Measurement of Ion Mobilities for the Ion-TPC of NvDEx Experiment

Abstract

In the N$\nu$DEx collaboration, a high-pressure gas TPC is being developed to search for the neutrinoless double beta decay. The use of electronegative ⁸²SeF₆ gas mandates an ion-TPC. The reconstruction of the z coordinate is to be realized by exploiting the feature of multiple species of charge carriers. As the initial stage of the development, we studied the properties of the ${\mathrm{SF}}_6$ gas, which is non-toxic and has a similar molecular structure to ${\mathrm{SeF}}_6$. In the paper, we present the measurement of drift velocities and mobilities of the majority and minority negative charge carriers found in ${\mathrm{SF}}_6$ at a pressure of 750 Torr, slightly higher than the local atmospheric pressure. The reduced fields range between 3.0 and 5.5 Td. This was performed using a laser beam to ionize the gas inside a small TPC, with a drift length of 3.7 cm. A customized charge-sensitive amplifier was developed to read out the anode signals induced by the slowly drifting ions. The closure test of the reconstruction of the z coordinate using the difference in the velocities of the two carriers was also demonstrated.

1. Introduction

The search for neutrinoless double beta decay ($0\nu \beta \beta$) is an ideal way to probe the Majorana nature of the neutrinos. In addition, its discovery will prove that the lepton number is not conserved and help to study the absolute masses of the neutrinos and their origin. Recent or future experiments worldwide search for $0\nu \beta \beta$ decay using diverse technologies, including high-purity germanium detectors (GERDA [1], majorana demonstrator [2], LEGEND [3], CDEX [4]), time-projection chambers (TPCs) with Xe (EXO-200 [5], nEXO [6], NEXT [7], PandaX-III [8], LZ [9], DARWIN [10]), liquid scintillators (KamLAND-Zen [11], SNO+ [12]), cryogenic calorimeters (CUORE [13], CUPID [14], CROSS [15], AMoRE [16]), and tracking calorimeters (NEMO-3 [17], SuperNEMO [18]).

The N$\nu$DEx collaboration [19] proposed to search for $0\nu \beta \beta$ decay of ⁸²Se using a high-pressure ⁸²SeF₆ gas TPC [20]. The ${\mathrm{SeF}}_6$ has a high electron affinity, and the electrons produced by the ionization process are quickly captured by the ${\mathrm{SeF}}_6$ molecules to form negative ions. The negative ions are to be collected by the readout plane [21,22], consisting of CMOS integrated charge sensors named Topmetal-S [23], without being amplified in the gas. The main feature of Topmetal-S is its exposed metal on the top layer of the chip to sense the drifting charge carriers in the gas, hence integrating the functions of both the charge sensor and the readout application-specific integrated circuit in one chip. With this design, low noise can be realized, which is important for direct sensing. Both negative and positive ions are envisaged to be detected by the charge sensors, while in the first phase of the experiment with 100 kg ⁸²SeF₆ at 10 bar [19], only negative ions will be probed.

It is expected that in ${\mathrm{SeF}}_6$, the negative ions are predominantly ${\mathrm{SeF}}_5^{-}$ and ${\mathrm{SeF}}_6^{-}$, like in ${\mathrm{SF}}_6$, which has a similar molecular structure. One advantage is that, by using the different drift velocities of the two charge carriers, the z coordinate can be calculated without the need for a start time, which is difficult to implement in the N$\nu$DEx experiment. The ${\mathrm{SeF}}_6$ is toxic and needs to be handled with care. So in the first phase of the gas property study for the N$\nu$DEx experiment, we begin by studying ${\mathrm{SF}}_6$ gas. The properties of ${\mathrm{SF}}_6$ have been studied in a low-pressure environment [24] for dark matter experiments. In our study, we aim to observe and measure the properties of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ at atmospheric pressure and to study the z coordinate reconstruction.

The paper is structured as follows. The experimental apparatus and the method are described in Section 2. The results of the measurements, including the waveforms, velocities, and mobilities, are presented in Section 3. The reconstruction of the z coordinate using the different drift velocities of the two charge carriers is demonstrated in Section 4, followed by the conclusion in Section 5.

2. Experimental Apparatus and Method

2.1. Device Setup

The overall device setup for the measurement is shown in Figure 1. A Quantel Q-smart (450 mJ) laser is used to generate a pulsed laser beam with a wavelength of 266 nm. It also sends a trigger signal, which marks the start time of the event. The laser beam ionizes the gas in the TPC, and the anode plane below the grid is used to collect the negative ions. The anode plane is connected to a charge-sensitive amplifier (CSA), which turns the current signal into a voltage signal. Both the trigger signal and the signal from the CSA are sent to a Tektronix MSO5034B oscilloscope for further analyses. The high voltages of the TPC are provided by the iseg EHS 80-60n module.

