Nanoscale thermal conductivity measurements

By: Sourabks
With the ever decreasing size of the computer chips, thermal management at the nano and micro scales is fast becoming a topic of heightened research. Thermal gradients play an important role in determining the chip performance and reliability. This makes chip-thermal models a necessity in the chip design industry. Apart from other factors, obtaining efficient thermal models depends on the accuracy of the thermal conductivity values at the nanoscale resolutions.

While the optical methods have reached their maturity and remain limited by diffraction to half a micron, contact probes were considered as the only means to reach 10-100nm scale resolutions. The Scanning Thermal Microscope (SThM) based on an Atomic Force Microscope mounted with a thermal probe was invented in 1986 by Williams and Wickramasinghe to provide the topography of electrically insulating materials. Since then, various techniques have been proposed with spatial resolutions varying between 5 microns and a few tens of nanometers.

Recent advances in metrology allow us to obtain the thermal map of a silicon sample on the nanoscale; however quantitatively obtaining the thermal conductivity values still remains a challenge.

The 3ù Scanning Thermal Microscope (SThM) is an attempt to quantify the thermal conductivity with a nanometer level resolution. The 3ù method uses an alternating current to heat the thermal probe. Quantifying the unknown tip-sample thermal interaction had been a major challenge in the past. However, force and pressure monitoring at ambient and at very low pressures can be successfully used to quantify this effect. The thermal resistance between the tip and the sample is due to conduction in air, through the solid-solid contact and through the water meniscus between tip and sample. Consequently, the spatial resolution is drastically decreased by heat conduction in air. At low pressures, spatial resolution of 20 nm can be achieved because the air and liquid contributions are removed.

This allows one to arrive at fairly accurate values of thermal conductivity at the nanometer scales through pressure and force monitoring at low pressures.
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