A heat transfer analysis for quartz microresonator IR sensors

Abstract

To aid the design of uncooled IR sensors based on quartz microresonators, a heat transfer analysis is carried out for the time-dependent temperature distribution in the resonator. The quartz resonator is taken to be circular, homogeneous isotropic, with a ring electrode on its front surface which is IR illuminated. It is assumed that the microresonator array is packaged in high vacuum; the side and back surfaces of the resonator are thermally insulated. Only heat conduction within the quartz resonator is considered; radiation at the surfaces and heat conduction through the bridges that link the resonator to the base structure are neglected. The boundary value problem of heat conduction in the resonator is solved analytically; expressions for the temperature distribution before and after the photon flux is turned off are given. It is found that for the quartz resonator under study, the time is required to reach a uniform temperature distribution in the entire resonator (the time constant) is critically dependent on the photon absorptivity of the ring electrode on the front surface. For example, when the ring electrode has no effect on photon absorption, t8 = 9.52 microseconds; however, if the ring electrode is fully reflective, t8 = 4.76 milliseconds. These time constants are expected to play an important role in the design of the quartz microresonator IR sensors.