Radiation effects on NDL prototype LGAD sensors after proton irradiation

This paper focuses on one type of NDL sensor BV60, with image shown in Fig.2. The front side of one sensor has four square 1.00$\times$1.00 mm² pads with backside fully metalized. Each pad has a square readout electrode, and surrounded by six floating guard rings. The active thickness is 33 $\mu$m processed on epitaxy silicon ($\sim$300$\Omega$$\cdot$cm) with Boron doped $p^{+}$ layer.

Fig.3 (left) shows the experiment setup including thermocouple, graphite, refrigerator, aluminum foil and sensors. The beam direction is from right to left as indicated by the red line (color online). The beam uniformity is less than 1% and the beam size is around 2$\times$2 cm², confirmed by simulation and fluorescent film test. During the experiment, the stability of the beam luminosity is around 1% monitored every 30 minutes. The beam current is 100 nA corresponding to a beam flux of 10¹¹ hadrons/(cm${}^{2}\cdot$s) converted from the ratio between current and elementary charge. The irradiation fluence is calculated by beam flux times the beam time.

The LGAD sensors are fixed with kapton tape on five aluminum plates for different fluences (Fig.3 right). The five aluminum plates are arranged in sequence perpendicular to the beam direction. Based on the simulation, the attenuation of the beam over these plates is negligible. The irradiation fluence on each plate is rather uniform.

During the whole irradiation process, the temperature of the sensors was kept below 0^∘C with a Peltier and monitored by thermocouple to prevent the thermal annealing, which could alter the effective doping concentration and defects concentration [8]. The graphite block placed at the end of the beam serves as an absorber to prevent protons from hitting the interior wall of the terminal that can produce harmful substances. The sensors were annealed for 70 minutes at 60 ^∘C after irradiation and then kept in fridge to prevent further annealing.

Usually, the leakage current of a standard silicon sensor increases linearly with irradiation fluence [9]. However, the situation of LGAD is more complicated due to the gain layer. The leakage current of NDL BV60 increased by 5 to 6 orders of magnitude after irradiation and has non-linear features at different fluences as shown in Fig.4. For LGAD, the leakage current depends on the generation current $I_{gen}$ and the gain factor M: $I_{leak}$=M$\cdot I_{gen}$ [10]. Usually $I_{gen}$ in silicon sensor follows [9]:

where $\alpha$ is the irradiation damage rate, S is the active area, d is the thickness and $\Phi_{eq}$ is the irradiation fluence. $\alpha$ is about 3.9$\times 10^{-17}$ A/cm [9] with annealing time of 70 min at 60^∘C. Since S and d are constant for a given sensor, the increase of irradiation fluence leads to the increase of $I_{gen}$. M decrease with fluence because radiation reduces the effective doping concentration of gain layer. As the gain decreases and the $I_{gen}$ increases with irradiation, the $I_{leak}$ does not necessarily increase monotonically with fluence. For example, the $I_{leak}$ of sensors at 2$\times 10^{15}$ $n_{eq}/cm^{2}$ and 3$\times 10^{15}$ $n_{eq}/cm^{2}$ are equal.

The gain factor M can be estimated from the measured $I_{leak}$ and the calculated $I_{gen}$. For five irradiation fluences from 7$\times 10^{14}$ $n_{eq}/cm^{2}$ up to 4.5$\times 10^{15}$ $n_{eq}/cm^{2}$, the M are 4.7, 4.4, 3.6, 2.3, and 11.0 at the bias voltage of 50 V. The sudden increase of M at the highest fluence 4.5$\times 10^{15}$ $n_{eq}/cm^{2}$ in some NDL sensors might caused by unknown mechanism that leads to the miscalculation of $I_{gen}$. Further tests with $\beta$ source is necessary in order to justify the calculation procedure.

