Extended Abstract

As we move further into the twenty-first century, energy consciousness and environmental awareness have become staples of everyday life; yet, a renewed interest in an old technology might hold the key to the problem. The measure of efficiency in thermoelectric materials is governed by the dimensionless figure of merit, ZT = S²σ/k, where and S, σ, and k are the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity of the material respectively¹. An ideal thermoelectric material exhibits a high Seebeck coefficient and electrical conductivity, but has a low thermal conductivity. Enhancement of the figure of merit is accomplished by enhancing the power factor, S²σ, or by reducing the thermal conductivity of the material; for either approach, the accurate measurement of the material parameters is essential for the proper development of optimized structures for use in energy conversion devices.

The first step to developing high efficiency thermoelectric materials is the ability to precisely measure the performance of each device and confidently compare the results across different samples. The figure of merit is pivotal for the characterization of thermoelectric materials. In this work, we develop and optimize a measurement structure to measure the thermal and electrical conductivities, as well as the Seebeck coefficient, from the same sample without removal from the test fixture. This strategy reduces error associated with connecting and positioning the device, while also ensuring that the recorded measurements are from the exact same sample geometry under identical conditions. Here we consider square samples with side lengths of 10 mm and a thickness of approximately 3 mm. Although this is relatively large, it is close to the device scale and operating conditions. Additionally, it is simpler to fabricate materials at the device scale rather than incorporating very small samples for measurement [2].  For this measurement, platinum electrodes are deposited on silicon wafers (using silicon nitride to insulate the electrodes from the substrate). The thermoelectric material (Bismuth Telluride) is electrodeposited on the electrodes and coated with a second platinum electrode layer for electrical conductivity and Seebeck coefficient measurements. For thermal measurements, a double spiral pattern platinum electrical resistance heater structure is patterned on the top surface of the measurement structure. The upper electrical interface must have a 300nm layer of Si₃N₄ to passivate the sensing layer from the current that is passed through the top heater pattern.

We measure the thermal conductivity with the 3ω technique, where an input current of frequency ω results in Joule heating within the metal heater at frequency 2ω. The resulting voltage response of the heater has a component at a frequency of 3ω, which is measured using a lock-in amplifier for accuracy, and is related to the temperature rise in the heater (ΔT_2ω). The 3ω technique is used to determine the thermal conductivity of the device; however, the electrical conductivity and Seebeck coefficient are still required, both of which depend on temperature. Since the sample is already being heated during the 3ω measurement, the ratio of the voltage difference between the top sensing pad and the bottom sensing pad (ΔV_2ω) and the temperature gradient across the sample,  ΔV_2ω/ΔT_2ω, yields the Seebeck coefficient².

In this work, a COMSOL multiphysics model simulates the experimental conditions and verifies simplifying assumptions, such as 1D thermal transport, typically used for data analysis. Typically, heaters for 3ω measurements consist of a single, straight metal line; however, this measurement requires a larger area to be heated uniformly and we optimize the geometry of the patterned metal heater to yield a uniform temperature profile across the entire measurement surface using a coupled electro-thermal model. Coupling the detailed model with the design of the experiment allows optimization of sample geometry and configuration including the double spiral heater pattern and passivation layer thickness on heat transfer through the multi-layer structure. It is impractical to use the full 3D electro-thermal COMSOL model for fitting experimental data due to the computational cost. Thus, the experimental data is analyzed using these simplified 1D models. Here, the impact of spatial temperature variations, convective and radiative heat losses, and other non-ideal experimental conditions are studied through virtual experiments using the multiphysics models and data analysis with a 1D thermal transport model in order to identify optimal heater designs and experimental regimes.

In summary, in this work, COMSOL multiphysics models validate the design of a measurement structure to simultaneously characterize the thermal, electrical, and thermoelectric properties of nanostructured or bulk thermoelectric materials. We observe the impact of spatial temperature variations and non-ideal experimental conditions on the extracted properties, which allows characterization of the expected measurement uncertainty in order to optimize the experimental design. This measurement structure will improve the accuracy and repeatability of thermoelectric characterization.

References:

1. Rowe, D. M. CRC Handbook of Thermoelectrics. New York 16, 1251–1256 (1995).

2. Sadhu, J. S., Hongxiang, T., Ma, J., Kim, J. & Sinha, S. Simultaneous Measurements of Thermal Conductivity and Seebeck Coefficients of Roughened Nanowire Arrays. Mater. Res. Soc. 1456, (2012).