Thermal characteristics of silicon nitride membranes at sub-Kelvin temperatures

Abstract

We have performed calorimetric measurements on 200 nm thin silicon nitride membranes at temperatures from 0.07 to 1 K. Besides full windows, membranes cut into a thermally isolating suspended bridge geometry were investigated. Based on dc and ac measurements employing normal-metal/insulator/superconductor (NIS) tunnel junctions both as a thermometer and a heater, we report on heat transport and thermal relaxation in silicon nitride films. The bridge structure improves thermal isolation and, consequently, energy sensitivity by two orders of magnitude over those of the full membrane with the same size, and makes such a structure very attractive for bolometric and microrefrigeration applications.

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

“…The voltage bias V refr across the SINIS structure allows us to change the electron temperature in the N region; at the same time, a measure of the voltage drop across the two probe junctions ͑V th ͒ at a constant bias current ͑I 0 ͒ yields the electron temperature T e,N in the normal electrode ͑Rowell and Tsui, 1976͒. Figure 27͑c͒ illustrates the experimental data of Leivo et al ͑1996͒ of the measured electron temperature T ϵ T e,N versus V refr , taken at different bath temperatures ͑i.e., those at V refr =0͒. As can be seen, the electron temperature rapidly decreases by increasing the voltage bias across the SINIS structure, reaching the lowest value around V refr Ϸ 2⌬ Ӎ 360 eV ͑note that two junctions in series are involved in the process͒.…”

“…The issue of how thermal conductivity and heat capacity of thin membranes and wires get modified due to geometrical constraints on the scale of the thermal wavelength of phonons has been addressed experimentally by several authors ͑Holmes et al, 1998; Leivo and Pekola, 1998;Woodcraft et al, 2000͒ and theoretically ͓see, e.g., Anghel et al ͑1998͒, Kuhn et al ͑2004͔͒. The main conclusion is that structures with one or two dimensions d Ͻ ph restrict the propagation of ͑ballistic͒ phonons into the remaining "large" dimensions and thereby reduce the magnitude of the corresponding quantities and C at typical subkelvin temperatures, but the temperature dependences get weaker.…”

“…The first observation of heat extraction from a normal metal dates back to 1994 ͑Nahum et al, 1994͒ in which cooling of conduction electrons in Cu below the lattice temperature was demonstrated using an Al/ Al 2 O 3 /Cu tunnel junction. A significant improvement was made two years later, still in the Al/ Al 2 O 3 / Cu system, by Leivo et al ͑1996͒, who recognized that using two NIS junctions in series and arranged in a symmetric configuration ͑i.e., as a SINIS͒ leads to a much stronger cooling effect. This fact can be understood by keeping in mind that Q is a symmetric function of V so that, at fixed voltage across the structure, quasielectrons above ⌬ are extracted from the N region through one junction, while at the same time quasiholes are filled in the N region below −⌬ from the other junction ͓see Fig.…”

“…Decreasing the temperature leads to a reduction of both the optimal T and the transmissivity window where cooling takes place. In real NIS contacts used for cooling applications, the average T is typically in the range 10 −6 -10 −4 ͑Nahum et al, 1994; Leivo et al, 1996͒ corresponding to junction-specific resistances R c ͑i.e., the product of the junction normal-state resistance and the contact area͒ from tens to several thousands ⍀ m 2 . This limits the achievable Q A to some pW/ m 2 .…”

Fluctuation-Limited Noise in a Superconducting Transition-Edge Sensor

“…Here we assume validity of the Wiedemann-Franz law. The thermal conductivity of the 250 nm thick SiN membrane is given by M ' 14:5 10 ÿ3 T 1:98 [8], and at temperatures present in the system (20 -150 mK) it is typically 3 orders of magnitude smaller than S . As the thicknesses of the SiN and the TES are comparable, the problem reduces to two dimensions, and due to symmetry further to one dimension.…”