The photo of the laser and the steel gas vessel is shown in Figure 2 (left). The laser beam enters the field cage of the TPC through a quartz window in the gas vessel. The photo of the field cage inside the gas vessel is shown in Figure 2 (right). It has a length of 40 mm, and the maximum drift distance (between the cathode and the grid) is 38 mm. The grid is made of wires with a diameter of 50 μm, and there is a 2 mm gap between the grid and the anode. The field rings are made of 2 mm wide copper strips at a pitch of 4 mm. They are connected by the 10 MΩ resistors.

2.2. The CSA

To detect the signal induced by the slowly drifting ions, a CSA has been specifically developed for the measurement, with its structure and photo shown in Figure 3.

It has two amplification stages. The current signal from the anode plane passes through the blocking capacitor ${\mathrm{C}}_1$ and then enters the first amplification stage, which is composed of a transistor and an OPA211 [25] amplifier chip. A JFET 2N4416 is used for its small gate leakage current and high transconductance. The resistors ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, and ${\mathrm{R}}_3$ are used to adjust the quiescent point of the JFET to make it work in the amplification regime. The decay time constant of the CSA is determined by the product of the feedback resistor ${\mathrm{R}}_{\mathrm{f}}$ and the feedback capacitor ${\mathrm{C}}_{\mathrm{f}}$. The ${\mathrm{C}}_2$ and ${\mathrm{R}}_4$ form a high-pass filter. The output of the first stage is filtered and then enters the second amplification stage with another OPA211 chip, with the gain determined by ${\mathrm{R}}_6$/${\mathrm{R}}_5$. The output impedance is 50 Ω. A test pulse could be injected into the TESTIN pin to calibrate the CSA with the injection capacitance ${\mathrm{C}}_{\mathrm{inj}}$.

The values of ${\mathrm{C}}_{\mathrm{f}}$ and ${\mathrm{R}}_{\mathrm{f}}$ were adjusted to achieve the desired decay time constant and noise performance of the CSA. In the subsequent measurements, 50 fF and 1 GΩ were adopted for ${\mathrm{C}}_{\mathrm{f}}$ and ${\mathrm{R}}_{\mathrm{f}}$, respectively. The main reason for the rather short 50 μs decay time constant was to avoid the saturation of the CSA during the measurement, which will be improved to allow longer decay time in the future.

3. Results of Measurement

3.1. Waveforms of $S{F}_6$

The laser beam, with a diameter of about 1 mm, enters the field cage through a 2 mm wide gap below the cathode. The laser beam is parallel to the cathode, and the distance between the beam center and the grid is 37 mm, which defines the drift length of the measurement. The trigger signal from the laser gives the start time of the event. The gas pressure is 750 Torr, slightly higher than the local atmospheric pressure of 630 Torr. The measurement was carried out at a room temperature of about 20 °C. The electric field strength of the drift region varies between 735 V/cm and 1351 V/cm. The electric field strength between the grid and the anode is fixed at 5000 V/cm.

The waveforms of the voltage signals from the CSA are acquired by the oscilloscope. The rise time of the CSA is about 1 μs, which is three orders of magnitude smaller than the typical time scale of the signal development. Therefore, the current signal is calculated from the voltage signal using the equation [24]:

$$I\left(t\right)\propto \frac{dV}{dt}-(-\frac{V}{\tau })$$

(1)

where $\tau$ is the decay time constant of the CSA. The current waveforms are then smoothed with a Butterworth filter to suppress high-frequency noise.

Figure 4 and Figure 5 show the typical waveforms of the voltage signals and the resulting current signals, respectively. It is estimated that approximately 3 M to 10 M negative ions were collected per laser beam. The trigger signals from the laser are also shown in the voltage waveforms. Due to the small decay time of CSA, the waveform of the current signal is similar to the corresponding waveform of the voltage signal. For the current waveforms, the amplitudes of the majority of the peaks are normalized to the unit.

Due to the small drift length and finite laser beam width, the waveforms of the two charge carriers are not quite separated from each other. But it can indeed be seen that there are at least two charge carriers in the current waveform, and the minority peak becomes more obvious for a higher drift field. The minority charge carrier, and the faster one, is postulated to be ${\mathrm{SF}}_5^{-}$, while the majority charge carrier, and the slower one, is postulated to be ${\mathrm{SF}}_6^{-}$. There is also a long tail on the right side of the majority peak. This could be due to ${\mathrm{SF}}_5^{-}{\left({\mathrm{SF}}_6\right)}_n$ and ${\mathrm{SF}}_6^{-}{\left({\mathrm{SF}}_6\right)}_n$, as well as ${\mathrm{SF}}_6^{-}{\left({\mathrm{H}}_2\mathrm{O}\right)}_n$, which drifts at a slower speed than the ${\mathrm{SF}}_6^{-}$.

