About my work
Manufacturing micro-mechanical systems on a large scale is a challenging problem because existing fabrication processes are beset with numerous sources of uncertainty. Since hundreds of devices are typically fabricated as a batch on a wafer, it is very difficult to enforce tight tolerances on process uniformity. As a result, there are large variations in properties not only across devices from different wafer batches but also within a single wafer from one device to the next. Therefore, we need a comprehensive framework to quantitatively include the effect of these uncertainties at the design stage, in order to make reliable predictions on the final performance of the device.
The field of uncertainty quantification throws up many interesting research questions:
- What are the sources of uncertainty?
- How does one model a random quantity?
- How does this random quantity affect the physics of the device?
- Can we simulate the effect of these variations on a computer in a reasonable amount of time?
I try to answer some of these questions in my research. I am building a software framework that can generate stochastic models for random parameters, which can then be propagated through a high-fidelity physical model of the system to quantify the effect of uncertainties in a computationally efficient manner. The goal is to make reliable predictions about device performance given practical constraints like limited availability of data and finite computational resources. A selected list of my publications that are relevant to this work is given below. To see the complete list, click here.
, "Analysis of the effect of spatial uncertainties on the dynamic behavior of electrostatic microactuators", Communications in Computational Physics, Vol. 20, No. 2, pp. 279-300, 2016
, "Data-driven stochastic models for spatial uncertainties in micromechanical systems", Journal of Micromechanics and Microengineering, Vol. 25, No. 11, Art. No. 115009, 2015
, "A nonstationary covariance function model for spatial uncertainties in electrostatically actuated microsystems", International Journal for Uncertainty Quantification, Vol. 5, No. 2, pp. 99-121, 2015
, "Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation", Journal of Computational Physics, Vol. 255, No. 15, pp. 521-539, 2013
, "Uncertainty quantification of MEMS using a data-dependent adaptive stochastic collocation method", Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 45-46, pp. 3169-3182, 2011