Deep Diffused Avalanche Photodiodes for Charged Particles Timing

The upgrades of ATLAS and CMS for the High Luminosity LHC (HL-LHC) highlighted physics objects timing as a tool to resolve primary interactions within a bunch crossing. Since the expected pile-up is around 200, with an r.m.s. time spread of 180 ps, a time resolution of about 30 ps is needed. The timing detectors will experience a 1-MeV neutron equivalent fluence of about $\Phi_{eq}=10^{14}$ and $10^{15}$ cm$^{-2}$ for the barrel and end-cap regions, respectively. In this contribution, deep diffused Avalanche Photo Diodes (APDs) produced by Radiation Monitoring Devices are examined as candidate timing detectors for HL-LHC applications. To improve the detector's timing performance, the APDs are used to directly detect the traversing particles, without a radiator medium where light is produced. Devices with an active area of $8\times8$ mm$^2$ were characterized in beam tests. The timing performance and signal properties were measured as a function of position on the detector using a beam telescope and a microchannel plate photomultiplier (MCP-PMT). Devices with an active area of $2\times2$ mm$^2$ were used to determine the effects of radiation damage and characterized using a ps pulsed laser. These detectors were irradiated with neutrons up to $\Phi_{eq}=10^{15}$ cm$^{-2}$.


Introduction
The high luminosity upgrade of the CERN Large Hadron Collider (HL-LHC), foreseen to start in 2026, will provide an instantaneous luminosity of up to 7.5 · 10 34 cm −2 s −1 with a bunch spacing of 25 ns, and an average pile-up of up to 200 collisions per bunch crossing [1]. To reduce the effects of pile-up on the physics analyses, both the ATLAS and CMS experiments are planning to implement dedicated systems to measure the time of arrival of minimum ionizing particles (MIPs) with an accuracy of about 30 ps [2,3].
By providing the time of arrival information of MIPs, these systems allow for the correct association of particles to their primary vertexes in the case the latter have a proximity in space that renders their separation impossible. These timing detectors will be subjected to radiation levels corresponding to a 1-MeV neutrons fluence (Φ eq ) of up to 4.9 · 10 15 cm −2 for the goal integrated luminosity of HL-LHC of 4000 fb −1 .
This paper summarizes the characterization of deep diffused Avalanche Photo Diodes (APDs) produced by Radiation Monitoring Devices [4] used as timing detectors for charged particles. Studies of these sensors as MIP timing detectors, using an AC-coupled readout, were performed previously and showed promising results [5,6]. The timing performance as well as the radiation hardness of these devices are addressed. Section 2 describes the devices used in this study. Section 3 summarizes a radiation hardness study of devices with an active area of 2 × 2 mm 2 . Section 4 contains the results of a beam test of devices with 8×8 mm 2 active area. Finally, section 5 summarizes the results presented in this paper.

Deep Diffused APDs
Deep diffused APDs are silicon detectors based on charge multiplication.
They consist of a pn-junction operated in reverse bias. Their doping profile and operation bias voltage allow for the electric field to reach values high enough to achieve impact ionization. The typical bias voltage is close to 1800 V, resulting in a gain of about 500 and a 150 µm thick depletion region. The pn-junction lies a few tens of microns below the surface of the detector. The fabrication process used to obtain such a configuration gives the name to the devices. The depletion region does not reach the surfaces of the detector, therefore these APDs never reach full depletion. A schematic cross section of the detector is shown in figure 1. Further details about these devices can be found in [7][8][9].
Two kinds of APDs were used for the studies presented in this paper. APDs with an active area of 2 × 2 mm 2 and a die dimension of 3.1 × 3.1 mm 2 were used for a radiation hardness study. Devices with an active area of 8 × 8 mm 2 , on a 10 × 10 mm 2 die, were characterized in a beam test.

