# First time-space characterization of an AC-LGAD

After a lot of assembling, programming, measuring, analyzing and calibrating, today I finally arrived to my very first results of spacial and temporal resolution in an AC-LGAD. Though it was a lot of work until I reached here, the methods still have to be improved. The results I obtained, however, are pretty good. In this post I will summarize my current results so I don’t forget.

## Introduction

AC-LGADs[1]AC coupled LGAD. (also known as RSDs[2]Resistive AC-Coupled Silicon Detectors.) are one of the candidates for the implementation of the 4D pixels capable of measuring both time and position of impact of particles with resolution of $$\mathcal{O}(10 \text{ ps})$$ for the time and $$\mathcal{O}(10 \text{ µm})$$ for position. We have a number of these devices in our lab and since some months ago I have been playing with them using our TCT setup[3]See my other posts on AC-LGADs here.. In this post I will only be using the device labeled

• RSD1 W8-A -2,5 3×3 100, alias Paul.

This is a device from the first RSD production (RSD1) which was characterized by its creators in this paper. You can ignore the alias, it is just a name by me to easily identify the devices in the lab. This is how a similar device looks like under the microscope:

Today I performed a series of measurements and analyses, described below, to get a first number for the spatial and the temporal resolution of this device.

### Setup description

All the measurements were taken using our TCT at UZH. It is a Particulars large scanning TCT to which we have added a laser splitting-delay line to do time measurements. Below there are two block diagrams of the setup:

#### Laser intensity calibration

One important aspect to determine the spatial and temporal resolution is to correctly adjust the laser intensity in order to produce a ionization equivalent to that of a MIP[4]For more details see this and this posts.. For this I used as a reference a PIN diode “AIDA V2 RUN 12916 IP47 W3-DB45” which has a thickness of 50 µm, the same as the AC-LGADs from the RSD1 production[5]Mandurrino M., et al. “High Performance Picosecond- and Micron-Level 4D Particle Tracking with 100% Fill-Factor Resistive AC-Coupled Silicon Detectors (RSD).” ArXiv:2003.04838 [Physics], March … Continue reading. The laser intensity was calibrated against a radioactive beta source using the PIN diode[6]See in this post. To be specific, a “laser pulse width” of 64.8 % was used. and then the same laser intensity was used for the AC-LGAD.

#### Amplifiers gain calibration

In order to maintain the symmetry between the four pads, the gain of each of the amplifiers connected to each channel in the oscilloscope must be as equal as possible. The four amplifiers were carefully selected from a group of more than 4 amplifiers in order to match as much as possible the gain and keeping as low as possible the noise floor.

Furthermore, an offline gain correction for each channel was applied. For this I first performed a high granularity (1 µm) scan of the device throughout the whole active area of interest, which I will here refer to as “scan 1” (the full reference to this scan is “20210224075953_AC-LGAD_Paul_MIP_10um_555trigs” as seen in the title of the plots below). Then I adjusted the gain of each channel until the total collected charge inside a “Swiss flag region” (see plot below) was the same for all channels. While doing this I varied the size of the Swiss flag region and optimized its center. As a result both the gain of each channel and also the center of the structure were found. After this procedure was completed I ended up with this “fitted Swiss flag”:

where the colormap is the sum of the average collected charge by each channel after applying the gain correction. The average charge share after the gain correction was performed for each channel looks like this:

The small black cross is the center of the fitted Swiss flag. Due to the symmetry of the structure we expect that exactly in the center the charge is shared in equal parts by the four channels, i.e. we expect this quantity to be 0.25 for all the channels. As can be seen in these plots, the 0.25 contour line passes just under this marker for the four channels . The corrections to the gain of each channel were in the order from 5 to 8 %, though not a big corrections it can be appreciated in these plots before and after this correction (not shown here the plots before the correction).

## Spacial characterization

With the gain calibration completed I performed a second scan on the same device which I will call “scan 2” (full reference is “20210224075953_AC-LGAD_Paul_MIP_10um_555trigs”). In this scan I increased the granularity to 10 µm and at each point I captured 555 laser shots. In this scan I kept only the first of the two light pulses. So basically it is the same as “scan 1” but with a different granularity and with 555 laser shots at each xy point. As an example, below there are four plots showing the mean amplitude of each channel:

I used this scan to train the “machine learning likelihood algorithm” I presented in this post. Then I applied this algorithm to reconstruct the position using the “scan 1” data. This is what I obtained:

These plots show the mean and the standard deviation of the reconstruction error defined as

$\text{Reconstruction error} = \sqrt{(x_\text{TCT} – x_\text{Reconstructed})^2 + (y_\text{TCT} – y_\text{Reconstructed})^2}$

where $$x_\text{TCT},y_\text{TCT}$$ are the coordinates where the laser was shined according to the TCT software. In both plots the black dots show the points where the reconstruction algorithm was trained (you can switch off these points by clicking the “Training points” legend). The scan used to reconstruct has high granularity but only two events at each point. Thus, it lacks the desired statistics to obtain a precise spacial resolution at each single point. However, we can plot the distribution of the reconstruction error inside the “Swiss flag region” denoted in the plots.

