Effect of a thin AlO_x layer on transition-edge sensor properties
JJournal of Low Temperature Physics manuscript No. (will be inserted by the editor)
K. M. Kinnunen, M. R. J. Palosaari and I. J.Maasilta
Effect of a thin AlOx layer on transition-edgesensor properties
Abstract
We have studied the physics of transition-edge sensor (TES) deviceswith an insulating AlOx layer on top of the device to allow implementation ofmore complex detector geometries. By comparing devices with and without theinsulating film, we have observed significant additional noise apparently causedby the insulator layer. In addition, AlOx was found to be a relatively good thermalconductor. This adds an unforeseen internal thermal feature to the system.
Keywords
TES, transition-edge, AlOx, thermal conductivity, thermal model,noise
PACS
To improve transition-edge sensor (TES) performance, many designs have beentried, one example being the Corbino-geometry (CorTES) . The main benefits ofthe design are the possibility to control the TES resistance over a wide range ofvalues and being able to model the superconducting transition analytically. Tra-ditionally the CorTES has shown a large excess noise component, which wasoriginally explained by fluctuation superconductivity noise (FSN) . Our recentexperiments involving the measurement of the complex impedance of the de-vices suggest that there is a significant internal thermal fluctuation noise (ITFN) part, which may account for most of the excess noise. When trying to model themeasured impedance and noise features, we find that a two-body thermal modelis insufficient and often even a three-body system fails to fully fit the data.As the CorTES differs from simple TES designs by the addition of an insu-lating AlOx layer on top of the TES film, with a narrow strip of the insulator Nanoscience Center, Department of Physics, P. O. Box 35, FI-40014 University of Jyv¨askyl¨a,Finland
E-mail: kimmo.m.kinnunen@jyu.fi a r X i v : . [ c ond - m a t . s up r- c on ] D ec extending from the TES to bulk Si, one may worry about the role of the AlOxlayer. To investigate what effect it could have on the TES film itself, we set outto fabricate a standard square Ti/Au TES that would have an AlOx layer partiallycovering it.We first fabricated a bare pixel and measured the R-T, I-V and noise proper-ties. Then a 120 nm thick AlOx layer was fabricated by e-beam evaporation onthe same pixel, and the same measurements were repeated. The AlOx layer wasdeposited at about 5 · − mBar pressure at a rate of 0.1 nm/s and the sourcematerial was Al O with 99.99 % purity and 2-4 mm grain size.Unfortunately, the AlOx process shifted the critical temperature down by 10mK so it is difficult to make firm conclusions from that data. We only commentthat the AlOx layer seemed to smoothen and decrease the total α , calculated fromI-V as α tot = ( T / R ) dR / dT , but that could also be related to the same heatingeffect that caused the T C to shift. The noise spectra look qualitatively similar.Another set of square pixels was fabricated so that this time there were identi-cal pixels on the same chip; one was covered with AlOx while the other was leftbare. We shall refer to these pixels as pixel A (with AlOx) and pixel B (bare). Byaccident, the AlOx layer was patterned with a wrong mask that was too large, sothat it also covered most of the SiN membrane and touched on bulk Si, as shownin Fig. 1. We chose to perform the measurements anyway and got some interestingresults. Fig. 1
A scanning electron micrograph of the pixel A with the AlOx layer. The size of the TESis 300 x 300 µ m and it is on a 460 x 410 µ m SiN membrane. Thickness of SiN is 750 nm. Pixels A and B both had T C ≈
165 mK and normal state resistance R N ≈
400 m Ω .As shown in Fig. 2, pixel A has a peculiar transition shape with some very steepregions. This is reflected in the measured total α shown in Fig. 3B. Perhaps themost surprising result was the thermal conductance shown in Fig. 3A. While the Fig. 2 (Color online) R-T curves of the pixels. Circles: four-probe lock-in measurement of pixelA. Solid and dotted lines are the R-T curves calculated from I-V measurement of pixels A andB, respectively.
AlOx is relatively thin compared to the SiN layer (120 nm vs. 750 nm), it almostdoubles the heat transport.
