# Developing a Universal Mirror-mirror Laser Mapping System for Single Event Effect Research
## 2 Materials and Methods
### Verification of the Beam Scan Module (BSM)
#### 2.2.3 Spot Size and Spatial Resolution  
Unlike particles based SEE testing, the spot size of a laser beam is a key factor to the testing results. There are several studies that try to specify the effect of spot size to SEE testing [13; 14], but most of them are based on the SPA process. Based on the TPA theory [15], the generation of EHPs is highly dependent on laser irradiation and EHPs can be only generated in the focused zone of laser beam. Because the laser beam has a profile of Gaussian distribution, by precisely controlling the laser energy, the actual part of the laser spot that generates extra EHPs can be much smaller than the calculated spot size.  
There are two main ways to calculate the spot size of a laser beam. One is based on Gaussian distribution theory and the other is based on Airy ring theory. Due to the wavelength using in our testing set to 1250 nm, the value of spot size based on Airy ring theory is more accurate, calculating out to 5.08 um with a 10X objective lens (NA: 0.3) and 2.35 um with a 50X objective lens (NA: 0.65).  
A verification experiment was designed to find the relationship between spot size and resolution. A small ROI was first drawn at the edge just outside the photodiode. Then, laser pulses with different energy level from 500 pJ to 6 nJ were projected into that ROI. By comparing the output amplitude with each laser energy level, the change trend of the spot size with the energy level can be plotted, as shown in Figure 8.  
Figure 7: (**a**) Pulses waveform in the entire scanning period; (**b**) pulse waveform in one scanning step.  
The trend in Figure 8 clearly shows that an increase in the laser input energy corresponds to an increase in the spot size. This result indicates that a smaller spot size can be attained by using smaller laser input energy.  
Another very important but easily neglected factor was the injection angle of the laser beam. Unlike traditional stage-move systems, the projected laser beam from the BSM is not exactly orthogonal to the DUT surface. This leads to a shadow area which forms under the focus zone of the laser beam due to the tilted injection beam. Fortunately, in the TPA process, extra EHPs can only be generated inside the focused area. This means that the shadow area should be quite small. An experiment was designed to verify this effect. First, the testing in Figure 8 was done at the central location of the photodiode where the beam was projected vertically. Second, the photodiode was horizontally moved rightwards by 100 \(\upmu\)m and the testing was repeated by orienting the laser on the same spot on the DUT. This process was repeated three more times and each time the photodiode was moved 100 \(\upmu\)m rightwards. This operation allows the amplitude from the same ROI to be measured for different injection angles. Figure 9 illustrates the correlation between the injection angle and the amplitude of the photodiode.  
Figure 8: Change of output amplitude with different laser energy levels.  
Figure 9: Injected angle effect via different offset distance.  
From Figure 9, there was no obvious change in the first 200 \(\upmu\)m movement. However, when the ROI moves 300 \(\upmu\)m rightwards from the laser's vertical axis, a clear increase in the amplitude can be observed. This result shows that the injection angle could affect the testing results, but only for a relatively large spatial movement.