Design support for a real pressure sensor by means of finite element analysis

The design process of innovative microelectronic and micromechanical systems (MEMS) requires the thermal and thermo-mechanical behaviour to be taken into account beginning already in the initial design phase in order to achieve high functionality and reliability. For this purpose, numerical studies by means of finite element (FE) analyses are very efficient to check the desired properties. In the presented paper, the authors' approach for a low pressure sensor, which was designed based on the well-known Pirani principle, is outlined. The sensor consists of two meander-shaped resistors acting as a heater which is positioned at a thin membrane in an evacuated cavity between two silicon dies and a temperature reference respectively. First, several basic ideas of the meander arrangement and of the membrane layers were compared numerically in order to preoptimise the heater design. Second, the influence of technologically feasible cavities was investigated. Third, temperature- and pressure-dependent data could be taken into account for the thermal conductivity of the gas medium inside. It could be shown, that already a qualified 2d FE analysis allows the pressure dependent sensor functionality to be represented with very good accuracy. This was proved by corresponding measurements at the first real devices. Finally, the FE models have been parameterised in order to take into account different cavity depths above as well as below the membrane which is important due to the unavoidable process tolerances. This approach, an interesting example for computer-aided MEMS design, is presented in this work. It takes into account geometric as well as constitutive issues before any real parts are available. The procedure helps to reduce cost and time to market by minimising real tests and expensive redesign.