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Thermal conductivity of micromachined low-stress silicon-nitride beams from 77 to 325 K
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View: Figures


Image of FIG. 1.
FIG. 1.

Left: Overall view of device A and device B fabricated on a single Si chip, Middle: device A with two islands connected to the Si frame through eight legs with Mo heaters and thermometers patterned on each. Right: device B with two Si–N islands connected together by a long, wide, and 500 nm thick Si–N suspended beam.

Image of FIG. 2.
FIG. 2.

(a) Thermal model of device A with no Si–N beam between islands, (b) thermal model of device B with Si–N beam bridging two islands and (c) thermal model of device C with sample thin film deposited on Si–N beam.

Image of FIG. 3.
FIG. 3.

(a) Predicted vs for a simple model of the thermal platform that includes radiation losses at two temperatures, 95 K (upper lines) and 285 K (lower lines). The solid lines are calculated for a platform with a heated area, dashed lines for a heated area, and dotted line for no radiation contribution. The symbols represent measured values for device A, which match the low radiation loss prediction extremely well. (b) Predicted for the radiation models. The upturn caused by radiation losses would complicate thermal transport measurements for large-area platforms. Inset: Schematic of the simple thermal radiation model.

Image of FIG. 4.
FIG. 4.

Example calibration of the micromachined thermometer. Inset: SEM micrograph of Mo wires patterned as thermometer and heater (the four wires used to measure each resistor are also visible).

Image of FIG. 5.
FIG. 5.

Temperature vs heater power at for (a) device A and (b) device B. (’s), (triangles), and (boxes) are the temperatures on frame, hot island, and cold island, respectively. Lower right insets: optical image of devices. Upper left insets: zoomed in regions for low heater power.

Image of FIG. 6.
FIG. 6.

Thermal conductance through the legs and through the Si–N beam vs temperature. Upper left inset: Thermal model. Lower right inset: SEM micrograph of device.

Image of FIG. 7.
FIG. 7.

Comparison of our measured thermal conductivity of Si–N, , with previously reported values for LPCVD Si–N [LP1 (Ref. 13) and LP2 (Ref. 8)] and for PECVD (Ref. 10). Vitreous silica is shown for comparison [ (Ref. 14)].

Image of FIG. 8.
FIG. 8.

Results of preliminary structural investigation using x-ray diffraction (the upper three data sets are shifted vertically for clarity). Small but well-defined peaks are seen in scans for device B-1 and device B-4. Peaks caused by the underlying silicon are also visible, except when the substrate was slightly misaligned. Scans of suspended Si–N islands with no metal features and of an unpatterned Si–N film did not show observable crystallite peaks, but this is most likely due to the variation in crystallite size from run to run.

Image of FIG. 9.
FIG. 9.

Comparison of results from three thermal platforms (of the device B type) fabricated on a single Si wafer. (a) Measured thermal conductances, , shown above the axis break and, , shown below. The large differences in are caused by thickness variation in the Mo leads that dominate the leg thermal conductance. (b) Thermal conductivity of the Si–N forming the three bridges. Thicknesses were measured at several points on the frame of each platform by ellipsometry; the resulting error is approximately ±3 nm on each measurement. Devices B-1 and B-2 give very similar thermal conductivity, while device B-3 is somewhat higher, but still within of the other values.

Image of FIG. 10.
FIG. 10.

Comparison of thermal conductance with after background subtraction . Upper left inset: Optical picture of device. Lower right inset: Thermal model.

Image of FIG. 11.
FIG. 11.

Thermal conductivity of measured compared with measured and Wiedemann–Franz (divided by a scale factor of 1.05).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Thermal conductivity of micromachined low-stress silicon-nitride beams from 77 to 325 K