Matthew D. Zotta

Measurement of the Electron Beam Point Spread Function (PSF) in a Scanning Electron Microscope (SEM)

A knowledge of the spatial distribution of the electron beam current density, often referred to as the point spread function (PSF), is valuable for understanding the behavior of scanning electron microscopes (SEM) and various other instruments. Previously, a number of attempts at PSF determination have been made based on experimental measurements or electron optical calculations [1-7]. Some of the experimental methods employed knife edge or other scans[1, 8]. Liddle et al. [5] used a TEM image of a reference sample to determine the PSF for an electron beam lithography tool. They assumed an elliptical Gaussian shape for the electron beam and determined its standard deviations in two orthogonal directions using an iterative method to match the reference and blurred images. Babbin et al. developed a test sample that can be used to estimate the PSF using a Fourier transform method[6]. All these approaches are limited in the sense that they do not provide the fine, often irregular, details in the electron beam shape that may not be symmetric or monotonic. A more accurate determination of a PSF is critical, however, if the goal is to improve SEM resolution by deconvolution using the method described by Lifshin et. al [9].

Scanning Electron Microscope Point Spread Function Determination Through the Use of Particle Dispersions

Over the years, significant advances have been made in scanning electron microscope (SEM) resolution primarily due to hardware improvements including higher brightness electron sources with smaller energy spreads and better electron optics that decrease the final probe size. Although these advancements represent significant developments, they commonly come with added complexity and cost. In addition, while a small probe diameter may be necessary for high resolution imaging, it may not be attainable in all instances, most notably low voltage where chromatic aberrations in the electron optics limit the minimum probe size. Other scenarios such as long working distance settings as with retractable backscatter detectors and other analytical operating conditions can lead to larger beams at the sample surface. Situations in which there is a need for a high signal to noise ratio can also present an issue as the probe size often increases with probe current leading to decreased resolution due to beam broadening.

Viability of Point Spread Function Deconvolution for SEM

An image is understood as the point spread function (PSF) of an imaging system convolved with the scene being imaged. An image can be restored to more accurately depict the scene by performing a deconvolution of the PSF and the image. In a scanning electron microscope (SEM), the PSF describes the shape of the electron beam. PSF deconvolution is a promising image restoration technique for SEM images [1] and is of special interest at low beam voltages (< 3kV), where resolution is hindered by multiple factors. This technique’s viability for SEM application is based on invariance of beam shape with respect to position and sample. Using Aura Workstation [2], we can determine the beam shape to test for invariance and perform restorations for image quality evaluation.

SEM resolution improvement using semi-blind restoration with hybrid L1-L2 regularization

Scanning electron microscopy (SEM) resolution is limited by many factors that include sample specific properties, microscope stability, noise, the three dimensional nature of the sample and the excitation volume, and the spatial distribution of electrons in the probe known as the point spread function (PSF). If all, but the latter are optimized, the loss of resolution is principally due to blurring by the convolution of the PSF with the structure of interest. Image resolution can then be increased by deconvolution combined with the mathematical process known as regularization. To accomplish this task, a novel high resolution semi-blind image restoration technique incorporating hybrid L1 and L2 regularization terms has been developed. The original optimization is divided into the efficient solution of three subproblems, and has been validated with a variety of actual SEM images.

An Evaluation of Image Quality Metrics for Scanning Electron Microscopy

It has been previously demonstrated that SEM image quality and resolution can be improved by a combination of deconvolution and regularization using the point spread function (PSF) of a focused electron beam to produce a restored image [1]. One benefit of this technique is that the performance of a less expensive thermionic source SEM approaches that of a more costly Schottky or FEG instrument. If the restored image is an attempt to duplicate an image taken with a high performance microscope, then it is important to assess how closely the former matches the later.

Improved Low Voltage SEM Image Resolution Through the Use of Image Restoration Techniques

Low voltage SEM or LV-SEM ( 5 keV) and introduce a retarding field at the end of the column to lower the landing energy of the electrons.