The blue curve shows the distribution of ALL the data, including when the laser was shined on top of the metallic pads (i.e. the laser could not reach the silicon). The green curve shows the distribution for events outside the Swiss flag region and, finally and more interesting, the red curve is the distribution of reconstruction error for events within the Swiss flag region. A Gaussian fit was made, shown in the plots. As can be seen in both cases the spacial resolution according to this fit is $$\lesssim$$ 4 µm. A plot of the $$\text{Reconstruction error}$$ as defined above looks like this:

A curious fact: The machine learning algorithm learned to reconstruct the hit position even when the laser shined onto one of the metallic pads, which is supposed to block the light and so the detector does not work in this regions (with photons). We can see this fact in the previous distribution for the events outside the Swiss flag region (green curve). Despite being a big tail of events with bad spacial resolution (greater than 20 µm) there is a lobe with maximum around 7 µm.

## Temporal characterization

For the temporal characterization I performed a third scan, “scan 3” (“20210225005001_AC-LGAD_Paul_MIP_10um_555trigs_2_pulses”), which was basically identical to “scan 2” but taking data from both the two light pulses coming one with and the other without the 100 ns delay produced by the optic fiber. Using this data I proceeded with a very rudimentary analysis: I considered each pad as a simple LGAD and I performed the timing analysis we usually do with the single pad (common) LGADs. So basically for each pad and each x,y I did the same as in this post was done for a regular LGAD.

Let me start exposing the results. The plots below show the time resolution at each x,y point I got for each channel:

This time resolution is $$1/\sqrt{2}$$ times the standard deviation of the time difference at some optimized value of the constant fraction discriminator $$k_\text{CFD}$$. So basically if we chose some particular x,y, say the very first point starting from the bottom left in the previous plots, we have (for channel 1 which is the one with high amplitude due to proximity to this point):

The plot on the left shows the time resolution for different combinations of the CFD constant for the pulse 1 and the pulse 2. The plot on the right shows the time difference distribution specifically for 90 % of both CFD constants (which gives the best result, it is indicated with a red point in the plot on the left). In this plot on the right we can see that the mean value es 98 ns (the ~100 ns from the fiber optic delay line) and the standard deviation, assumed to be only attributable to the AC-LGAD itself, of 18.24 ps which when divided by sqrt(2) gives the 12.9 ps that go to the time resolution as a function of x,y for channel 1 in the previous plots. The channels 2, 3 and 4 have very bad time resolution in this point so they are not even shown.

In the regions close to the pads the time resolution is on the order of 14 ps which is remarkable. “Far from the pads”, e.g. in the center of the four pads, the time resolution gets worse up to ~25 ps. It has to be noted that this time resolution was obtained treating each pad as a completely independent device, i.e. without any combination of information from the four pads. If information from the four pads is used to reconstruct the time this is expected to improve[7]Mandurrino M., et al. “High Performance Picosecond- and Micron-Level 4D Particle Tracking with 100% Fill-Factor Resistive AC-Coupled Silicon Detectors (RSD).” ArXiv:2003.04838 [Physics], March … Continue reading.

## Conclusions

• I performed my first time-space characterization of an AC-LGAD using the TCT at UZH.
• The spacial resolution obtained today is on the order of 4 µm (slightly better). This analysis used the same detector for training and evaluation. This is valid, though, because the two data sets used are different. The evaluation data set has even a granularity 10 times higher than the training data set and the algorithm is still performing very well.
• Variations in the spacial resolution from one detector to another still have to be determined.
• The temporal analysis I made today is very basic and does not combine in any way the information from the different readout pads. Despite this, the time resolution I obtained is between 13-16 ps which is really nice. A more refined analysis can only improve this time resolution, I think.

References

↑1 AC coupled LGAD. Resistive AC-Coupled Silicon Detectors. See my other posts on AC-LGADs here. For more details see this and this posts. Mandurrino M., et al. “High Performance Picosecond- and Micron-Level 4D Particle Tracking with 100% Fill-Factor Resistive AC-Coupled Silicon Detectors (RSD).” ArXiv:2003.04838 [Physics], March 24, 2020. See in this post. To be specific, a “laser pulse width” of 64.8 % was used.