Effect of large-angle incidence on particle identification performance for light-charged ($Z\leq 2$) particles by pulse shape analysis with a pad-type nTD silicon detector

Particle identification by DPSA of the preamplifier output was performed similarly as in Ref. [3]. The flow of DPSA and example waveforms during the analysis are in depicted Figs. 3 and 4, respectively. The symbols in Fig. 3 correspond to the waveforms of the same color, as displayed in Fig. 4. In the first step, the baseline of the digitized signal of Si detectors, calculated by averaging the first 800 samples, was subtracted from the waveform. An example of a baseline-subtracted waveform is indicated by the black line in Fig. 4. In order to identify light ions, two feature values were extracted from the digitized waveforms. One is the maximum current ($I_{\mathrm{max}}$) and the other is the energy deposit ($E$), as explained in the following subsections.

It has been found that particle performance improves more at lower biases as compared to the over-depletion bias of the nTD-Si detector [2]. In this study, measurements were also made at various bias voltage settings to investigate the optimal voltage for light ion discrimination.

Figure 6 depicts the PID plots for different bias voltages.

As the bias voltage increases, $I_{\mathrm{max}}$ tends to increase for the same energy loss. This is because a higher bias voltage shortens the charge collection time. As the bias is lowered from 300 V, which is the nominal full-depletion bias of the MSX04-500, the PID performance improves, particularly in the low-energy region. On the other hand, the measurement at 310 V bias shows poor particle discrimination for low-energy hydrogen isotopes.

In order to quantitatively evaluate the particle discrimination performance under each measurement condition, the figure of merit (FOM) was defined in the same manner as done in Ref. [6]:

where $\mu$ and $\sigma$ are the mean and standard deviation of the distribution of $I_{\mathrm{max}}$ for a given energy loss by a given particle, respectively. Using this definition, an FOM greater than 1.5 can generally be considered to have sufficient discrimination power.

Figures 7 (a) and (b) depict FOMs for $p$-$d$ and $d$-$t$ discrimination for various bias voltages and energy losses. Points corresponding to conditions in which the two particles were indistinguishable are not plotted. As a general trend, smaller bias voltages improved the performance of particle discrimination for hydrogen isotopes, and satisfactory discrimination was achieved for hydrogen ions of 3 MeV or higher at 260 V or lower. However, if the bias voltage is set too low, the charge collection efficiency will also decrease and the signal wave height will also be low, which may cause low-energy particles to be missed. In fact, a decrease in the pulse height and deterioration in energy resolution was observed at 240 V for the alpha particles used in the energy calibration. Therefore, 260 V was selected as the optimal bias in this study, and all subsequent measurements hereafter were made at 260 V bias.

The dependence of the particle discrimination performance on the incident position is discussed on the basis of the results of measurements when charged particles are injected into the four regions depicted in Fig. 2 using the collimator and when charged particles are irradiated without the collimator — that is, the entire detector is irradiated with charged particles. Figure 8 presents the PID plots for different incident regions. For the measurements with the collimator, there is little difference in the PID plot, except for the difference in statistics. The locus between the hydrogen isotope loci and the helium isotope loci present when the collimator was absent is eliminated by using the collimator to limit the incident area. In addition, the use of the collimator significantly reduces the smearing of events from the respective loci to the low $I_{\mathrm{max}}$ side. This limitation of the incident area improves the discrimination performance, particularly between ⁴He and ⁶He in the energy region below 15 MeV. The absence of such events, even when charged particles are incident not only in the central area but also in the edge and the corner areas, suggests that these events occur when particles are incident at the very edge of the chip area of the detector.

Figure 9 depicts the variation of $I_{\mathrm{max}}$ for different incident areas for different incident energies. Each symbol and error bar represents the mean and standard error of the $I_{\mathrm{max}}$ distribution. For all energy regions, $I_{\mathrm{max}}$ is slightly smaller when particles are incident at the center. The reason for this is not clear, but it will not be discussed in this paper because this decrese does not affect the particle identification performance that is of interest here.