Radiation Hardness Study Using 2 × 2 mm 2 APDs
The radiation hardness of the APDs was determined using devices with an active area of 2 × 2 mm 2 . The APDs were irradiated with neutrons at the irradiation facility of the Jožef Stefan Institute in Ljubljana [10]. The accumulated fluences ranged from Φ eq = 3 · 10 13 to 10 15 cm −2 .
The sensors were characterized using a pulsed infrared laser. The details of the setup used and a broader range of results are given in [11,12].
The evolution of the signal amplitude as a function of voltage and fluence can be seen in figure 2. The measurements were performed at −20 • C using laser pulses with an intensity corresponding to a charge deposit in the sensor of 15 MIP. The signal amplification was 10 dB. The irradiation decreases the gain of the detectors, for a given bias voltage. The sensor irradiated to Φ eq = 10 15 cm −2 shows little to no gain. The sensor irradiated to Φ eq = 3 · 10 14 cm −2 is unstable above 1550 V and was not measured at voltages above this value. This fluence is considered the limit for the radiation hardness of these sensors since they cannot sustain the bias necessary for time of arrival measurements.
The jitter of the APD signal was measured using a pulsed infrared laser with a 0.8 MIP intensity and 40 dB amplification. The setup used for this measurement comprised an optical system that allows to project two light pulses on the sensor for each pulse generated by the laser. The time difference between the pulses is 50 ns, fixed by the optical system, and their amplitudes differ by less than 5%. The time resolution of the APDs can be extracted by measuring the time difference between the pulses. In this configuration, no time reference detectors are needed, and the jitter of the laser does not influence the measurement. Additional details about the setup and method used for this measurement can be found in [12]. The jitter as a function of bias voltage and fluence is shown in figure 3. The jitter remains below 10 ps for fluences up to Φ eq = 6 · 10 13 cm −2 , although the bias voltage necessary to achieve this performance increases with irradiation.
The jitter was found to scale as one over the signal to noise ratio (1/SNR),

Beam Test of 8 × 8 mm 2 APDs
APDs with an active area of 8 × 8 mm 2 were characterized in a beam test.
A metal layer was deposited on the detector surfaces to improve the uniformity of response. The metal layer provides a DC-coupled readout of the detectors.
Additional details about the uniformity of response of these detectors can be found in [12]. The main goals of the beam test were to measure the properties of the APD signal as a function of position on the detector, and the APD time resolution for MIPs.
The particles used were 100 GeV muons at the H4 beam line at the CERN north area [13]. The beam test setup consisted of a microchannel plate photomultiplier (MCP-PMT), a beam telescope, trigger scintillators, and the APDs being tested. The MCP-PMT was used as a time reference [14], while the beam telescope allowed for the reconstruction of the point where the particles traversed the APDs. The trigger scintillators defined the acceptance of the setup. The results presented in this paper were obtained using one metallized APD operated at 1775 V.
The median amplitude of the APD signal as a function of position is shown in figure 5. The red lines represent the geometrical cuts used in the analysis.
The area considered for the analysis is 7.5 × 7.4 mm 2 .     It is worth to remark that the readout scheme used for the APDs in the beam test was not optimal for timing measurements, and that the performance of the detectors is expected to improve with an improved readout scheme. During the beam test, the readout was done connecting the detector in series with the amplifier. The high voltage is dropped on the detector, with the amplifier directly connected to the detector side close to ground potential. In this configuration, the RC constant that contributes to the leading edge of the pulse is affected by: the detector capacitance, the input impedance of the amplifier, and the impedance of the cable that connects the detector to the high voltage power supply. The readout can be improved by using a bias tee, connecting the detector in parallel to the amplifier through a capacitor. In this case, the impedance of the cable between detector and high voltage supply does not affect the RC constant, resulting in a steeper leading edge of the signal and therefore improving the time resolution. The mechanical constrains of the setup unfortunately did not allow to use a bias tee for the APD readout.

Summary
Deep diffused APDs were proposed as MIP timing detectors. The radiation hardness of these devices was assessed using devices with a 2 × 2 mm 2 active area. The jitter of these detectors was measured using a pulsed infrared laser and it remains below 10 ps up to a fluence Φ eq = 6 · 10 13 cm −2 . The detectors are expected to operate up to a fluence Φ eq ≈ 10 14 cm −2 . Devices with an active area of 8 × 8 mm 2 and a DC-coupled readout were characterized in a beam test. The time resolution of these detectors was found to be 44 ± 1 ps over a 7.5 × 7.4 mm 2 area, at a bias of 1775 V. This performance is expected to be improved by changing the readout scheme.