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Casino simulation

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The speed of the ball and wheel are randomized. The sample consists of Sn balls with different diameters on a carbon substrate. Two different incident electron energies were used 1 keV and 10 keV.

Simulated images of tin balls on a carbon substrate. The tin ball diameters are 20, 10, 5, and 2 nm.

The field of view is 40 nm with a pixel size of 0. The nominal number of electrons for each scan point was 1, For each image, the contrast range was maximized to the minimum and maximum intensity of the image.

The contrast C was calculated to compare the images using the following definition Goldstein and others, These three quantities are reported in Table I for each image.

Comparison of the contrast values calculated from backscattered electron and secondary electron images shown in Figure 5 for 1 and 10 keV incident electron energies.

For both signals, the smaller Sn nanoparticles are visible, because the interaction volume at 1 keV is of the order of few nanometers for both BSE and SE signals.

For BSE images, the contrast decreases with the increase of incident energy. The larger interaction volume decreases the signal from Sn nanoparticles as less electron interaction occurs in the particle.

The decrease of the contrast at 10 keV increases the importance of the noise on the image resolution.

The resolution changes drastically between the two energies. At 10 keV, the smaller tin balls 2 nm diameter are not visible and the 5 nm diameter balls are barely visible.

Similar change in resolution are observed on the SE images for the smaller tin balls 2 nm diameter , but the 5 nm diameter balls are easier to see than on the BSE image.

The SE emission decreases by a factor 10 when the incident energy is increase from 1 to 10 keV. The decrease does not change the contrast as both the carbon substrate and Sn nanoparticle are similarly affected.

Again the decrease of the signal, increases the effect of the noise on the image resolution. The topographic information from the SE signal is clearly observed in the large ball where the edges are brighter than the center.

These images are used to understand the impact of microscope parameters on image resolution and features visibility.

The number of electrons emitted by the electron gun is not constant, but oscillates around an average value. Figure 6 shows the effect of two different numbers of electrons on the BSE image quality.

The sample is a typical microelectronic integrated circuit shown in Figure 1A. At 20 keV, the interaction volume reaches the copper interconnects, which are buried nm depth from the sample surface and increase the BSE emission.

The presence of the tungsten via will increase the BSE emission. The increase by the W via was barely observed in Figure 6B with 10, electrons, but not visible in Figure 6A with 1, electrons.

The decrease of the nominal number of electrons from 10, to 1, illustrates the impact of the electron source noise on image quality. The shot noise feature in CASINO is useful to calculate the visibility of feature of interest with different instrument parameters and feature size.

Effect of the shot noise on the backscattered electron images of integrated circuit ST sample. The nominal number of electrons for each scan point was A: The incident electron energy was 20 keV.

The field of view is nm with a pixel size of 10 nm. Under certain conditions, two close line patterns, separated only by 50 nm, are connected after the development of the resist.

Monte Carlo simulations of the sample and pattern were done for two different electron doses number of electrons: The expected patterns are clearly observed by their dark red color.

The absorbed energy in the pattern mainly comes from the incident beam. At 20 keV the electrons pass through the 50 nm resist film and nm dielectric film with little deviation.

Most of the elastic collisions occur in the Si substrate. With a pattern composed of more than , scan points, the contribution of the BSE on the absorbed energy cannot be neglected.

This is the background energy observed between patterns in Figure 7C and 7D. The long range combined with the random nature of the BSE exit position created a uniform and noisy background signal.

The average value of the absorbed energy background is proportional to the electron dose. We suspect that for a specific value of the electron dose, the absorbed energy background reaches the threshold value for the breakdown of the PMMA molecule and development of the resist occurs outside the expected patterns as observed in Figure 7B.

However, this is just one possible explanation of the failure. The electron exposure is only the first step of electron beam lithography.

The resist development and profile evolution could be the source of the problem as well. Improved simulation software for modeling signals generation in electron microscope from electron — sample interactions, which include a full 3D sample geometry and efficient 3D simulation model, has been developed.

All features are available through a graphical user interface. The software features like scan points and shot noise allowing for the simulation and study of realistic experimental conditions.

With the improved energy range, this software can be used for SEM and STEM applications, but with the limitation that the sample is considered as amorphous by the models and the simulation scheme used.

The software can be downloaded at this website: The software is in constant development for our research need and from user comments.

