Pulsed heating of the self-actuated cantilever: an exact solution investigation of non-axial temperature gradients

Abstract

Self-actuated bimorph cantilevers are implemented in a variety of micro-electro-mechanical systems. Their tip deflection relies on the unmatched coefficients of thermal expansion between layers. The thermal bimorph phenomenon is dependent on the temperature rise within the cantilever and while previous studies have investigated variations in the thermal profile along the cantilever length, these have usually neglected variations in the thermal profile along the cantilever thickness. The current study investigates the thermal distribution across the thickness of the cantilever. The exact closed form solution to the problem of heat conduction in the composite (layered) domain subjected to transient volumetric heating is developed using the appropriate Green’s function. This solution is applied to a 3-layer cantilever with an Aluminium heater, a Silicon Dioxide resistive layer, and a Silicon base layer. The Aluminum heater experiences volumetric heating at a rate of 0.2 mW/μm3 of 5μs duration at 100 μs intervals. Benchmark solutions of the temperature at select times and positions are provided. It is shown that there are non-negligible temperature gradients across the cantilever thickness during the heating and the first 5μs afterwards. These short-lived temperature differences are significant in magnitude and are positively biased with the unmatched thermal expansion coefficients between the layers. These temperature differences, which have previously been neglected, are important because they will act to enhance bending.