Thermal models and noise in transition edge sensors

Abstract

Detectors based on transition edge sensors (TESs) must achieve theoretically predicted noise levels if they are to be suitable for the next generation of space-borne astronomical telescopes. The noise of an ideal detector is determined by the sum of three contributions: (i) thermal-fluctuation noise in the heat link to the bath, (ii) Johnson noise in the sensor itself, and (iii) noise in the electrical read-out circuit. Many groups have reported TESs with noise levels significantly above the theoretical predictions. We use two well-defined experimental configurations to measure the read-out noise spectra of Mo–Cu TESs with transition temperatures of 370 and 200mK. The TESs are geometrically simple, comprising superconducting and normal metal films on a silicon nitride (SiNx) membrane. The measurements are compared with a multiparameter noise model, which is based on a physical model of the thin-film devices. Taking into consideration separate, accurate measurements of the heat capacity of identical SiNx membranes, we are able to provide a good account of both the magnitude and frequency dependences of the measured current-noise spectra. We find that an important excess noise mechanism involves the random exchange of heat between the heat capacity of the bilayer and the heat capacity of the nitride membrane, with either the thermal conductance of the membrane, or in some cases the thermal conductance of the bilayer, being the mediating path. Clear design recommendations are given to achieve the best possible noise performance.

Transition edge sensors with few-mode ballistic thermal isolation

“…8 shows the readout noise-power spectrum of one of the devices, and from this we calculated the NEP based on the power-to-current responsivity. The responsivity was determined through a small signal model that was based on precise TES impedance measurements [21][22][23] . The small-signal model was then used to calculate the contributions from the key noise sources as a function of readout frequency.…”

Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two- and three-block thermal models

“…1(c) (numerically studied in Ref. 14), the extra block is connected to both the TES and the heat bath as in case (b), but an additional parallel heat path exists between the TES and the bath. We call this the parallel model.…”

“…[7][8][9]14 The formalism is kept general so that we do not need to decide on the physical picture a priori.…”

“…[4][5][6][7][8][9] Therefore, theoretical modeling has been advanced in recent years to include more complex thermal circuits. 4,5,[10][11][12][13][14][15] One way to approach the problem is to generalize the problem fully to any number of heat capacity blocks and thermal conductances, and solve the obtained (large) linearized system of equations numerically. 11,16 This approach has the advantage that it is straightforward to move from simple models to more complex models within the same formalism, and for the most complex models this may be the only approach available.…”

Normal metal-superconductor decoupling as a source of thermal fluctuation noise in transition-edge sensors

“…This was later shown to influence the Johnson noise directly 13 , and some of the excess noise could then be explained as non-equilibrium Johnson noise. In addition, it has become clear that for many detectors, the simplest thermal circuit of one heat capacity connected to heat bath through one thermal conductance is not adequate 7,[14][15][16][17]19,20 . A more complex thermal circuit then adds new components to the thermal fluctuation part of the noise spectrum 5,21,22 .…”