Exploring the Parameter Space of Point Spread Function Determination for the Scanning Electron Microscope-Part II: Effect on Image Restoration Quality.

Point spread function (PSF) deconvolution is an attractive software-based technique for resolution improvement in the scanning electron microscope (SEM) because it can restore information which has been blurred by challenging operating conditions. In Part 1, we studied a modern PSF determination method for SEM and explored how various parameters affected the method's ability to accurately estimate the PSF. In Part 2, we extend this exploration to PSF deconvolution for image restoration. The parameters include reference particle size, PSF smoothing (K), background correction, and restoration denoising (λ). Image quality was assessed by visual inspection and Fourier analysis. Overall, PSF deconvolution improved image quality. Low λ enhanced image sharpness at the cost of noise, while high λ created smoother restorations with less detail. λ should be chosen to balance feature preservation and denoising based on the application. Reference particle size within ±0.9 nm and K within a reasonable range had little effect on restoration quality. Restorations using background-corrected PSFs had superior quality compared with using no background correction, but if the correction was too high, the PSF was cut off causing blurrier restorations. Future efforts to automatically determine parameters would remove user guesswork, improve this method's consistency, and maximize interpretability of outputs.

Exploring the Parameter Space of Point Spread Function Determination for the Scanning Electron Microscope-Part I: Effect on the Point Spread Function.

The point spread function (PSF) of the scanning electron microscope (SEM) can be determined using a recently developed nanoparticle calibration method. Many parameters are involved in PSF determination and introduce a previously unstudied amount of uncertainty into the PSF size and shape. Signal type, support material thickness, reference particle size, PSF smoothing (K), and background correction were investigated regarding their effect on the PSF. Experimental data were complemented by CASINO simulations. Differences in detector position between the observed particles and the method's simulated reference particles caused shifting between secondary electron PSFs and backscattered electron PSFs. Support material thickness did not have a practical effect on the PSF at the tested voltages. Uncertainty in reference particle size varied the PSF full width at half maximum (FWHM) within ±0.7 nm at 2σ, with virtually no uncertainty in some cases. K and background correction within a reasonable range of values resulted in PSF FWHM differences within ±0.9 nm, except at 2 kV for K with an upper bound of ±1.9 nm due to increased noise. Tailoring K and background correction case-by-case would result in smaller differences. The interconnection of these parameters may help in future efforts to calculate their best selection.

The Determination and Application of the Point Spread Function in the Scanning Electron Microscope.

A method is presented to determine the spatial distribution of electrons in the focused beam of a scanning electron microscope (SEM). Knowledge of the electron distribution is valuable for characterizing and monitoring SEM performance, as well as for modeling and simulation in computational scanning electron microscopy. Specifically, it can be used to characterize astigmatism as well as study the relationship between beam energy, beam current, working distance, and beam shape and size. In addition, knowledge of the distribution of electrons in the beam can be utilized with deconvolution methods to improve the resolution and quality of backscattered, secondary, and transmitted electron images obtained with thermionic, FEG, or Schottky source instruments. The proposed method represents an improvement over previous methods for determining the spatial distribution of electrons in an SEM beam. Several practical applications are presented.

Improving scanning electron microscope resolution for near planar samples through the use of image restoration.

A method is presented for determining the point spread function (PSF) of an electron beam in a scanning electron microscope for the examination of near planar samples. Once measured, PSFs can be used with two or more low-resolution images of a selected area to create a high-resolution reconstructed image of that area. As an example, a 4× improvement in resolution for images is demonstrated for a fine gold particle sample. Since thermionic source instruments have high beam currents associated with large probe sizes, use of this approach implies that high-resolution images can be produced rapidly if the probe diameter is less of a limiting factor. Additionally, very accurate determination of the PSFs can lead to a better understanding of instrument performance as exemplified by very accurate measurement of the beam shape and therefore the degree of astigmatism.

Development of a new quantitative X-ray microanalysis method for electron microscopy.

Quantitative X-ray microanalysis of thick samples is usually performed by measuring the characteristic X-ray intensities of each element in a sample and in corresponding standards. The ratio of the measured intensities from the unknown material to that from the standard is related to the concentration using the ZAF or ϕ(ρz) equations. Under optimal conditions, accuracies approaching 1% are possible. However, all the experimental conditions must remain the same during the sample and standard measurements. This is not possible with cold field emission scanning electron microscopes (FE-SEMs) where beam current can fluctuate around 5% in its stable regime. Very little work has been done on variable beam current conditions (Griffin, B.J. & Nockolds, C.E., Scanning 13, 307-312, 1991), and none relating to cold FE-SEM applications. To address this issue, a new method was developed using a single spectral measurement. It is similar in approach to the Cliff-Lorimer method developed for the analytical transmission electron microscope. However, corrections are made for X rays generated from thick specimens using the ratio of the characteristic X-ray intensities of two elements in the same material. The proposed method utilizes the ratio of the intensity of a characteristic X-ray normalized by the sum of X-ray intensities of all the elements measured for the sample, which should also reduce the amplitude of error propagation. Uncertainties in the physical parameters of X-ray generation are corrected using a calibration factor that must be previously acquired or calculated. As an example, when this method was applied to the calculation of the composition of Au-Cu National Institute of Standards and Technology standards measured with a cold field emission source SEM, relative accuracies better than 5% were obtained.

Win X-ray: a new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope.

A new Monte Carlo program, Win X-ray, is presented that predicts X-ray spectra measured with an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM) operating between 10 and 40 keV. All the underlying equations of the Monte Carlo simulation model are included. By simulating X-ray spectra, it is possible to establish the optimum conditions to perform a specific analysis as well as establish detection limits or explore possible peak overlaps. Examples of simulations are also presented to demonstrate the utility of this new program. Although this article concentrates on the simulation of spectra obtained from what are considered conventional thick samples routinely explored by conventional microanalysis techniques, its real power will be in future refinements to address the analysis of sample classifications that include rough surfaces, fine structures, thin films, and inclined surfaces because many of these can be best characterized by Monte Carlo methods. The first step, however, is to develop, refine, and validate a viable Monte Carlo program for simulating spectra from conventional samples.

Minimizing Errors in Electron Microprobe Analysis.

Errors in quantitative electron microprobe analysis arise from many sources including those associated with sampling, specimen preparation, instrument operation, data collection, and analysis. The relative magnitudes of some of these factors are assessed for a sample of NiAl used to demonstrate important concerns in the analysis of even a relatively simple system measured under standard operating conditions. The results presented are intended to serve more as a guideline for developing an analytical strategy than as a detailed error propagation model that includes all possible sources of variability and inaccuracy. The use of a variety of tools to assess errors is demonstrated. It is also shown that, as sample characteristics depart from those under which many of the quantitative methods were developed, errors can increase significantly.