FROM : Operation of BGO with SiPM Readout at Dry Ice 1 and Liquid Nitrogen Temperatures

Comments from Reviewer 1

This paper reports the measurement results of BGO crystal with SiPM readout operating at low temperatures. Even though the performance of the system is not exceptional, they do serve as a good reference for similar experiments. Before giving the final decision, there are some items to be addressed.

1. Line 66. The crystal surfaces were unpolished for the same reason. Does this mean that the parts directly facing the SiPM are also not polished?

Answer: You are right. Surfaces facing SiPMs are also unpolished. This is not great for light collection. Originally, we had two crystals, one with all surfaces fully polished, another with all surfaces unpolished. We planned to make comparison measurements. However, the polished one got damaged, and we had to postpone the planned measurements. We are in the process of purchasing new crystals to continue our measurement. However, we’d like to get what we already measured published. We replaced “The crystal surfaces were unpolished for the same reason” with the following explanation in our new version of draft:

Side surfaces of the crystal were unpolished for the same reason. The top and bottom surfaces in direct contact with the SiPMs were also unpolished. Light loss is likely to happen in such an interface. There is room for improvement. We are in the process of designing new experiments with various surface conditions to investigate in detail how surface treatment affects the light collection efficiency. The result will be published in a separate manuscript.

2. Line 119~121. The explanation for the increase in MeanSPE was not clear. The correct reason is that as the temperature decreases, the Vbd of the SiPM decreases, so the Vover is larger at the same bias, leading to a larger gain. It should be improved.

Answer: We totally agree with you. We replaced the second sentence of that paragraph with detailed explanation below.

In general, the breakdown voltage, , of a SiPM decreases as the temperature goes down. As we kept the same bias voltage, , for all measurements, the over voltage, , was higher at lower temperatures.  This led to an increased gains of both SiPMs at liquid nitrogen temperature.

3. Table 1,2,3,4. For the uncertainties of light yield. I think it is more reasonable to use the sigma of the Gaussian fitting result.

Answer: We’d love to use only the uncertainty of fitting as the overall uncertainty. This will make our measurement look much more precise. However, based on our experience, we anticipate variations of the measured SiPM gain at ~5% level in different runs even at the same temperature. Possible causes include unstable power supply, unstable amplifier, electronic noise, loose cable connections, etc. We agree that these experimental conditions can be improved to reduce the uncertainty. We will keep refining our setup to deliver better result in the future. For the moment, we feel more comfortable to quote a larger uncertainty to be conservative.

4. Line 148. The yield decreases slightly as the energy goes down. I think the authors cannot get this conclusion. The light yields are consistent within the errors.

Answer: We agree. We replaced the second sentence in that paragraph with the following description.

Yields measured at different energy points are consistent with each other within the uncertainty. However, there is a hint that the yield decreases slightly as the energy goes down. If this is true, it could be explained by ....

5. Lines 161-162. Why do you use different functions to fit? It should be explained.

Answer: That’s a good suggestion. We added the following explanation at the beginning of that paragraph:

As mentioned in the introduction, the decay time of scintillation emission in BGO increases dramatically as the temperature goes down. This demands different ranges for analysis at different temperatures. At dry ice temperature, the selected range for analysis is [1600, 5000]x4 ns, while at liquid nitrogen temperature, the selected range is [1600, 12000]x4 ns. Note that at dry ice temperature a single exponential decay function can describe the averaged waveform in the analysis range very well, while at liquid nitrogen temperature a fast and a slow exponential decay must be used to describe the average waveform in the selected range. The corresponding fitting functions and results are shown in Fig. 5.

6. Eq.3. While calculating the intrinsic light yield of the crystal, the effect from the crosstalk and afterpulses of SiPM should be taken into consideration. The following references introduce how the iCT and eCT from SiPMs affect the measured light yield: https://doi.org/10.1140/epjp/s13360-023-04263-z [2212.11515] Reactor neutrino physics potentials of cryogenic pure-CsI crystal (arxiv.org)

Answer: Thank you for pointing this out! Yes, we should have taken this into account when we calculated the intrinsic yield. We included cross talk correction in equation (3), modified the paragraph below it and corrected all the numbers in that paragraph. The essential part of the change is copied below:

Optical cross talks between neighboring cells within a SiPM or between two face-to-face SiPMs increases the number of observed photon-electrons artificially~\cite{ihepCsI22, kims, ihepSiPM23, ihepSiPM23a}. This effect must be corrected. According to Ref.~\cite{ihepSiPM23a}, the breakdown voltage of the SiPMs used in this measurement is about 21 V. Biased at 29 V, both SiPMs were operated with a breakdown voltage of about 8 V. The number of detected photoelectrons should be doubled due to cross talk~\cite{ihepSiPM23}. The cross talk correction should hence be around 200\%.

