrm{r}^{2}\)/\(d^{2}\) (referred to hereafter as the hole-area opening ratio).