Automatic electron beam calibration on periodic nanostructures
Systems, methods, and media for calibrating a scanning electron microscope (SEM). The system includes a processor and a memory. The memory stores instructions that, when executed by the processor, configure the system to perform operations. An electron microscope image of a periodic structure is generated by the SEM. A Fourier transform of the electron microscope image is computed to generate a spectrum. Reciprocal lattice vectors are computed based on a known periodicity of the periodic structure. A pixel mask is generated based on the reciprocal lattice vectors and applied to filter the spectrum. A quality metric is generated based on an aggregate magnitude of the filtered spectrum and a magnitude of a zero-frequency component of the filtered spectrum. A pixel scaling parameter, focus parameter, and/or stigmation parameter of the SEM are determined based on the quality metric.
1 . A system comprising: at least one processor; and a memory storing instructions that, when executed by the at least one processor, configure the system to perform operations comprising: obtaining an electron microscope image of a periodic structure, the electron microscope image being generated by a scanning electron microscope (SEM); computing a Fourier transform of the electron microscope image to generate a spectrum; computing reciprocal lattice vectors based on a known periodicity of the periodic structure; generating a pixel mask based on the reciprocal lattice vectors; generating a filtered spectrum by applying the pixel mask to the spectrum; computing a quality metric based on: an aggregate magnitude of components of the filtered spectrum; and a magnitude of a zero-frequency component of the filtered spectrum; and determining one or more operating parameters of the SEM based on the quality metric, the one or more operating parameters comprising at least one of: a pixel scaling parameter; a focus para meter; or a stigmation parameter.
2 . The system of claim 1 , wherein: the one or more operating parameters comprise the pixel scaling parameter, the focus parameter, and the stigmation parameter.
3 . The system of claim 2 , wherein: the determining of the pixel scaling parameter of the SEM based on the quality metric comprises: repeating, one or more times, operations comprising: varying the pixel scaling parameter; applying the pixel scaling parameter to the electron microscope image to generate a re-scaled electron microscope image; re-computing the Fourier transform of the re-scaled electron microscope image to generate a re-scaled spectrum; re-generating the filtered spectrum by applying the pixel mask to the re-scaled spectrum to generate a re-scaled filtered spectrum; and re-computing the quality metric based on the re-scaled filtered spectrum; and determining a calibrated value for the pixel scaling parameter based on the computed and re-computed values of the quality metric.
4 . The system of claim 3 , wherein: the determining of the focus parameter and stigmation parameter of the SEM based on the quality metric comprises: generating a plurality of values for the quality metric by repeating, one or more times, operations comprising: varying at least one of the focus parameter or the stigmation parameter; applying the focus parameter and the stigmation parameter to the SEM; and the operations of obtaining the electron microscope image of the periodic structure using the SEM, computing the Fourier transform, generating the filtered spectrum, and computing the quality metric; and determining calibrated values for the focus parameter and stigmation parameter based on the plurality of values of the quality metric.
5 . The system of claim 4 , wherein: the determining of the calibrated values for the focus parameter and stigmation parameter based on the plurality of values of the quality metric comprises: fitting a Gaussian curve to the plurality of values of the quality metric relative to the focus parameter or the stigmation parameter; and determining the calibrated values for the focus parameter or stigmation parameter based on an optimum value of the quality metric on the Gaussian curve.
6 . The system of claim 4 , wherein: the determining of the pixel scaling parameter of the SEM is performed on a reference sample of the periodic structure; and the determining of the focus parameter and stigmation parameter of the SEM is performed for each of a plurality of test samples of the periodic structure.
7 . The system of claim 6 , wherein the operations further comprise: imaging each test sample with the SEM one or more times using the calibrated values for the pixel scaling parameter, the focus parameter, and the stigmation parameter; and re-determining the focus parameter and the stigmation parameter after each M images, M being a positive integer greater than one.
8 . The system of claim 7 , wherein the operations further comprise: re-determining the pixel scaling parameter after each N images, N being a positive integer greater than M.
9 . The system of claim 1 , wherein: the generating of the filtered spectrum by applying the pixel mask to the spectrum comprises: tiling the pixel mask across the spectrum based on the reciprocal lattice vectors, thereby generating a tiled mask; and filtering the spectrum using the tiled mask to generate the filtered spectrum.
