Dr. Thomas Verduin Profile

Dr. Thomas Verduin

Engineer at Intel Corp

SPIE Involvement:

Author

Publications (7)

Proceedings Article | 21 April 2016 Paper

GPU accelerated Monte-Carlo simulation of SEM images for metrology

T. Verduin, S. Lokhorst, C. Hagen

Proceedings Volume 9778, 97780D (2016) https://doi.org/10.1117/12.2219160

KEYWORDS: Scanning electron microscopy, Metrology, Particles, Monte Carlo methods, Interfaces, Line edge roughness, Lithography, Critical dimension scanning electron microscopy, Modeling and simulation, Numerical simulations, Electrons, Silicon, Computer simulations, Scattering, Dimensional metrology

Read Abstract +

In this work we address the computation times of numerical studies in dimensional metrology. In particular, full Monte-Carlo simulation programs for scanning electron microscopy (SEM) image acquisition are known to be notoriously slow. Our quest in reducing the computation time of SEM image simulation has led us to investigate the use of graphics processing units (GPUs) for metrology. We have succeeded in creating a full Monte-Carlo simulation program for SEM images, which runs entirely on a GPU. The physical scattering models of this GPU simulator are identical to a previous CPU-based simulator, which includes the dielectric function model for inelastic scattering and also refinements for low-voltage SEM applications. As a case study for the performance, we considered the simulated exposure of a complex feature: an isolated silicon line with rough sidewalls located on a at silicon substrate. The surface of the rough feature is decomposed into 408 012 triangles. We have used an exposure dose of 6 mC/cm², which corresponds to 6 553 600 primary electrons on average (Poisson distributed). We repeat the simulation for various primary electron energies, 300 eV, 500 eV, 800 eV, 1 keV, 3 keV and 5 keV. At first we run the simulation on a GeForce GTX480 from NVIDIA. The very same simulation is duplicated on our CPU-based program, for which we have used an Intel Xeon X5650. Apart from statistics in the simulation, no difference is found between the CPU and GPU simulated results. The GTX480 generates the images (depending on the primary electron energy) 350 to 425 times faster than a single threaded Intel X5650 CPU. Although this is a tremendous speedup, we actually have not reached the maximum throughput because of the limited amount of available memory on the GTX480. Nevertheless, the speedup enables the fast acquisition of simulated SEM images for metrology. We now have the potential to investigate case studies in CD-SEM metrology, which otherwise would take unreasonable amounts of computation time.

Proceedings Article | 8 March 2016 Paper

Simulation of shotnoise induced side-wall roughness in electron lithography

T. Verduin, S. Lokhorst, C. Hagen, P. Kruit

Proceedings Volume 9778, 97781Z (2016) https://doi.org/10.1117/12.2219295

KEYWORDS: Line edge roughness, Monte Carlo methods, Lithography, Image processing, Diffusion, Photoresist processing, Scanning electron microscopy, Process control, Metrology, Dimensional metrology, 3D image processing, Interfaces, Scattering, Silicon, 3D modeling, 3D vision, Optical simulations

Read Abstract +

We have developed a fast three dimensional Monte-Carlo framework for the investigation of shotnoise induced side-wall roughness (SWR) formation. The calculation outline is demonstrated by an example for an exposure of a 100nm thick layer of negative tone resist (NTR) resist on top of an infinitely thick silicon substrate. We use our home built Monte-Carlo simulator for electron-matter interaction for the purpose of lithography. A pattern of an isolated line is written into the resist layer by scanning a beam with 20 keV electrons over an area of 32nm×1μm (width and length). During the exposure, we use a spot size of 20 nm, beam step size of 4nm and a Poisson distributed exposure dose of 80 μC/cm², 60 μC/cm² and 40 μC/cm². During the exposure of the sample, we record the locations of the inelastic events within the resist layer. The distribution of released acids is determined under the simplified assumption that every inelastic event corresponds to a release. We now construct a three dimensional image of the (in)solubility of the resist layer within a cuboid of 128 nm(256px) wide, 800 nm(1024px) in length and 100 nm(128px) in height. It is obtained by summing the contribution of all acids to every voxel in the three dimensional image. We have used a three dimensional Gaussian with σ_x,y,z = r_d =5nm for the diffusion of the acid. The boundary between exposed and unexposed resist is determined by a threshold. The resulting image of the (in)solubility is analyzed in different ways by considering slices and three dimensional views of the border. The average line edge roughness (LER) is obtained by calculating the standard deviation (one-sigma) of the left and right border from yz-slices. By considering all slices, ranging from the top of the resist layer to the bottom of the substrate, the average LER as a function of the depth from the top surface of the resist layer is obtained. Shotnoise effects are observed as we decrease the exposure dose. An increased effect of shotnoise is observed near the vacuum and substrate interface. One contribution relates to the actual number of acids, which due to the scattering is less near the interface than away from the interface. Another contribution stems from the fact that no acids are found on the vacuum side nor on the substrate side.

