System Design, Noise Reduction, and Improved Dimension Reconstruction for High Performance Ellipsometry

Abstract

The advancement in nano-manufacturing and many other industries calls for high-performance metrology and inspection methods. Nano-manufacturing has witnessed shrinking critical dimension and demonstrated mass production capability: the lithography process has reached 5nm node and could potentially reach 2nm node by 2024; one production line can produce 125 wafers in one hour, each 300mm in diameter. Therefore, the desired metrology method must be non-invasive to achieve full sample and batch inspection, have high resolution to keep up with the shrinking critical dimensions, and feature high speed to be compatible with high-throughput manufacturing needs.

Ellipsometry gains popularity due to its advantages of non-invasiveness, high speed, and high resolution. The technology is an important metrology and inspection tool in many industries. Ellipsometry is a major tool in new material characterization, and considered an important metrology method for the next generation of semiconductor devices in nano-manufacturing. In addition, the technology finds its application in biomedical detection and surface roughness estimation. The working principles of ellipsometry are as follows. An ellipsometer experimentally measures the samples’ changing effects on a light beam’s polarization state, quantified by ellipsometric parameters or a Mueller matrix. The experimental results are then fitted to an optical model to extract the sample’s critical dimensions and/or optical properties.

This thesis improves the performance of ellipsometry through three aspects.

The first part of this thesis quantifies and mitigates the mixed Poisson-Gaussian noise induced errors to improve ellipsometer’s measurement accuracy and precision. The measurement accuracy can be significantly affected by the existence of PoissonGaussian noise originated from detection and environment. This work characterizes and quantifies the noise through experiments on an in-house setup. Error propagation analysis is then performed to quantify the measurement error in terms of normalized Mueller matrix elements. The effects of system parameters on the Poisson-Gaussian noise induced errors are studied, including signal strength, the signal sampling frequency, and the first-order coefficient between the signal variance and mean. This thesis then proposes a signal demodulation method in spectroscopic ellipsometry based on maximum likelihood, in order to reduce the effects of Poisson-Gaussian noise. The method accounts for the signal’s statistical distribution and solves for the Fourier coefficients by maximizing the probability of the observed signal. The method’s capability of achieving higher Mueller matrix accuracy as well as higher dimension precision is demonstrated.

The second part develops a reconstruction method for dimensions. The objective is to improve the dimension reconstruction precision and the reconstruction’s sensitivity to changes in dimensions. The reconstruction algorithm along with weights’ selection are formulated. The method assigns higher weights to the more important configurations, where the measurement is sensitive to dimension changes. The selection is based on partial derivatives of the Mueller matrix elements with respect to dimensions. Improved precision is demonstrated through experimental measurements of thin film standards and gratings.

The third part of this thesis shows the design and effectiveness of a Faraday effect-based photometric ellipsometer. The new instrument eliminates mechanical motions and enables high-speed and controllable modulation frequency. In addition, it features a linear relationship between the applied current and the rotation of the polarization plane and thus enables fast and easy demodulation. This thesis presents the design, data reduction and the calibration procedure. Air and thin film sample experiments validate the effectiveness of the prototype.