10 . The system of claim 1 , wherein: the computing of the quality metric comprises: normalizing the filtered spectrum by dividing a magnitude of one or more components of the filtered spectrum by the magnitude of the zero-frequency component of the filtered spectrum, thereby generating a normalized spectrum; performing an inverse Fourier transform of the normalized spectrum to generate an inverse spectrum; and summing absolute values of one or more components of the inverse spectrum.
11 . The system of claim 1 , wherein the operations further comprise: applying a windowing function to the electron microscope image, the windowing function being configured to mitigate edge effects when generating the spectrum.
12 . A method, performed by at least one processor, comprising: obtaining an electron microscope image of a periodic structure, the electron microscope image being generated by a scanning electron microscope (SEM); computing a Fourier transform of the electron microscope image to generate a spectrum; computing reciprocal lattice vectors based on a known periodicity of the periodic structure; generating a pixel mask based on the reciprocal lattice vectors; generating a filtered spectrum by applying the pixel mask to the spectrum; computing a quality metric based on: an aggregate magnitude of components of the filtered spectrum; and a magnitude of a zero-frequency component of the filtered spectrum; and determining one or more operating parameters of the SEM based on the quality metric, the one or more operating parameters comprising at least one of: a pixel scaling parameter; a focus parameter; or a stigmation parameter.
13 . The method of claim 12 , wherein: the one or more operating parameters comprise the pixel scaling parameter, the focus parameter, and the stigmation parameter.
14 . The method of claim 13 , wherein: the determining of the pixel scaling parameter of the SEM based on the quality metric comprises: repeating, one or more times, operations comprising: varying the pixel scaling parameter; applying the pixel scaling parameter to the electron microscope image to generate a re-scaled electron microscope image; re-computing the Fourier transform of the re-scaled electron microscope image to generate a re-scaled spectrum; re-generating the filtered spectrum by applying the pixel mask to the re-scaled spectrum to generate a re-scaled filtered spectrum; and re-computing the quality metric based on the re-scaled filtered spectrum; and determining a calibrated value for the pixel scaling parameter based on the computed and re-computed values of the quality metric.
15 . The method of claim 14 , wherein: the determining of the focus parameter and stigmation parameter of the SEM based on the quality metric comprises: generating a plurality of values for the quality metric by repeating, one or more times, operations comprising: varying at least one of the focus parameter or the stigmation parameter; applying the focus parameter and the stigmation parameter to the SEM; and the operations of obtaining the electron microscope image of the periodic structure using the SEM, computing the Fourier transform, generating the filtered spectrum, and computing the quality metric; and determining calibrated values for the focus parameter and stigmation parameter based on the plurality of values of the quality metric.
16 . The method of claim 12 , wherein: the generating of the filtered spectrum by applying the pixel mask to the spectrum comprises: tiling the pixel mask across the spectrum based on the reciprocal lattice vectors, thereby generating a tiled mask; and filtering the spectrum using the tiled mask to generate the filtered spectrum.
17 . The method of claim 12 , wherein: the computing of the quality metric comprises: normalizing the filtered spectrum by dividing a magnitude of one or more components of the filtered spectrum by the magnitude of the zero-frequency component of the filtered spectrum, thereby generating a normalized spectrum; performing an inverse Fourier transform of the normalized spectrum to generate an inverse spectrum; and summing absolute values of one or more components of the inverse spectrum.
18 . The method of claim 12 , further comprising: applying a windowing function to the electron microscope image, the windowing function being configured to mitigate edge effects when generating the spectrum.
19 . A non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by at least one processor of a system, cause the system to perform operations comprising: obtaining an electron microscope image of a periodic structure, the electron microscope image being generated by a scanning electron microscope (SEM); computing a Fourier transform of the electron microscope image to generate a spectrum; computing reciprocal lattice vectors based on a known periodicity of the periodic structure; generating a pixel mask based on the reciprocal lattice vectors; generating a filtered spectrum by applying the pixel mask to the spectrum; computing a quality metric based on: an aggregate magnitude of components of the filtered spectrum; and a magnitude of a zero-frequency component of the filtered spectrum; and determining one or more operating parameters of the SEM based on the quality metric, the one or more operating parameters comprising at least one of: a pixel scaling parameter; a focus parameter; or a stigmation parameter.
20 . A kit comprising: the non-transitory computer-readable storage medium of claim 19 ; and a reference sample of the periodic structure.