Matías Senger
May 31st 2021

The spacial resolution of a 200 µm pitch AC-LGAD was determined using a TCT and the machine learning algorithm .

# Introduction

In my previous work I have always studied AC-LGADs with 100 µm pitch . Today I repeated the studies but with a 200 µm pitch LGAD. The device I used today is RSD1 W10-A -5,3 3x3 200. Without more preamble I will go directly to the results. In there is a picture of the actual device used for this study.

Picture of the device used for this study.

# Results

As usual I made two scans:

1. Training scan: 999 samples at each point with a spacing of 11 µm between each point.
2. Testing scan: 9 samples at each point with a spacing of 1 µm between each point.
Using these two scans and the reconstruction error defined as $$\text{Reconstruction error}=\sqrt{\left(x_{\text{Laser}}-x_{\text{Reconstructed}}\right)^{2}+\left(y_{\text{Laser}}-y_{\text{Reconstructed}}\right)^{2}}$$ the sensor performance was evaluated. The $x_\text{Laser}$ and $y_\text{Laser}$ are the values configured in the experimental setup. The $x_\text{Reconstructed}$ and $y_\text{Reconstructed}$ are computed from the measured waveforms from each of the four channels using the machine learning algorithm , which was previously trained using the training scan. shows the reconstruction error fluctuations as a function of position. As can be seen in the region between the pads this is more or less uniform with an average value of about 5.5 µm, which is remarkable for a device with a pitch of 200 µm.

Reconstruction error standard deviation as a function of position. For the color map, at each point it is shown the standard deviation in the reconstruction error of the 9 samples of the testing scan.

A number of regions were defined on the surface to focus the study. These regions are shown in . The distribution of the reconstruction error in such regions in directions $x$ and $y$ is shown in , together with Gaussian fits. We start with Region 1: The standard deviation of this region, according to the fit, is around $\sigma = 6 \text{ µm}$ for both $x$ and $y$ coordinates, as was noticed before. For Region 2 we expect a worse behavior in $x$ direction but not a degradation in $y$, and we find looking into the fits $\sigma_x \approx 12 \text{ µm}$ and $\sigma_y \approx 5\text{ µm}$ respectively. So the spacial resolution in $x$ is about two times worse. The reason for this is that there are no pads to the left of Region 2 so the "reconstruction power" in $x$ gets worse as we move away from the two rightmost pads. In Region 3 and Region 4 we can compare what happens inside a pad. Due to the fact that the opening in the pad is along the $y$ direction, and thus "breaks the symmetry in $x$ direction, the resolution for Region 3 in $x$ direction should be ignored. If we look into the spacial resolution in $y$ we see that for Region 3 we have $\sigma_y \approx 7.5 \text{ µm}$ and for Region 4 we have $\sigma_y \approx 5 \text{ µm}$. The resolution is degraded, however this is probably due to the fact that in Region 3 we are further away from the bottom left pad. A more detailed analysis can be found in .

Reconstruction error distribution, left in $x$ and right in $y$, for the different regions indicated in .

# Conclusions

The overall resolution of a 200 µm pitch AC-LGAD was studied using a laser. Under the best conditions, i.e. in the region between the four pads, a spacial resolution of the order of 6 µm was achieved.

# References

First application of the empirical likelihood function to position reconstruction in AC-LGAD detectors, Matías Senger, https://msenger.web.cern.ch/first-application-of-the-empirical-likelihood-function-to-position-reconstruction-in-ac-lgad-detectors/. First time-space characterization of an AC-LGAD, Matías Senger, https://msenger.web.cern.ch/first-time-space-characterization-of-an-ac-lgad/. Spacial Resolution of AC-LGAD Within a Pad, Matías Senger, https://sengerm.github.io/html-github-hosting/210425_spacial_resolution_of_AC-LGAD_within_a_pad/210425_spacial_resolution_of_AC-LGAD_within_a_pad.html.