Modeling and Characterization of Adapted 3$\omega$-Method for Thermal Conduction Measurement of Thermal Radiation Sensors

In this letter, a thermal conduction measurement method for thermal radiation sensors, such as vacuum-packaged bolometers, is presented. The idea of the method is deduced from the classical 3ω-method proposed by Cahill [1]. Here, the measurement geometry is a complete sensor geometry, which is suspended from the substrate by thermal isolation legs. The most relevant performance factor for such a sensor is the thermal isolation; this is why the thermal conduction measurement is so important to design better sensors. Additionally, the thermal loss mechanisms need to be investigated because the sensors are normally operated at the thermal radiation limit. Therefore, these loss mechanisms are modeled with an electrothermal equivalent circuit of the whole measurement setup. The measurement method is then used to measure and derive the thermal conduction of known single microbolometer structures.

I. Introduction

Due to continuing miniaturization and to increase the performance of infrared devices, such as resistive bolometers or thermopiles, new materials and methods for characterization are needed. There already exist studies about the performance of nanotube bolometers, e.g., [2], but it is difficult to measure the thermal conductivity of the nanotubes themselves. One of the crucial parameters is the thermal isolation of the sensors membrane, which needs to be optimized and, hence, must be well understood. One possibility to measure the thermal conduction is the step response the system (bolometer) needs for thermal stabilization. A better and more accurate approach is to measure in the frequency domain, because much more data points are easily available. For solid 2-D layer systems, there is the possibility of measuring the thermal conductivity using the -method. This method was used for the first time by Cahill [1]. The -method established itself over time in simulation and measurement techniques, such as for multilayer systems [3] or for a bottom heater structure [4]. Additionally, it was also expanded, with some changes in the evaluating equations, to other systems, such as thermal conductivity measurements of fluids with a microbridge heater [5] or vertically oriented carbon nanotubes [6]. Nevertheless, a limitation for ultrathin materials is that two-dimensional (2-D) measurements do not reflect surface effects because they comprise of a layered system. Furthermore, the thermal conductivity is hard to measure for such ultrathin films (e.g., 20 nm) in layered systems, due to small height variations during the processing of sample and reference. For bolometers, the thermal conductivity is one of the most significant performance parameters, besides the heat capacity and the thermal coefficient of resistance (TCR). Here, we show a method for measuring thermal conduction of bolometers deduced from the -method, where a heater structure is already included as a temperature-sensitive membrane.