# Rising vs falling edge for timing in AC-LGAD

After my first timing measurement with the TCT, presented in this post, I started to play a little bit with timing in an AC-LGAD installed in the TCT. Playing around with different settings in the oscilloscope I noted that the temporal resolution seems to improve if, instead of using the rising edge, the falling edge is used. I don’t know if this should be surprising, if it is useful, or whatever, but anyway I want to keep record of this fact.

## Setup description

The setup for this test is very simple. I placed an AC-LGAD[1]RSD 1 W4-A -2,5 3×3 100, alias John. in the TCT and connected it to the oscilloscope without any amplifier, as shown below:

Then I positioned the laser in the region between the four pads, having previously adjusted the focus, and after this I started playing. Below there is a screenshot of the oscilloscope showing the signals from each pad.

I am using the laser splitting system described in this post, that is why there are two pulses separated by 100 ns.

## Rising vs falling edge

After playing for a while, I used the math functions of the oscilloscope to compute the sum of the four signals:

$\text{F3} = \text{C1} + \text{C2} + \text{C3} + \text{C4}.$

(F3 is the name this quantity was given by the oscilloscope, see pictures below.) I did this to reduce the non-correlated components (i.e. the noise). This sum is basically the “total signal”, because in this AC-LGADs it is shared by all the pads so the sum must be approximately equal to the signal without splitting.

I activated the persistence function in the oscilloscope and zoomed into one of the peaks of this signal, and I noticed this:

If we look carefully we note that $$\sigma_R > \sigma_F$$. In regular LGADs we usually measure time by using the rising edge. In this case, however, it seems that it could be better to use the falling edge. This is (probably) related to the fact that this detector is AC coupled.

I configured a “Period@level” measurement for the F3 signal and compared the two scenarios: Rising edge vs falling edge. These are my results:

Taking into account that both pulses are “statistically identical” and assuming that the fluctuations are only due to intrinsic effects from the AC-LGAD, the time resolution is the standard deviation over sqrt(2), i.e.

\left\{ \begin{aligned} & \sigma_{\text{AC-LGAD}}^{\text{Rising edge}}=44.5\text{ ps}\\ \\ & \sigma_{\text{AC-LGAD}}^{\text{Falling edge}}=32.9\text{ ps} \end{aligned} \right.

## Conclusion

By using the falling edge instead of the rising edge there is an improvement of 25 % in this time resolution for this AC-LGAD.

## Open question

Consider a regular LGAD, not an AC-LGAD. What is better, to couple to it in DC as we usually do[2]See e.g. this post and this post. or instead change to an AC coupling and exploit this effect? Still don’t know. It may happen that adding the AC coupling degrades the time resolution in such a way that the improvement after using the falling edge is not enough to compensate such degradation. Or not.

References

↑1 RSD 1 W4-A -2,5 3×3 100, alias John. See e.g. this post and this post.