Thermal Analysis of a Constant Temperature Pirani Gauge Based on Micro-hotplate

A micro-hotplate (MHP) based Pirani gauge is fabricated using surface-micromachining technology and measured with a typical constant temperature circuit. The measured results show that its sensitive range is at least 10-10⁵ Pa and can be widen when increasing working temperature. According to Fourier method and energy conservation law, heat conduction differential equations of the supporting beams are built and solved to determine the temperature distribution along the beams and heat losses through solid heat conduction at different pressure. Other heat loss mechanisms of the MHP square membrane are also investigated and it has proven that heat losses through solid heat conduction in micro Pirani increase with gas pressure at constant temperature, whereas they were always considered to be independent of gas pressure in previous studies