Silicon Drift Detectors for the Measurement and Reconstruction of Beta Spectra

Abstract

The ASPECT-BET project, or An sdd-SPECTrometer for BETa decay studies, aims to develop a novel technique for the precise measurement of forbidden beta spectra in the 10 keV-1 MeV range. This technique employs a Silicon Drift Detector (SDD) as the main spectrometer with the option of a veto system to reject events exhibiting only partial energy deposition in the SDD. A precise understanding of the spectrometer's response to electrons is crucial for accurately reconstructing the theoretical shape of the beta spectrum. To compute this response, GEANT4 simulations optimized for low-energy electron interactions are used and validated with a custom-made electron gun. In this article we present the performance of these simulations in reconstructing the electron spectra measured with SDDs of a ¹⁰⁹Cd monochromatic source, both in vacuum and in air. The allowed beta spectrum of a ¹⁴C source was also measured and analyzed, proving that this system is suitable for the application in ASPECT-BET.

Keywords: GEANT4 simulations; silicon drift detectors; β spectra.

Figure 1

47-pixel SDD matrix used for all the measurements here reported (left). Scheme of the 47 pixels: only the 7 red ones were acquired (right).

Figure 2

Vacuum chamber in the Milano-Bicocca laboratory. The main detectors operated in this setup, a 47-pixel SDD matrix and a Pixet, are indicated. The e-gun, attached to a xy-movable stage, is also highlighted.

Figure 3

(Left): picture of the e-gun. (Center): anode with 7 LEDs used to illuminate the cathode and the aluminum cylinder with UV light. (Right): gold-coated cathode used to collimate the electron beam. The aluminum cylinder, where electrons are produced, is visible in its center.

Figure 4

(Left): CAD drawing of the e-gun. The most important components are highlighted. (Right): COMSOL simulation of the electron beam produced with the e-gun.

Figure 5

(Top): measurement of the e-gun beam spot performed with the Pixet. A beam size of ∼0.5 mm and a rate ${10}^4$ electrons/s were found. (Bottom): measurement of a 10 keV electron spectrum acquired with an SDD. Only the central part of the pixel was hit with the e-gun beam. The best fit of the spectrum done with the detector model is also shown.

Figure 6

CAD schematics of the setup used in the measurements. Section of source and detector (top), and side view (bottom).

Figure 7

M1 Data acquired with the SDD main pixel in a 3-h measurement. The energy of the X-ray peaks and the tag of the different IC electrons are shown.

Figure 8

Data-MC comparison for different values of the effective Mylar thickness (top). Reduced ${\chi }^2$ as a function of the effective Mylar thickness (bottom). The best-fit value of 7.2 μm is extracted through a parabolic fit.

Figure 9

Best fit of MC prediction to the data set acquired with the ¹⁰⁹Cd source in vacuum. The fit is done only in the non-shaded area.

Figure 10

Comparison of MC prediction to the dataset acquired with the ¹⁰⁹Cd source in air. The comparison is done only in the non-shaded area.

Figure 11

Data acquired with the main SDD in a 6 h measurement using a ¹⁴C source (top). ${\chi }^2$ as a function of the effective Mylar thickness for the two models: the Fermi theory prediction and the one including the experimental shape factor (bottom). The best fit for the effective Mylar thickness is 4.5 μm.

Figure 12

Fit to the data set acquired with the ¹⁴C source in vacuum using the MC prediction. The fit is performed only in the non-shaded area. The theoretical input is also shown.

Figure 13

Fits obtained by varying $\lambda$ (top), the baseline resolution $\sigma$ (center) and the charge cloud width in Si (bottom).

Figure 13

Fits obtained by varying $\lambda$ (top), the baseline resolution $\sigma$ (center) and the charge cloud width in Si (bottom).

Figure 14

Fits obtained by varying the production cut for secondaries in GEANT4 (top) or the physics list used (bottom) in the simulations.