Proceedings Article | 17 March 2015 Paper

The effect of sidewall roughness on line edge roughness in top-down scanning electron microscopy images

T. Verduin, S. Lokhorst, P. Kruit, C. Hagen

Proceedings Volume 9424, 942405 (2015) https://doi.org/10.1117/12.2085768

KEYWORDS: Electrons, Line edge roughness, Scanning electron microscopy, Polymethylmethacrylate, Scattering, Silicon, Monte Carlo methods, Chemical elements, Metrology, Dielectrics

Read Abstract +

We have investigated in a numerical study the determination of sidewall roughness (SWR) from top down scanning electron microscopy (SEM) images. In a typical metrology application, top-down SEM images are acquired in a (critical-dimension) SEM and the roughness is analyzed. However, the true size, shape and roughness characteristics of resist features are not fully investigated in the analysis of top-down SEM images. In reality, rough resist features are complex three-dimensional structures and the characterization naturally extends to the analysis of SWR. In this study we randomly generate images of rough lines and spaces, where the lines are made of PMMA on a silicon substrate. The lines that we study have a length of 2 µm, a width of 32nm and a height of 32 nm. The SWR is modeled by using the power spectral density (PSD) function of Palasantzas, which characterizes roughness by the standard deviation σ, correlation length ξ and roughness exponent α . The actual roughness is generated by application of the method of Thorsos in two dimensions. The images are constructed by using a home-built program for simulating electron-specimen interactions. The program that we have developed is optimized for complex arbitrary geometries and large number of incident low energy primary electrons by using multi-core CPUs and GPUs. The program uses the dielectric function model for inelastic scattering events and has an implementation specifically for low energy electrons. A satisfactory comparison is made between the secondary electron yields from the home-built program and another program found in literature. In order to reduce the risk of shrinkage, we use a beam energy of 300 eV and a spot size of 3 nm. Each pixel is exposed with 20 electrons on average (≈ 276 µC/cm²), following the Poisson distribution to account for illumination shot noise. We have assumed that the detection of electrons is perfect and does not introduce additional noise. We measure line edge roughness (LER) in simulated top-down SEM images of randomly generated rough lines by using PSD analysis. The measurements are then compared to the actual SWR that was used to generate the rough lines. We conclude that the bias in the determination of SWR is a non-linear function of the correlation length ξ3D of the actual SWR. The measured correlation length ξ 2D shows a linear trend with the correlation length ξ 3D of the SWR. From another simulation run, we conclude that the relation between measured LER in the top-down image and the standard deviation ξ 3D of the SWR is linearly biased. We see that the amount of bias relates to the correlation length ξ 3D of the SWR: The bias in the determination of SWR from top-down images increases for decreasing correlation length ξ 3D of the actual SWR. The results of this study, with respect to the metrology of rough resist features, touches upon the reliability and comparability of roughness characterization in top-down images.

