Digital Platform for Wafer-Level MEMS Testing and Characterization Using Electrical Response

Towards Reliable Parameter Extraction in MEMS Final Module Testing Using Bayesian Inference

In micro-electro-mechanical systems (MEMS) testing high overall precision and reliability are essential. Due to the additional requirement of runtime efficiency, machine learning methods have been investigated in recent years. However, these methods are often associated with inherent challenges concerning uncertainty quantification and guarantees of reliability. The goal of this paper is therefore to present a new machine learning approach in MEMS testing based on Bayesian inference to determine whether the estimation is trustworthy. The overall predictive performance as well as the uncertainty quantification are evaluated with four methods: Bayesian neural network, mixture density network, probabilistic Bayesian neural network and BayesFlow. They are investigated under the variation in training set size, different additive noise levels, and an out-of-distribution condition, namely the variation in the damping factor of the MEMS device. Furthermore, epistemic and aleatoric uncertainties are evaluated and discussed to encourage thorough inspection of models before deployment striving for reliable and efficient parameter estimation during final module testing of MEMS devices. BayesFlow consistently outperformed the other methods in terms of the predictive performance. As the probabilistic Bayesian neural network enables the distinction between epistemic and aleatoric uncertainty, their share of the total uncertainty has been intensively studied.

A New Non-Invasive Air-Based Actuator for Characterizing and Testing MEMS Devices

This research explores a new ATE (Automatic Testing Equipment) method for Micro Electro Mechanical Systems (MEMS) devices. In this method, microscale aerodynamic drag force is generated on a movable part of a MEMS sensor from a micronozzle hole located a specific distance above the chip that will result in a measurable change in output. This approach has the potential to be generalized for the characterization of every MEMS device in mass production lines to test the functionality of devices rapidly and characterize important mechanical properties. The most important testing properties include the simultaneous application of controllable and non-invasive manipulative force, a single handler for multi-sensor, and non-contact characterization, which are relatively difficult to find with other contemporary approaches. Here we propose a custom-made sensing platform consisting of a microcantilever array interconnected to a data acquisition device to read the capacitive effects of each cantilever’s deflection caused by air drag force. This platform allows us to empirically prove the functionality and applicability of the proposed characterization method using airflow force stimuli. The results, stimulatingly, exhibited that air force from a hole of 5 µm radii located 25 µm above a 200 × 200 µm2 surface could be focused on a circular spot with radii of approximately 5 µm with surface sweep accuracy of <8 µm. This micro-size airflow jet can be specifically designed to apply airflow force on the MEMS movable component surface. Furthermore, it was shown that the generated air force range could be controlled from 20 nN to 60 nN, approximately, with a linear dependency on airflow ranging from 5 m/s to 20 m/s, which is from a 5 µm radius microhole air jet placed 400 µm above the chip. In this case-study chip, for a microcantilever with a length of 400 µm, the capacitance curve increased linearly from 28.2 pF to 30.5 pF with airflow variation from 5 m/s to 21 m/s from a hole. The resultant curve is representative of a standard curve for testing of the further similar die. Based on these results, this paper paves the way towards the development of a new non-contact, non-invasive, easy-to-operate, reliable, and relatively cheap air-based method for characterizing and testing MEMS sensors.

Mechanical Characterization of Polysilicon MEMS: A Hybrid TMCMC/POD-Kriging Approach

Microscale uncertainties related to the geometry and morphology of polycrystalline silicon films, constituting the movable structures of micro electro-mechanical systems (MEMS), were investigated through a joint numerical/experimental approach. An on-chip testing device was designed and fabricated to deform a compliant polysilicon beam. In previous studies, we showed that the scattering in the input–output characteristics of the device can be properly described only if statistical features related to the morphology of the columnar polysilicon film and to the etching process adopted to release the movable structure are taken into account. In this work, a high fidelity finite element model of the device was used to feed a transitional Markov chain Monte Carlo (TMCMC) algorithm for the estimation of the unknown parameters governing the aforementioned statistical features. To reduce the computational cost of the stochastic analysis, a synergy of proper orthogonal decomposition (POD) and kriging interpolation was adopted. Results are reported for a batch of nominally identical tested devices, in terms of measurement error-affected probability distributions of the overall Young’s modulus of the polysilicon film and of the overetch depth.