Leak rate prediction methods for hermetically sealed devices

摘要

Hermetic packaging is crucial for enclosing sensitive components such as those found in implantable biomedical devices and MEMS devices. Knowledge of the leak rate of the packaging is also required so that the service lifetime of these devices can be predicted. Determining the leak rate of a hermetically sealed device is typically performed by measuring the leak rate of a tracer gas into said device, then using Graham's law of effusion to determine the leak rate of other gases. Reports from the literature demonstrate that predictions made using this method are not always accurate when predicting the flow rates of not only condensable gases (e.g. water vapour), but also non-condensable gases. Experimental testing of soldered samples with seals like those in hermetically sealed devices confirmed that predictions using Graham's law could be inaccurate. Investigation of Graham's law showed that it may be derived from Knudsen's equation for molecular flow, which assumes completely diffuse reflections of the gas molecules from channel walls, i.e. a tangential momentum accommodation coefficient (TMAC) of 1. A modified version of Graham's law was derived from Smoluchowski's equation, itself a modification to Knudsen's equation that incorporates TMAC. To use this new equation, experimentation and simulation were used to demonstrate that Knudsen number and molecular mass both have an effect on TMAC. Also, over the course of these experiments, a model for flow in the transitional flow regime developed by Cha and McCoy was validated using multiple gases. Finally, the modified version of Graham's law and the relationship between TMAC and molecular mass were tested against the leak rate results from the soldered samples, demonstrating an improvement in accuracy over the original form of Graham's law. This result is of practical significance in the testing of hermetically sealed devices. Furthermore, Cha and McCoy's equation will be of benefit in making flow rate predictions in several flow regimes if channel dimensions are known.