1. 1 THERMAL CONDUCTIVITY OF SILICATE BONDED SAMPLES Status of measurements with the thermal conductivity facility in Firenze June, 7 th 2007

2. 2 MEASUREMENT & SETUP Recall the measurement main features: steady state measurement PT1000 sensors connected in a Wheatstone bridge sample homogeneity and heat flux homogeneity INSULATOR BOX HEATER COPPER BOX CLAMP SAMPLE THERMOMETERS SAMPLE HEATER cryogenic liquid cold plate Elba GWADW 2006 test measurement on pure Si reed

3. 3 SILICATE BONDING MEASUREMENT By moving to the new peculiar geometry of silicate bonded disks, several difficulties arise: Sample with 1” diameter, 12 mm thick PT1000 position against the lateral surface should be known as precisely as possible, since: Very high conductance requires the power flowing to be pretty high for temperature gradient to become measurable; Thermal contacts are a determinant issue, and in general heat flux must be kept homogeneous ; Sample (bonding) inhomogeneities spoil the measurement accuracy by bending the heat path. (K is the conductance)

4. 4 CURRENT SETUP PT1000 INDIUM FOILS

5. 5 CURRENT SETUP 1 mK With the current setup (with old copper heating coil), we obtained the first good measurement at room temperature : Pure Si across Bonding 160 W/mK 150 W/mK (Si @300K has ~150 W/mK) calibration power geometry PT1000 calibration

6. 6 HEATING TOOL Long time has been spent in understanding the behaviour of the setup, testing and improving almost all of its parts. Homogeneity of heat flux has proved to be determinant. The first heater we made contact surface Rear with Joule coils Carved groove for hosting a PT1000 Aluminum heater now employed thickness helps the flux to become homogeneous flat constantan coil flat contact face

7. 7 TEMPERATURE SENSORS PT1000 PT1000 flat surfaces are too wide for having a precise determination of sensing point on the sample… sharp contact region two PT1000s in series (doubled sensitivity) PT1000 wires soldered in a robust way With aluminum rings: Three point measurement allows  to be evaluated on pure Si and across bonding

8. 8 A GOOD THERMAL CONTACT In order to have a homogenous heat flux, thermal contacts must be realized carefully. We found that the contact between sample and heater (and sink) was not good, even with grease. By inserting indium disks, contact is good all across the surface SINK HEATER

9. 9 HISTORY OF SAMPLES MEASUREMENTS N° 1 & 2, 1” samples - test of the apparatus, no good data - both broke after cooling cycle - both showed inhomogeneity in the bonding layer N° 3, 1” sample - First good measurement at room temperature - first cooling cycle seemed to result in worsening of the bonding: datepure Sibondingactions 8/3 160150 Final setup but with copper heating coil 11/4 186102 After the first cooling cycle 26/4 184115 After a new cooling cycle, sample has been removed and placed again. New indium disks, new constantan heating coil 17/5 180134 New calibration, acquisition problems resolved, indium disks have been changed with better ones 4/6 179109 After two cooling cycles ROOM T MEASUREMENTS

10. 10 INHOMOGENEITIES IN THE BONDING LAYER If the bonding realizes a bad thermal contact in some point between the two disks, measurements can be severely altered.

11. 11 Temperature on an aluminum sensor with a 2mm cut in the bonding layer (1K is set across the whole sample) INHOMOGENEITIES IN THE BONDING LAYER On the ring sensor, a 2mm lateral cut in the bonding results in 30 mK spread of T over a 1K temperature gradient on the whole sample. Depending on the position of PT1000s, that leads to an error as high as 3%.

12. 12 FIRST CONDUCTIVITY CURVE A first complete curve of conductivity for the third sample has been obtained: Temperature [K] Thermal Conductivity [W/(m K)]

13. 13 CONCLUSIONS In its final version, the facility seems to behave well, even for 1” disk samples; We can go ahead by measuring ½” samples, but that needs new sensors, new heater…; Going down to helium will request new sensors (like CERNOX, already available) and represents a major improvement; A possible way ahead: samples with new geometry.