Due to the scanning strategy, the detection chain has to be stable from 16mHz to 100Hz which defines the useful frequency range. In the space-qualified version of the dilution refrigerator, random sequences of pure 3He bubbles in the 3He/4He diluted phase produce low frequency fluctuations of the 100mK stage temperature that can be detected by bolometers as a signal. A 100mK bolometer plate temperature stability of 20nK.Hz-0.5 will degrade the overall HFI sensitivity by less than 5%, which defines the HFI 100mK temperature stability requirement. This requirement will be reached using a combination of a passive thermal filter and an active regulation stage. Therefore, Planck-HFI needs high sensitivity thermometers both for temperature fluctuations monitoring and temperature regulation. In order to have a reasonable safety margin, the goal was set to reach a sensitivity level of 10nK.Hz-0.5 between 16mHz and 100Hz.

Design of high sensistivity NTD Ge thermometers

We define the responsivity as Resp = dV/dTph where V is the thermometer voltage bias and Tph the phonon temperature to measure. It is related with the sensitivity S (expressed in K.Hz^-0.5) by S x Resp = ASDV, where ASDV is the Amplitude Spectral Density of the voltage across the thermometer (expressed in V.Hz^-0.5). Responsivity can be used as a guideline for optimisation since we generally find that it varies more rapidly than sensitivity with all free parameters. In the case of a perfect thermometer with a resistance depending only on temperature, the responsivity increases simply by increasing the bias current I. However, real thermometers at low temperature exhibit two non-linear effects that degrade somewhat their sensitivity:

• The electrical field effect for variable range hopping in a disordered semi-conductor [6].
• The electron/phonon decoupling effect [7].

We have realised a numerical model of these non-linearity effects. This model was validated on NTD Ge thermometer and on NbSi thin films. It allowed us to evaluate the non-linearity parameters of Haller-Beeman Associates (H-B) NTD Ge materials and to calculate theoretical sensitivities with different geometry, doping level and bias current. As shown on figure 1, this optimization process leads to the choice of two NTD Ge thermometers with size larger than usual: H-B type H with 400µm inter-electrodes length and a volume of 400 x 250 x 250 µm^3 and H-B type G with 400µm inter-electrodes length and a volume of 400 x 1000 x 1000 µm^3.

Simulated sensitivity H-B NTD G (250µm)^3

Simulated sensitivity H-B NTD G (250*1000*1000)µm^3

Measured perfrmances on optimized NTD Ge thermometers

The NTD Ge crystals have been mounted as shown on figure 2. The copper setting is a screw in order to ease its positioning on the cold plate. Two sets of increased sizes H-B type G and H-B type H NTD Ge thermometers have been tested on the Symbol cryostat: one is glued with silver epoxy and the other with gold epoxy.

Setting of the tested H-B thermometers

The thermal architecture of Symbol is a two-stage passive low-pass filter, the first one supporting the regulation system. It allows us to obtain a temperature stability better than 20nK.Hz-0.5 down to about 0.1Hz [8]. The readout electronics are based on a square bias electrical modulation obtained through a capacitive load impedance [9], [10]. This system has an input noise level of less than 5nV.Hz-0.5 in the useful frequency band and has been calibrated in order to reduce the uncertainty on the bias current to about 1%.

The following figure represents a temperature noise spectrum obtained on the Symbol cryostat at 102mK with a H-B Ge NTD G thermometer with a volume of 495 x 1050 x 1050 µm^3 (R=3MOhm, I=10nA). The thermometer was placed on the bolometer plate of the Symbol thermal architecture V2.1. The thermal fluctuations of the cryogenic system dominate at frequency lower than 1Hz. The ultimate sensitivity is about 8nK.Hz-0.5, which is consistent with the model.

Temperature noise spectrum measured with optimized H-B NTD G at 102mK on the Symbol test bed.

References

 Haller-Beeman Associates web site
 “Modelling and optimising high sensitivity semiconducting thermistors at low temperature”, M. Piat, J.-P. Torre, J.-M. Lamarre, J. Beeman, R.S. Bhatia. Journal of Low Temperature Physics, Vol.125, Nos. 5/6, 2001.

 “Design and tests of high sensitivity NTD Ge thermometers for the Planck-High Frequency Instrument”, M. Piat, J.P. Torre, J.M. Lamarre, J.W. Beeman, R.S. Bhatia, B. Leriche, J.P. Crussaire, F. Langlet. Proc. 9th Workshop on Low Temperature Detectors LTD-9¨, AIP Conference Proceeding Series, 605, 79-82, 2002.