**3. Characterization of laser micromachining**

### **3.1. Depth of micro-trenches as a function of the scan cycles**

After laser micromachining, the depth of the micro-trenches pattern can be observed by scanning electron microscopy (SEM) to check the effectiveness of the approach. The quality of the cleave can be quantified by the width, depth, linearity and sidewall roughness of the trench formed by the laser beam. Because the focal length of the focusing lens (*f* = 75 mm) is much longer than the thickness of the GaN layer on the sapphire wafer (*t* = 420 µm), the depth of the trench depends mainly on the number of micromachining cycles. The number of cycles is controlled by configuring the translation stage to repeat its linear path several times. As the position reproducibility of the stage is better than 5 µm, increasing the number of cycles should not contribute significantly to the width of the feature. X.H. Wang et al. [11] reported the cross-sectional optical image of a GaN layer on a 420 µm thick sapphire wafer that had been micro-machined with an incident beam inclined at 45° with scan cycles ranging from 1 to 10. These incisions were carried out by setting the laser pulse energy to 54 µJ at a repetition rate of 2 kHz. Figure 2 shows the relationship between the inclined cutting depth and the number of passes of the beam. After the first pass of the beam, a narrow trench with a width of ~20 µm and depth of ~220 µm was formed. Successive scans of the beam along the trench resulted in further deepening and widening but the extent was increased at a decreasing rate. The depth of the trench depends on the effective penetration of the beam. From the second scan onwards, the beam needs to pass through the narrow gap before reaching the bottom of the trench for further machining. The energy available at this point was attenuated, which is partly due to lateral machining of the channel (causing undesirable widening), absorp‐ tion and diffraction effects. Therefore, the depth of the trench tends to saturate after multiple scans.

**Figure 2.** (a) Cross-sectional optical micrograph of laser micro-machined micro-trenches at an inclination angle of 45° at a range of scan cycles of between 1 and 10 (left to right then down), and (b) depth of tiling micro-trenches as a function of the scan cycles.
