# Investigation on Key Parameters in the Fabrication of Stamps for Transfer Printing of Micro Devices
## 3 Results and Discussion
### Development Effect under Different Conditions  
Figure 3a-e shows several types of morphologies of photoresist molds during the development process, including successful and failed ones. We apply semi-ellipsoid fitting to the successful morphologies as shown in Figure 3a,f and Equation (1) for the purpose of exploring development laws of the mold and providing the reference for subsequent researchers to fabricate molds and stamps. After the photoresist has been developed, it remains in the exposed parts of the photoresist mask, as shown in Figure 2a. Figure 3 provides morphologies of the photoresist during the development. The photoresist in patterned parts on the silicon substrate is gradually removed over time. The morphologies of the mold fall into five categories, as illustrated in Figure 3. Among them, the semi-ellipsoidal shape illustrated in Figure 3a is of the majority. A variation of this kind is a truncated-cone, with a relative flat bottom, as shown in Figure 3b. Figure 3a shows the normal  
Figure 3: Several morphologies of molds during the development process, including successful and failed ones; (**a–e**) five different mold development morphologies under a laser confocal microscope (OLS 5000, Olympus Corp., Tokyo, Japan); (**f**) schematic illustration of a semi-ellipsoid. morphology during the development, and Figure 3b shows the morphology that the photoresist is about to be completely removed. Categories other than these two are considered as failures, as illustrated in Figure 3c,e, which show either a hill-like projection or a convex, or other irregular shapes. The morphology in Figure 3d is formed by the overflowed photoresist, and morphologies in Figure 3c,e can be attributed to uneven stirring during development. Thus, we only focus on regular ones, namely, the semi-ellipsoidal shapes. Other remaining results cannot be processed satisfactorily. During the development process, the central area has been developed faster than the surrounding has, resulting in the depth > the radius. The difference in the developing speed can be attributed to (a) during exposure, the curing intensity on side walls of the mold appears greater than that on the bottom of the mold, and (b) the developer will accelerate the etching of the photoresist at the bottom of the mold due to the gravity. For analyses, we fit the semi-ellipsoidal part at the bottom of molds fabricated under different development conditions with the semi-ellipsoid equation  
\[z=-c\sqrt{1-\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}}, \tag{1}\]  
where parameters \(a\), \(b\), and \(c\) represent the length of the three half axes of the semi-ellipsoid, respectively, as shown in Figure 3f. These data have been fitted with acceptable accuracies (average \(R^{2}=0.93\)). Due to isotropic etching of the lateral of the mold, we combine parameters \(a\) and \(b\) into one radius as  
\[r=\frac{a+b}{2}. \tag{2}\]  
During the development, since the etching speed at the bottom of the mold exceeds those of laterals, the value of \(c\) should surpass that of \(r\). Therefore, we linearly fit values of \(c\) with \(r\), as shown in Figure 4a and  
\[c=-3.04+1.37r\ (24.44\leq r\leq 94.70,R^{2}=0.982), \tag{3}\]  
showing a slope of 1.37--etching speed in the vertical direction reaches 1.37 times that in the lateral direction. Primarily, the deviation between measurement dots and the fitting curve in Figure 4a originates from the deviation between morphologies of the developed mold and the semi-ellipsoid. Values of \(c\) and \(r\) are fitted from Figure 3, in which the shape of the mold during development is assumed to be semi-ellipsoidal shape. However, it is somewhat difficult for the actual shape of the mold during the development to precisely match the semi-ellipsoidal. During the development process, both \(c\) and \(r\) are growing, whereas the growth is also infected by the setting width. We plot both \(c\) and \(r\) with the developing time duration \(t\), at each setting width \(w\), as shown in Figure 4b,c.