The ratio of the amplitude of the minority carrier to that of the majority carrier increases from 0.13 to 0.28 as the drift field increases from 735 V/cm to 1351 V/cm. These are larger than the values reported in the measurement at low pressure [24]. We suspect that it is mainly due to the different signal generation mechanisms, i.e., we use a laser beam to ionize the gas. The cross section of ${\mathrm{SF}}_5^{-}$ has a strong dependence on the electron energy and could be enhanced in our case. The relative amplitude between ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ under different conditions will be further studied in the next step.

3.2. Drift Velocities and Mobilities

The drift times of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ are extracted by fitting a double-Gaussian function to the current waveform to extract their separate contributions, and the two μ values are used as their drift times. Examples of the double-Gaussian fit are shown in Figure 5 for four different drift fields. Due to the long tail on the right side of the majority peak, as explained in Section 2.2, the range of the fit is only up to about one standard deviation above the majority peak. The distributions of drift times for ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ are shown in Figure 6, for four different drift fields.

The drift velocity $v_{\mathrm{d}}$ is then calculated as the ratio between the 37 mm drift distance and the drift time. A total of 1.5 mm systematic uncertainty is considered on the drift length, including a ∼1 mm uncertainty for the position and width of the laser beam, and a ∼0.5 mm uncertainty for the impact of a 2 mm gap between the grid and anode at 5000 V/cm. Figure 7 (left) shows the drift velocities of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ as a function of the drift field.

The reduced mobility ${\mu }_0$ is also calculated, defined as:

$${\mu }_0=\frac{v_{\mathrm{d}}}{E}\frac{N}{N_0}$$

(2)

where $N_0=2.687\times {10}^{19}$ ${\mathrm{cm}}^{-3}$ is the gas density at STP (°C and 760 Torr). A conservative 1% uncertainty is considered on the pressure and temperature, taking into account the <1 °C variation and 1 °C accuracy of the temperature measurement, and the <0.1 mbar variation and 0.1% accuracy of the pressure measurement. Figure 7 (right) shows the reduced mobilities of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ as a function of the reduced field $E/N$ in Townsend units (1 Td = ${10}^{-17}$ ${\mathrm{Vcm}}^2$).

The reduced fields range between 3.0 and 5.5 Td. The reduced mobilities of ${\mathrm{SF}}_5^{-}$ vary between 0.576 ± 0.024 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and 0.587 ± 0.025 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, while the reduced mobilities of ${\mathrm{SF}}_6^{-}$ vary between 0.511 ± 0.021 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ and 0.520 ± 0.022 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$. The values are consistent with what was reported in Ref. [24] under the uncertainties.

4. Reconstruction of z Coordinate

Without using the start time, the z coordinate could be reconstructed by using the difference in the arrival times of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$, and their pre-calibrated drift velocities. The z coordinate reconstruction is demonstrated using the same datasets of Section 3, following the equation:

$$z=\frac{v_{{\mathrm{SF}}_5^{-}}·v_{{\mathrm{SF}}_6^{-}}}{v_{{\mathrm{SF}}_5^{-}}-v_{{\mathrm{SF}}_6^{-}}}·\Delta t$$

(3)

where $\Delta t$ is the difference in the arrival times of ${\mathrm{SF}}_5^{-}$ and ${\mathrm{SF}}_6^{-}$ in each event, while $v_{{\mathrm{SF}}_5^{-}}$ and $v_{{\mathrm{SF}}_6^{-}}$ are the measured drift velocities in Section 3.2.

Figure 8 shows the distributions of the reconstructed z-coordinate of the laser beam for four drift fields between 735 V/cm and 1351 V/cm. For each drift field, half (∼50) of the laser pulses are used to calculate the drift velocities, and the other half is used for the z-coordinate reconstruction. The means of distributions range from 3.699 to 3.702 cm as expected, with the standard deviations varying from 0.046 to 0.069 cm. Figure 8 provides a closure test of the velocity measurements and z coordinate reconstruction.

5. Conclusions

For the first phase of the gas property study for the N$\nu$DEx experiment using high-pressure ⁸²SeF₆ gas TPC to search for $0\nu \beta \beta$ decay, a structurally similar ${\mathrm{SF}}_6$ gas was examined at 750 Torr and room temperature, with the drift fields ranging from 735 V/cm to 1351 V/cm. The corresponding reduced fields range from 3.0 to 5.5 Td.

The minority charge carrier ${\mathrm{SF}}_5^{-}$ and the majority charge carrier ${\mathrm{SF}}_6^{-}$ were observed in the waveforms, and their drift velocities and mobilities were measured using a small TPC and a custom-developed CSA. The signals were generated by ionizing the gas using a laser beam.

A closure test of the reconstruction of the z coordinate using the difference in the arrival times of the two negative ion species was successfully performed.

The work in the paper lays the groundwork for future studies on the properties of ⁸²SeF₆ gas. Measurements will be improved and extended to higher pressures close to the value in the N$\nu$DEx experiment, to positive ions, and to other gas properties including diffusion, W value, and the Fano factors.