Study of silicon sensors for precise timing measurement

LGADs are silicon sensors with the internal amplification mechanism, which already have been proved to realize the time resolution down to 30 psec [2]. However, the normal reach-through LGADs have an issue that the amplification factor heavily depends on the position of the hit, because the amplification region is not uniformly formed due to the surface structure. To overcome this, inverse-type LGADs have been proposed, which has amplification region at the bottom, in contrast to the reach-through type with amplification occurring just below the surface.

APDs are silicon sensors known as photon detectors, which have the same structure as LGADs. Table 1 shows the list of APD owned by Kyushu University, made by Hamamatsu. The pkg-10 and pkg-20 are LGAD prototype provided for Hamamatsu. In this paper, we used these APDs to study these characteristics.

We used the Testboard and SKIROCcms to read out signals from APDs. Testboard is a board to evaluate the characteristics of ASICs. It can be connected to APDs using the sensor boards as shown in Fig 2 and acquire data from APDs. The SKIROC2cms is an ASIC which can perform charge and time measurements. In these measurements, we put these equipments into an aluminum box for noise shielding.

We used a ${}^{90}\rm{Sr}$ beta source and a ${}^{133}\rm{Ba}$ gamma source. The beta source is used to observe the behavior when a MIP enters the APDs. The gamma source is used to measure the gain of APDs.

Figure 3 shows ADC histograms of APDs using beta source. These histograms showed that the signal height of reach-through type APDs is slightly larger than inverse type’s one, and S8664-55, which has the most largest active area, is larger than other APDs.

In the histogram of S12023-10, there is a small shoulder (Fig. 4, around 500 ADC counts). The ADC distribution should be landau distribution when the MIPs enter the APD, but if the APD has gain variation, the ADC distribution will be integration landau distributions. Assuming this ADC distribution is integration of landau distributions, the shoulder should be at the landau distribution of maximum gain. We fitted the peak using a function combing an error function and a linear function, as

The $\mu$ and $\sigma$ are the position and width of error function. We used the position of this shoulder to calculate active thickness of S12023-10A.

In order to calculate the active thickness, we have to measure the gain of APD. In this paper, we measured the gain of S12023-10A using gamma source.

Figure 5 (left) shows the ADC distribution of S12023-10A, with the bias voltage of 129 V. The edge of ADC distribution, at about 300 ADC counts, is due to the Compton edge, because the spectrum of ${}^{133}\rm{Ba}$ has a peak of photoelectric effect at 356 keV, and the Compton edge is at 207 keV. We fitted this edge using the same function as beta source measurement \eqrefeq:error, and calculated the gain using the mean of this function. The voltage dependence of the position of the shoulder is shown in Figure 5 (right).

We calculated the active thickness of S12023-10A using the results of beta and gamma sources measurements. A MIP makes 76 electron and hole pairs per 1 ${\rm\mu}$m in a silicon sensor, so the formula for calculating active thickness can be described by

with the $\mu$ is the mean of error function when measured using beta source and $e=1.602\times 10^{16}$ C. The $a$ is gradient of the correlation between ADC and charge in SKIROC2cms. Finally, the active thickness of S12023-10A is $\sim 1000{\rm\mu m}$.

However, it is said that the active thickness of APDs is a few tens of ${\rm\mu}$m and the gain of APD at 129 V is about 500 (according to the datasheets). Assuming the gain value is 500, the active thickness is $\sim 30{\rm\mu m}$ calculated by \eqrefeq:active.