The capacitance-voltage (C-V) scans are used to evaluate the full depletion voltage ($V_{FD}$). The measured C-V curves for NDL sensors before and after irradiation are shown in Fig.5. The curves exhibit a sharp fall-off at the bias voltage ($V_{GL}$) where the gain layer is fully depleted. As the irradiation fluence increase, the decrease of $V_{GL}$ indicates the reduction of the effective doping concentration in gain layer which agrees with the acceptor removal mechanism. After the full depletion of gain layer, the capacitance quickly reaches saturation due to lightly doped bulk.

For the $1/C^{2}$-V curves are shown in Fig.6, the $V_{GL}$ is recognized as the point where the curves start a sharp increase and $V_{FD}$ is the point where the curves turn to flat after sharp increase. The difference between $V_{FD}$ and $V_{GL}$ is proportional to the doping concentration of the sensor bulk: $V_{bulk}$= $V_{FD}$ - $V_{GL}$. The radiation effect of acceptor removal in the gain layer is clearly visible by the decrease of $V_{GL}$. Due to the change of $V_{bulk}$ is irregular with fluence, it can not be justified that the radiation can generate acceptor-like defects in bulk layer. There is no clear explanation of the larger $V_{FD}$ and capacitance at 4.5$\times 10^{15}$ $n_{eq}/cm^{2}$. Further low-temperature research and more data are necessary.

On the macroscopic level, the acceptor removal effect in LGAD can be observed as the radiation induced decrease of depletion voltage ($V_{dep}$), respectively effective doping concentration ($N_{eff}$). The experimental data available are based on the measurement of depletion depth ($W_{dep}$), which is converted under the assumption of a homogeneous space charge into the $N_{eff}$ [11]:

where $q_{0}$ is the elementary charge and $\epsilon$ the permittivity of silicon. $N_{eff}$ dependence on $W_{dep}$ for the NDL sensors measured at different fluences is shown in Fig.7. The effective doping concentration $N_{eff}$ in the gain layer decrease with irradiation fluence, which agrees well with the acceptor removal mechanism.

To explain the acceptor removal effect at the microscopic level, the dopant Boron in the gain layer is removed from the substitutional lattice site and bound into defect complexes like $B_{i}O_{i}$ which no longer exhibit shallow acceptor properties leading to the decrease of $N_{eff}$ [11]. At the same time, radiation can generate acceptor-like defects so that $N_{eff}$ will increase with fluence. The combined effects are described by [12]:

where $N_{A_{0}}$ is the acceptor’s initial concentration before irradiation and $g_{eff}$ is the introduction rate of stable deep acceptors for irradiation with protons in this paper. Moreover, $N_{A_{0}}e^{-c_{A}\Phi_{eq}}$ is the acceptor removal term and $g_{eff}\Phi_{eq}$ is related to the acceptor-like defects. The model also explains the phenomenon that the $N_{eff}$ decrease first and then increase in the bulk layer with fluence [13].

Assuming the $N_{eff}$ in bulk layer is constant, $V_{GL}$ is proportional to an average concentration of Boron and the evolution of $V_{GL}$ with the irradiation fluences  [14] can be described as:

where $V_{GL_{0}}$ is the depletion voltage of the gain layer of the unirradiated sensor and $\Phi_{eq}$ is the irradiation fluence. By fitting the data with Eq.4, one can extract the acceptor removal coefficient $c_{A}$ as $(6.07\pm 0.70)\times 10^{-16}~{}cm^{2}$. The data is consistent with the acceptor removal model on macroscopic level.

The parameter $g_{B}=c_{A}\times N_{A_{0}}$ represents the number of deactivated acceptors per unit volume and fluence. Fig.9 shows the initial acceptor removal rate $g_{B}$ as function of the initial doping concentration for p-type silicon sensors. The red star is the result of this experiment, which is the agreement with the results of other LGAD experiments indicating the NDL sensor has fairly good radiation resistance. However, there is still no reasonable explanation that the $g_{B}$ of sensors with high initial doping concentration is much larger than low initial doping concentration, so it is essential to clarify and parameterize the drastic changes of $g_{B}$. More microscopic data of the irradiation LGAD sensor is needed to better understand the acceptor removal mechanism.