7. Lines 179-181. The contribution of Cherenkov light to the total light yield is so limited that it is not reasonable to use the total light yield to be divided by the decay constant of Cherenkov light while calculating FOM.

Answer: Sorry that we did not make it clear. The idea is to use Cherenkov light for time information and use scintillation light for energy information. This way, we use the best from both channels. Yes, you are right, the Cherenkov light cannot contribute to the total yield at all. But as long as there is detectable Cherenkov light to provide fast time information, we can use that information for position reconstruction in PET.

8. Line 188. Add spaces before and after ±.

Answer: thank you for taking care of every single detail! We added spaces before and after as suggested.

Reviewer comment-2

Reviewer: Dear Authors Please see below comments. In general, I think this paper is intact in data processing but lack of the emphasis of innovation.

1. Line 153: These two temperatures seem specific. How do you choose them? I think it is more convinced if had simulated or tested a series of temperatures first.

Answer: that’s a good question! And you are right, it is more convincing if we test it in a series of temperatures. Lucky for us, this work has been done by others. We cited their paper (Ref. 10) in paragraph around line 35. We also added Fig. 1 (taken from Ref.10) in the introduction to show how the light yield and decay constants of BGO change over a wide temperature range. We expanded the last sentence of that paragraph to elaborate more about our choice in the updated draft:

The dry ice temperature, 194.7~K, which is convenient to obtain, seems to be a reasonable choice, where the light yield is already 3 times higher than that at room temperature while the decay constant is only twice higher than that at room temperature. Properties at 77~K are still worth probing as the light yield doesn't change much anymore below 77~K and it is easy to get to this temperature using liquid nitrogen. With a cryo-cooler, other temperatures can also be used. But practically, a cryo-cooler is much more expensive than liquid nitrogen and dry ice.

2. Line 173-177: The results look the same with Line 29, so what is the innovation of the whole experiment? For example, the instrument or technique enhances the FOM or light yield compared with others of different temperatures or scintillators etc.

Answer: You are right that the FOM from our measurement is not promising. This, by itself, is a result that can be reported, so that other people don’t have to repeat what we did. Instead, they can modify our setup, and try to get better results. In the discussion, we also pointed out possible directions for innovation, that is, to combine Cherenkov time information with the scintillation energy information to create much better FOM. This is what we are going to try next.

We humbly draw your attention to the following two points. First, the combination of SiPM + BGO at 77 K and 194.7 K is not reported in the literature before based on the authors’ limited knowledge. Second, we did achieve higher light yields using this combination. The FOM for PET is not satisfactory, but the high light yields are still meaningful for SPECT, as time information is not used there. We emphasized this point in the last paragraph of the “Discussion” section.

3. Line 178-180: The time information of Cherenkov radiation appears roughly. It should be a simple explanation of the process at least.

Answer: That’s a good suggestion! We expanded that paragraph with the following description:

Cherenkov photons are emitted from electrons moving fast than the speed of light in BGO. The differential Cherenkov photon yield can be calculated based on the Frank-Tamm formula~\cite{ftf},

\begin{equation} 

\frac{\text{d}N^2}{\text{d}x\text{d}\lambda}=\frac{2\pi\alpha}{\lambda^2}\left(1-\frac{1}{n^2(\lambda)\beta^2}\right),

\end{equation}

where, $x$ is the electron track length, $\lambda$ is the wavelength of the emitted photons, both have the unit of meter, $\alpha\approx1/137$ is the fine-structure constant, $\beta=v/c$, and $v$ is the speed of electron, $n$ is the refraction index of the medium, which is a function of $\lambda$. It shows in the formula that the larger the refractive index $n$ is, the more Cherenkov photons can be emitted. The refractive index of BGO is 2.39 at 310 nm and 2.2 at 420 nm, much higher than LSO, which is 1.83 at 420 nm. The Cherenkov light yield for 511 keV photons commonly used in a PET is about 20 photons (305--750 nm) for BGO and only 9 photons (390--750 nm) for LSO~\cite{PET1}. Some experimental investigation has shown the possibility to detect Cherenkov light in BGO~\cite{PET1}. The authors plan to try it with cooled SiPMs and that effort will be covered in a separate publication.

We highlighted all the changes in the updated pdf file to make your proof-reading a bit easier.