Fig. 3 (Color online) Dynamic thermal conductance (A) and total α (B) calculated from I-Vmeasurement. G dyn = dP / dT = nKT n − , where P is the Joule heating power of the bias current, T is the TES temperature, n and K are material specific thermal transport parameters. The opensymbols correspond to bias values where the noise spectra of Fig. 4 were measured. Figure 4 shows the measured electrical noise of the pixels. Immediately obvi-ous are the very large noise bumps in pixel A. They are related to the high valuesof α . Around the R / R N = . α but pixel Aseems to have slightly higher noise level. The feature around 10 kHz is similar towhat we usually see in the Corbino devices. However, in a CorTES they are not Fig. 4 (Color online) Measured electrical noise of samples with (A) and without (B) AlOx layer.The curves with same colors correspond to roughly similar bias points as shown in Fig. 3 . Noiselevels increase when going lower in the R-T curve. quite so pronounced and center closer to 1 kHz, possibly because the AlOx layeris a narrow strip, making thermal conductance lower.We have seen in several different pixel designs that in order to explain theobserved noise and complex impedance features, a thermal model where an inter-mediate thermal mass sits between the TES and the heat bath is usually consistentwith data. It seems logical to assume that the intermediate block is related to theSiN membrane. While data from devices without AlOx layers usually fit quitewell, as shown for example in ref. , in our CorTES pixels we still have difficultieswith fitting. This can be understood in light of the results presented here. The AlOxlayer creates an additional conduction path to the heat bath; thus we can constructa thermal block model shown in Fig. 5A. We therefore end up with additionalfeatures in both the noise and impedance data due to the AlOx layer.In the above, we have disregarded other possible additional thermal blocks,such as hanging ones. It is still unclear what is the full effect of the AlOx layer ontothe device. It is possible that the AlOx film will form an additional thermal block,or it can influence the temperature profile of the TES film. The high frequency(near 100 kHz) noise bumps in pixel A hint in that direction. Fig. 5 (Color online) (A) Thermal block model for pixel A, not taking into account other pos- sible thermal masses in the system. (B) Simple model used to estimate thermal conductance of
AlOx. TES is approximated by a circle of radius r = 150 µ m while the SiN and AlOx layershave radius r = 230 µ m. κ of the AlOxlayer. We assume that κ = aT , which is the universal temperature dependencefor amorphous insulators , where a is a sample dependent constant. To derivethermal conductance G from κ we use the approximate geometry shown in Fig.5B to obtain the equation G = π dln ( r / r ) κ , (1)where d is the layer thickness.We further set g in Fig. 5A to zero so that SiN and AlOx films can be treatedas parallel conductances. We can get an estimate for the thermal conductance ofAlOx from I-V data by subtracting G dyn of pixel B from that of pixel A. We choosea value from the middle of the transition and get roughly 0.8 nW/K for AlOx. Wecan now calculate the thermal conductivity using eq. (1) and get κ ∼ . · − W/cmK for AlOx and κ ∼ · − W/cmK for SiN. The result for SiN is consistentwith previous measurements . We are not aware of 0.1 K thermal conductivitymeasurements for AlOx. According to ref. , most amorphous glasses should have κ in the range of 1 · − − · − W/cmK at 0.1 K. We can therefore concludethat even though the value for AlOx we obtained is only approximate, it fallswithin this range and thus the layer seems to be amorphous, as expected.
We have shown that a thin layer of e-beam evaporated AlOx appears to be amor-phous and has about five times higher heat conductivity at low temperatures thansilicon nitride. We also showed that when the AlOx layer connects a TES to theheat bath, extra thermal fluctuation noise appears. This fact also lends weight tothe assumption that the SiN membrane present in most devices should be takeninto account when modeling the thermal circuit.
Acknowledgements
This work was supported by the Finnish Funding Agency for Technologyand Innovation TEKES and EU through the regional funds, and the Finnish Academy projectno. 128532. M. P. would like to thank the National Graduate School in Materials Physics forfunding.
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