SPIE Journal Paper | 13 August 2014

Determination of line edge roughness in low-dose top-down scanning electron microscopy images

Thomas Verduin, Pieter Kruit, Cornelis Hagen

JM3, Vol. 13, Issue 03, 033009, (August 2014) https://doi.org/10.1117/12.10.1117/1.JMM.13.3.033009

KEYWORDS: Scanning electron microscopy, Line edge roughness, Electrons, Image filtering, Edge detection, Digital filtering, Linear filtering, Error analysis, Metrology, Edge roughness

Read Abstract +

SPIE Journal Paper | 3 July 2014

Size and shape control of sub-20 nm patterns fabricated using focused electron beam-induced processing

Sangeetha Hari, Cornelis Hagen, Thomas Verduin, Pieter Kruit

JM3, Vol. 13, Issue 03, 033002, (July 2014) https://doi.org/10.1117/12.10.1117/1.JMM.13.3.033002

KEYWORDS: Electron beam lithography, Scanning electron microscopy, Molecules, Line width roughness, Control systems, Electron beams, Lithography, Silicon, Optical lithography, Electron microscopes

Read Abstract +

Proceedings Article | 2 April 2014 Paper

Determination of line edge roughness in low dose top-down scanning electron microscopy images

T. Verduin, P. Kruit, C. Hagen

Proceedings Volume 9050, 90500L (2014) https://doi.org/10.1117/12.2046493

KEYWORDS: Line edge roughness, Image filtering, Scanning electron microscopy, Edge detection, Metrology, Error analysis, Image processing, Computer simulations, Optical filters, Edge roughness

Read Abstract +

We investigated off-line metrology for LER determination in low-dose SEM images to reduce the acquisition time and the risk of shrinkage. Our first attempts are based on filtering noisy (experimental) SEM images and use peak detection to measure the edge displacements and calculating the discrete PSD. However, the result of the filtering is that the power spectrum of the filter leaks into the PSD. So it is better to avoid a filter at all. We subsequently developed a method to detect edge displacements without the use of a filter. This method considers the signal profile of a SEM by integrating an experimental image of lines in the direction of the edges. The signal profile of an isolated edge is modeled as two merged Gaussians. This signal profile is then fitted against the raw (unfiltered) data of the edge pattern using an interior trust-region-reflective minimization procedure. This gives the edge displacements without the use of a filter and a filter-free version of the discrete PSD is obtained. The determination of edge displacements without the use of a filter, enables us to study how much noise is acceptable and still determine LER. To answer this question we generate random lines using the model of Palasantzas and the algorithm of Thorsos. This gives random generated edge displacements for typical values of experimental lines for the parameters of the model: 2 μm long lines (256 pixels), a correlation length ξ of 25 nm and a roughness exponent of 0.75. A noise-free top-down SEM-like image of lines is created by shifting the profile signal according to the random generated edge displacements. The image is further processed by adding Poisson-distributed noise. We consider three noise cases where the average electron density is about 2, 20 and 200 electrons per pixel. This corresponds to a charge density of (in respective order) 10 μC/cm², 100 μC/cm² and 1000 μC/cm². The edge displacements of the random generated images are determined using our new developed filter-free displacement detection. The difference between the random generated displacements and the detected displacements (after adding Poisson-distributed noise) shows how pixel noise translates to noise in edge displacements. We conclude from running many simulations that this pixel noise translates to a noise in the edge displacements which is uniform (flat line) in the PSD. This means that pixel noise is classified as white noise in the edge displacements. Finally, we study simulated discrete PSDs as a function of the number of averages and analyze the convergence of the parameters (σ, σ_n, ξ and α) of the Palasantzas model extended with a white noise term. One of the conclusions is that a very noisy image with 12 lines and about 2 electrons per pixel on average (charge density ≈ 10 μC/cm²) already produces an estimation for LER with a relative error of about 10%.

Proceedings Article | 28 March 2014 Paper

Size and shape control of sub-20nm patterns fabricated using focused electron beam induced processing

S. Hari, C. Hagen, T. Verduin, P. Kruit

Proceedings Volume 9049, 90490M (2014) https://doi.org/10.1117/12.2046356

KEYWORDS: Electron beams, Electron beam lithography, Line edge roughness, Scanning electron microscopy, Molecules, Lithography, Silicon, Electron microscopes, Selenium, Semiconducting wafers

Read Abstract +

Showing 5 of 7 publications

View contact details

UPDATE YOUR PROFILE

Is this your profile? Update it now.

Sign into your SPIE.org account

Don’t have a profile and want one?

Create an account on SPIE.org

Keywords/Phrases

Search In:

Publication Years