Amorphous materials are used in thermoelectrics, photovoltaics, integrated circuits and LEDs. Understanding their thermal properties in detail can help to improve the performance of these devices. Thermal conductivity is one particular property that is critical to the performance. The thermal conductivity of amorphous materials is widely different from crystalline materials. Furthermore, the present theories that predict the thermal conductivity of amorphous materials are less accurate at low and high temperatures (<100 K and >400 K); this necessitates the need for a more comprehensive model that can accurately predict the thermal conductivity over a wide range of temperatures.
Leading theories to predict the thermal conductivity are the k-min model and the Einstein model.1 Certain assumptions involved while deriving these models questionable and may not apply over a wide range of temperatures. One study suggests the presence of distinct modes of vibration in amorphous materials, each corresponding to a different mean free path/diffusivity, exist and contribute to the thermal conductivity differently.2 Our research at STEEL involves extending this work and developing a theoretical model to predict the thermal conductivity in amorphous materials over a wide range of temperatures.
To do this we are developing a suite of measurement techniques to investigate the thermal conductivity temperature dependence from 10 K to 800 K. We will use the 3ω technique3 for this purpose. A sinusoidally varying current source at frequency ω is passed through a heater line deposited on the sample, whose properties are to be measured. This creates a sinusoidal heat generation at a frequency 2ω at the surface of the sample, which causes a temperature variation at the surface at the same frequency. The temperature variation is a function of the thermal conductivity of the sample. The varying temperature at the surface causes the resistance of the heater line to vary at a frequency 2ω. Due to the varying resistance at 2ω and the current at ω, a voltage of frequency 3ω is detected across the heater line. The measured voltage is directly related to the thermal conductivity, which can be extracted from the voltage data. These experimental data will be used to validate the theoretical model developed.
Figure 1: Conventional 3-Omega sensor. D. G. Cahill et al., Physical Review B, 46, No. 10, 1992-II.  P. B. Allen et al., Philosophical Magazine B, 79, 11/12, 1715-1732, 1999.  D. G. Cahill, Review of Scientific Instrumets , 61, No. 2, 1990.  C. Dames and G. Chen, Review of Scientific Instrumets, 76, 124902, 2005.