Investigation on the temperature correction in RoR method for the calibration of gas flow based on CFD analysis

The rate-of-rise (RoR) method determines flow by measuring the dynamic changes in gas pressure and temperature within a constant volume chamber during the measurement time. MFV devices based on the RoR method are commonly used to calibrate thermal mass flow controllers (MFCs), which are widely-used in semiconductor manufacturing or environmental monitoring. Starting point of valid data for RoR measurement is preferably after temperature equilibrium has been established. The thermal equilibrium time varies with inlet flow. Additionally, due to the flow work phenomena, the total gas temperature inside the chamber is higher than the temperature measured at the outer wall of the chamber at thermal equilibrium. Therefore, the temperature correction in RoR method and thermal equilibrium time significantly affect the accuracy level of the MFV. Particularly, thermal equilibrium time and convective heat transfer coefficient between the gas and the chamber is difficult to obtain directly.

We focus on the key parameters in the MFV temperature correction method: convective heat transfer coefficient and thermal equilibrium time. Based on transient computational fluid dynamics (CFD) simulations in a nitrogen medium, we have chosen to study pressure, temperature, and convective heat transfer coefficients over time during the RoR measurement process, defined the thermal equilibrium time applicable to actual measurements, and analyzed the influence of each parameter in the temperature correction, especially the mechanisms of the convective heat transfer coefficient and thermal equilibrium time on temperature. Finally, the temperature correction method for MFV which range is 3–3000 sccm N₂ equivalent is proposed based on simulation, which accuracy is lower than 1 %.