Abstract
In this paper, we present the application of a simplified thermal model in order to extract some of the fundamental parameters needed to understand the response function of low-temperature calorimeters consisting of \(\hbox {TeO}_{2}\) crystals read-out by neutron transmutation doped (NTD) thermistors operated at temperatures \(T \sim 10\) mK. To this aim, four detectors were hosted in two different holders, one made of copper and the other made of Stratasys \(\hbox {VeroClear}^{TM}\), a 3D-printed plastic material very similar to acrylic. The static characterization of the detectors through the analysis of their load curves at different temperatures, guided by the thermal model, enabled the identification of the main thermal link to the heat sink of the two systems: the glue between the crystal and the copper frame (scaling as \(T^3\)) for the detectors in the copper holder, and the NTD gold read-out wires (scaling as \(T^{2.5}\)) for the detectors in the plastic holder. As a subdominant contribution, we could also extract the electron–phonon decoupling characteristic of our NTDs, described by a thermal conductance scaling as \(T^4\).
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References
Ed.C. Enss, Cryogenic Particle Detection (Springer, Berlin, 2005)
C. Enss, D. McCammon, Physical principles of low temperature detectors: ultimate performance limits and current detector capabilities. J. Low Temp. Phys. 151, 5–24 (2008)
S. Pirro, P. Mauskopf, Advances in bolometer technology for fundamental physics. Annu. Rev. Nucl. Part. Sci. 67, 161–181 (2017)
M. Barucci, C. Brofferio, A. Giuliani, E. Gottardi, I. Peroni, G. Ventura, Measurement of low temperature specific heat of crystalline TeO\(_2\) for the optimization of bolometric detectors. J. Low Temp. Phys. 123(5–6), 303–314 (2001)
E.E. Haller, N.P. Palaio, M. Rodder, W.L. Hansen, E. Kreysa, NTD Germanium: A Novel Material for Low Temperature Bolometers (Springer US, Berlin, 1984), pp. 21–36
E.E. Haller, Advanced far-infrared detectors. Infrared Phys. Technol. 35(213), 127–146 (1994)
N.F. Mott, J.H. Davies, Metal-insulator transition in doped semiconductors. Philos. Mag. B 42(6), 845–858 (1980)
A.L. Efros, B.I. Shklovskii, Coulomb gap and low temperature conductivity of disordered systems. J. Phys. C Solid State 8(4), L49–L51 (1975)
A.L. Woodcraft, R.V. Sudiwala, E. Wakui. Measurement of anomalous resistance-temperature relation for neutron transmutation doped germanium, in AIP Conference Proceedings, vol. 605(99) (2002)
A.L. Woodcraft, R.V. Sudiwala, E. Wakui, C. Paine, Hopping conduction in NTD germanium: comparison between measurement and theory. J. Low Temp. Phys. 134(3/4), 925–944 (2004)
M. Barucci, J. Beeman, E. Olivieri, E. Pasca, L. Risegari, G. Ventura, Electrical characteristics of heavily doped NTD Ge at very low temperatures. Physica B 368, 139–142 (2005)
F. Pobell, Matter and Methods at Low Temperatures (Springer, Berlin, 2007)
B.K. Ridley, Hot electrons in semiconductors. Sci. Prog. 70(3), 425–459 (1986)
I. Nutini, The CUORE Experiment: Detector Optimization and Modelling and CPT Conservation Limit. PhD thesis, SISSA, Trieste (2019)
G. Ventura, L. Risegari, The Art of Cryogenics (Elsevier, Amsterdam, 2008)
R.J. Soulen, W.E. Fogle, J.H. Colwell, Measurements of absolute temperature below 0.75 K using a Josephson-junction noise thermometer. J. Low Temp. Phys. 94, 385–487 (1994)
D. McCammon, Semiconductor thermistors. Appl. Phys. 99, 35–61 (2005)
P. Stefanyi, R. Rentzsch, P. Fozooni, C.C. Zammit, M.J. Lea, J. Saunders, Electron-phonon interaction in NTD Ge irradiated in 1980, in Phonon Scattering in Condensed Matter VII. ed. by M. Meissner, R.O. Pohl (Springer, Berlin, 1993)
J. Soudee, Hot electrons effect in a #23 NTD Ge sample. J. Low Temp. Phys. 110, 1013–1027 (1998)
J. Zhang, W. Cui, M. Juda, D. McCammon, R.L. Kelley, S.H. Moseley, C.K. Stahle, A.E. Szymkowiak, Non-Ohmic effects in hopping conduction in doped silicon and germanium between 0.05 and 1 K. Phys. Rev. B 57(8), 4472 (1997)
W.A. Little, The transport of heat between dissimilar solids at low temperatures. Can. J. Phys. 37, 334 (1959)
A. Alessandrello et al., Development and optimization of a modular bolometer to search for rare decays. Czechoslov. J. Phys. 46, 2893–2894 (1996)
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This work was supported by Istituto Nazionale di Fisica Nucleare (INFN) and by Università degli Studi di Milano–Bicocca.
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Biassoni, M., Brofferio, C., Carniti, P. et al. A Thermal Model for Low Temperature \(\hbox {TeO}_{2}\) Calorimeters. J Low Temp Phys 206, 80–96 (2022). https://doi.org/10.1007/s10909-021-02639-y
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DOI: https://doi.org/10.1007/s10909-021-02639-y