For obvious reason, the name of the program is not enough to find it. National Center for Biotechnology Information , U. Author manuscript; available in PMC Jul Find articles by Hendrix Demers.

Find articles by Nicolas Poirier-Demers. Find articles by Dany Joly. Find articles by Marc Guilmain. Find articles by Niels de Jonge. Find articles by Dominique Drouin.

Author information Copyright and License information Disclaimer. The publisher's final edited version of this article is available at Scanning.

See other articles in PMC that cite the published article. Abstract Monte Carlo softwares are widely used to understand the capabilities of electron microscopes.

Monte Carlo simulation, scanning electron microscopy, secondary electron, three-dimensional 3D , scanning transmission electron microscopy.

Introduction Electron microscopes are useful instruments used to observe and characterize various types of samples: Features and Structure The simulation of electron transport in a 3D sample involves two computational aspects.

Shapes The 3D sample modeling is done by combining basic 3D shapes and planes. Open in a separate window. Regions Each shape is characterized by two sides: Triangles and Mesh The change of region algorithm has been modified to allow the simulation of 3D sample.

Microscope and Simulation Properties CASINO allows the user to choose various microscope and simulation properties to best match his experimental conditions.

The number of electrons for a specific pixel N i was obtained from a Poisson distribution P N random number generator with: Distributions for Each Scan Point The following distributions are used to understand the complex interaction between incident electron and the sample.

Global Distributions The following distributions either sum the contribution of all scan points or compare the information obtained from each scan point.

Representation of Collected Data For the analysis of the distributions presented previously it is useful to visualize the data directly in a graphic user interface before doing further processing using other software.

Special Software Features The simulation of an image needs a large number of scan points. Application Examples The following examples illustrate the application of the simulation tool in relation to backscattered electron BSE and secondary electron SE imaging, electron gun shot noise, and electron beam lithography.

Secondary Electron Yield In a similar manner, the evolution of secondary electron yield with the incident electron energy was used to validate the secondary electron generation implementation in CASINO.

Table I Comparison of the contrast values calculated from backscattered electron and secondary electron images shown in Figure 5 for 1 and 10 keV incident electron energies.

Shot Noise Effect on Imaging The number of electrons emitted by the electron gun is not constant, but oscillates around an average value.

Conclusions Improved simulation software for modeling signals generation in electron microscope from electron — sample interactions, which include a full 3D sample geometry and efficient 3D simulation model, has been developed.

Journal of Graphics Tools. Surface And Interface Analysis. Springer Berlin Heidelberg; National Institute of Standards and Technology.

A Database of Electron-Solid Interactions. Oxford University Press; b. Joy DC, Luo S. An empirical stopping power relationship for low-energy electrons.

Kieft E, Bosch E. Journal of Physics D: A simulation of electron scattering in metals. Japanese Journal of Applied Physics. Use of Monte Carlo modeling for interpreting scanning electron microscope linewidth measurements.

Monte Carlo simulation of scanning electron microscope signals for lithographic metrology. National Bureau of Standards; Physics of Image Formation and Microanalysis.

Dat betekent niet dat het een methode is die gebaseerd is op gokken. Monte-Carlosimulaties worden in verschillende wetenschappelijke toepassingen gebruikt, zoals bij verschillende NASA -projecten waar onzekerheden een belangrijke rol spelen.

Ook economische problemen maken veelvuldig gebruik van Monte-Carlosimulaties. De Monte-Carlosimulatietechniek is alleen maar mogelijk dankzij de beschikbaarheid van computers.

Immers, een enkele simulatie op zich vraagt in het algemeen al veel rekenkracht. Deze simulatie moet nu, afhankelijk van het gewenste betrouwbaarheidsniveau tientallen tot enkele duizenden malen herhaald worden, elke keer met een nieuwe set invoervariabelen.

Voor elke individuele simulatie wordt in de preprocessor een nieuwe set van invoervariabelen gegenereerd. Voor elk van deze variabelen wordt door de preprocessor een willekeurige waarde gekozen, binnen het opgegeven spreidingsgebied en met inachtneming van de kansverdeling.

Dit is het Monte-Carloaspect van de simulatie. Hier worden de simulaties uitgevoerd, elke simulatie met weer een andere door de preprocessor gedefinieerde set van invoervariabelen.

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