High-accuracy Thermal-conductivity Characterisation of Thin-film/Substrate Systems and Interfaces by Modified 3-Omega Method

Abstract

Temperature rise in electronic devices due to self-heating is a major barrier to increasing the capacity of devices because higher temperatures greatly deteriorate performance reliability. The primary cause of this temperature rise is the interface thermal resistance between a thin film and a substrate. Thus, the actual temperature rise in a thin-film electronic device such as a high-performance chip is a great deal more significant than the theoretical predictions made for that device because existing theory does not integrate atomic defects and interface thermal resistance. In contrast, measuring thermal conductivity in thin crystalline specimens by using the conventional three-omega (3ω) method is challenging because controlling the heat-penetration depth is a more difficult in high thermal-conductivity crystalline materials since the heat penetrates more rapidly into specimens.

This thesis develops a modified 3ω method for characterising high thermal-conductivity crystalline thin-film/substrate systems and interfaces by extending the conventional 3ω method. This research makes several contributions:

First, it offers a thorough investigation of one- and two-dimensional theoretical and numerical analyses of heat conduction in a multilayered medium conducted by Joule heating a metal strip. The effect of the metal-strip width on the measurement accuracy of the 3ω method was explored. It was found that the thermal conductivity measurement can be performed over a wide range of frequencies only if the width of the metal-strip element is small relative to the film thickness. Therefore, a modified 3ω method was established.

Second, experimental verifications of the theoretical investigations for the implementation of the modified 3ω method were systematically conducted. An extremely narrow and long nanostrip (height × width × length = 100 nm × 400 nm × 4 mm) was deposited on the specimen s surface using electron-beam lithography (EBL) and physical vapour deposition (PVD) techniques. Utilising the modified 3ω method, the thermal conductivity of bulk silicon (Si) wafers was successfully characterised.

Third, it was discovered that the heat-penetration depth into a thin-film specimen is controllable by varying the applied current frequency, and this was performed by investigating its thermal conductivity using the modified 3ω method. The nanostrip enables the heat penetration to be as shallow as tens of microns, which is not achievable by the conventional 3ω method. In addition, the method is applied on an aluminium nitride (AlN) thin film on Si substrate, which is a commonly used thin-film/substrate system in semiconductor manufacturing devices.

Fourth, the interface thermal resistance in multilayered thin-film/substrate systems were conveniently and accurately obtained by coupling theoretical predictions and experimental measurements. Specific case studies on silicon and AlN thin films on Si substrates were conducted to verify the reliability of the method. It was demonstrated that the thermal conductivity of the interface material can be obtained by the modified 3ω method in conjunction with high-resolution transmission electron microscopy (TEM). In addition, interface thermal resistance between the nanostrip material and the silicon surface and/or between the thin-film materials (i.e. Si and AlN) and the silicon substrate can be determined by the modified 3ω method.

The research concluded that the method developed is applicable to the characterisation of a wide range of thin-film/substrate systems in the semiconductor industry, and that this method can be used to optimise the crystalline thin film on substrate designs aimed at improving overall thermal conductivity and therefore device efficiency.