Figure 10 depicts the PID plots for incident angles of 0^∘, 15^∘, 30^∘, and 45^∘. For the incident angle at which the measurements were made, it was found that particle discrimination was possible even at large angles of 45^∘ if the incident angle distribution was sufficiently restricted. The maximum energy of stopped particles increases as the incident angle increases because the effective thickness increases by a factor of $1/\cos\theta$. In general, for particles with the same kinetic energy, $I_{\mathrm{max}}$ decreases as the incident angle increases. Figure 11 depicts the variation of $I_{\mathrm{max}}$ for each energy range and for each hydrogen ion as a function of the incident angle. The higher the neutron number and the lower the energy, the higher the rate of the reduction of $I_{\mathrm{max}}$. From these figures, we can conclude that hydrogen ions can be well discriminated by $I_{\mathrm{max}}$ if the incident angle is limited between 0^∘ and 30^∘. For example, assuming a point source of charged particles, sufficient PID can be achieved if the detector is at least 5 cm away from the source.

In order to understand how increasing the incident angle reduces $I_{\mathrm{max}}$, the relationship between the depth of penetration of the charged particle into the detector and the maximum current is discussed. $I_{\mathrm{max}}$ is considered to be approximately proportional to the charge collection rate. The charge collection rate is affected by the magnitude of the electric field in the silicon detector and the drift distance to the electrode, both of which are functions of the penetration depth of the detector by the charged particles. Thus, the ratio $\langle I_{\mathrm{max}}\rangle$/$Q$ can be considered proportional to the rate of charge collection and independent of the amount of charge. Figures 12 (a)–(f) depict $\langle I_{\mathrm{max}}\rangle$/$Q$ as a function of penetration depth for each hydrogen and helium isotope. Here, the penetration depth $d$ was defined in the following manner:

where $R(E)$ is the range in silicon as a function of total kinetic energy and was calculated using the methods in Refs. [11] (for H) and [12] (for He) implemented in the LISE++ code [13].

It is evident that the $\langle I_{\mathrm{max}}\rangle$/$Q$ ratio for each nuclide is almost independent of the incident angle of charged particles and can be well represented only by the penetration depth. Once this ratio has been measured for the detector to be used, the detector response can be simulated using the nuclide and its incident angle distribution as input. This enables us to evaluate the particle discrimination performance in future experimental setups.

In addition, this relationship may enable the nTD-Si detector to be used as an incident angle detector. If the incident nucleus is identified, the $\langle I_{\mathrm{max}}\rangle$/$Q$ ratio can be used to determine the penetration depth and, thus, provide information on the incident angle of low-energy charged particles. It can be used, for example, to evaluate the background events due to charged particles not originating from the target and to identify the target from which the charged particles are originating from in multiple target measurements.

Figure 13 depicts the $\langle I_{\mathrm{max}}\rangle$/$Q$ ratio as a function of penetration depth for different nuclides at an incident angle of 0^∘. The magnitude of the $\langle I_{\mathrm{max}}\rangle$/$Q$ ratios for hydrogen and helium are distributed in a similar range, but the slope is steeper for helium than that for hydrogen. The slope for nuclides with the same number of protons tends to increase slightly with an increasing mass number, although the difference is smaller than that for different proton numbers. The dependence on the number of protons and mass number at large penetration depths can be qualitatively discussed because as the number of protons and mass number increases, the width of the Bragg peak narrows and the position distribution of the energy loss becomes closer to the end of the range, thereby resulting in a larger $\langle I_{\mathrm{max}}\rangle$/$Q$ ratio. On the other hand, in the shallow penetration depth region, the electric field is weaker due to the under-depletion bias. It is possible that the space charge effect, although small, is present because the charge density generated at the Bragg peak is larger for particles with larger proton and mass numbers, thereby resulting in slightly longer charge collection times.