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It can be used to model backscattered, secondary, and transmitted electron signals as well as absorbed energy. This equation assumes an ideal solution for a homogeneous phase and gives a weight-averaged density of all elements in the sample. To help these users use CASINO for their research, all the information from the saved electron trajectories, such as each scattering event position and energy, can be exported in a text file for manual processing. This condition is not respected if, for example, two triangle surfaces overlap Figure 2B or intersect Figure 2C. The second category with two shapes contains 3D shape with only flat surfaces, like a box. For these 3D shapes the curved surface is approximated by small flat triangle surfaces. The type of distribution implemented was driven by our research need and various collaborations. From this new coordinate, a new segment is generated from the new event coordinate as described in the electron trajectory calculation section. For multiple elements, either the atomic fraction or the weight fraction can be used to set the concentration of each element. To accelerate this process, the software minimizes the number of triangles to be tested by organizing the triangles in a 3D partition tree, an octree Mark de Berg, , where each partition a box that contains ten triangles. The main aim of this work was to simulate more realistic samples. The change of region algorithm has been modified to allow the simulation of 3D sample. This category includes sphere, cylinder, cone, and rounded box shapes. The development of the 3D version of CASINO was guided by these goals: a graphical user interface, an efficient in relation to simulation time and memory use 3D simulation model, accurate physic models for electron microscopy applications, and lastly to make it available to the scientific community as done with the previous versions Drouin and others, ; Hovington and others, Two main challenges were encountered with the simulation of 3D samples: the creation of the 3D sample by the user and the slowdown inherent to the more complex algorithm needed for a true 3D simulation. The inside is the side right after the electron crosses the shape surface for the first time and is inside the shape. No overlapping triangles are possible with the small gap approach and the correct region will always been selected when the electron intersects a triangle.

Monte Carlo softwares are widely used to understand the capabilities of electron microscopes. Various softwares and code systems were developed to fill this need of a 3D Monte Carlo casino electron simulation tutorial Babin and others, ; Ding and Li, ; Gauvin and Michaud, ; Gnieser and others, ; Johnsen and others, ; Kieft and Bosch, ; Ritchie, ; Salvat and others, ; Villarrubia and Ding, ; Casino electron simulation tutorial and others, ; Yan and others, However, either because of their limited availability to the scientific community or their restriction to expert users only, we have extended the software CASINO Drouin and others, to 3D Casino electron simulation tutorial Carlo simulation.

This paper presents how we responded to these challenges and goals. The software does not verify that this condition is valid for all triangles when the sample is created.

Obviously, these distributions will not meet the requirements of all users. The mass density of the go here can be specified by the user casino electron simulation tutorial obtained from a database.

Figure 2A illustrates schematically the electron and triangle interaction and the resulting change of region. Because of the large amount of information generated, the software allows the filtering of the exported information to meet the user needs.

This software has an improved energy range for scanning electron microscopy and scanning transmission electron microscopy applications. In this section, a brief description of the Monte Carlo method is given and the physical models added or modified to extend the energy range of the software are presented.

B: two triangles overlap and ambiguity in the determination of the new region. The chemical composition of the sample is set by regions. E: another ambiguity in the determination of the new region the red dash lines define the lateral limit of the Au region of the plane shape. The 3D sample modeling is done by combining basic 3D shapes and planes. The detailed description of the Monte Carlo simulation method used in the software is given in these references. The software feature a graphical user interface, an efficient in relation to simulation time and memory use 3D simulation model, accurate physic models for electron microscopy applications, and it is available freely to the scientific community at this website: www. If the true density of the molecule or compound is known, it should be used instead of the value given by this equation. Schema of the intersection of an electron trajectory and a triangle and the change of region associate with it. The best approach is to always use a small gap 0. A: 3D view of the sample showing the different shapes and regions. Except for trivial cases, 3D structures are difficult to build without visualization aids. When the creation of the sample is finished, the software transforms all the shape surfaces into triangles. The new region is the region associated with the triangle side of emerging electron after the intersection. A region, which defines the composition of the sample, is associated to each side. The outside is the side where the electron will enter the shape. In that case, two regions are possible when the electron intersects the triangle and if these two regions are different, incorrect results can occur. The first category has only one shape, a finite plane. The sample used is a typical CMOS stack layer for 32 nm technology node with different dielectric layers, copper interconnects and tungsten via. The user can specify the number of divisions used to get the required accuracy in the curved surface description for the simulation conditions. D: small gap approach to resolve these two problems. Both are needed to successfully simulate the electron trajectory. From the simulated trajectories, various distributions useful for analysis of the simulation are calculated. However, the user has to be careful that the plane dimension is larger than the electron interaction volume because the plane does not define a closed shape and unrealistic results can happen if the electron travels beyond the lateral dimensions of the plane see Figure 2E and next section. The software features like scan points and shot noise allow the simulation and study of realistic experimental conditions. The finite plane is useful to define large area of the sample like a homogenous film. We also present the new models and simulation features added to this version of CASINO and examples of their applications. A typical 3D sample will generate a large number of triangles, for example , triangles triangles per sphere are required to model accurately the tin balls sample studied in the application section. The simulation of electron transport in a 3D sample involves two computational aspects. For each region, the composition can be a single element C or multiple elements like a molecule H 2 O or an alloy Au x Cu 1-x. A: single triangle where the new region is Au. For each new trajectory segment, the simulation algorithm needs to find if the electron intersects a triangle by individually testing each triangle using a vector product. For various reasons, but principally because of the long simulation time and large computer memory needed, the previous version of CASINO was limited to simple geometry Drouin and others, To apply the Monte Carlo method to more realistic applications with complex sample, three-dimensional 3D Monte Carlo softwares are needed. To study more realistic applications with complex samples, 3D Monte Carlo softwares are needed. Electron microscopes are useful instruments used to observe and characterize various types of samples: observation of complex integrated circuits, small nanoparticles in biological samples or nano-precipitates, and dislocations by cathodoluminescence just to name a few examples. B: Top view of the sample with the scan points used to create an image. The octree algorithm allows fast geometry calculation during the simulation by testing only 10 triangles of the total number of triangles in the sample , triangles for the tin balls sample and 8 partitions; and generating the minimum of number of new segments. For complex geometry, the geometry computation can involve a large effort simulation time , so fast and accurate algorithms are needed. Also the region composition can be added and retrieved from a library of chemical compositions. Each shape is characterized by two sides: outside and inside. To fully understand and extract all the information available from these instruments, the complex electron-matter interactions have to be understood. The first one is the geometry computation or ray tracing of the electron trajectory inside the sample. The 3D navigation tool rotation, translation and zoom of the camera allows the user to assert the correctness of the sample manually. Another type of ambiguity in the determination of the new region is shown in Figure 2E when an electron reaches another region without crossing any triangle boundaries. Each shape is defined by a position, dimension and orientation. If not, the program found the nearness partition that contains the new segment from the 8 neighbour partitions and created a node intersection event at the boundary between the two partition boxes. Complex 3D sample can thus be modeled by using these basic shapes as shown in the examples presented in this paper. C: Electron trajectories of one scan point with trajectory segments of different color for each region. The definition of outside and inside is from the point of view of an incident electron from the top above the shape toward the bottom below the shape. The search inside the partitions tree is very efficient to find neighbour partitions and their associated triangles. For correct simulation results, only one region should be possible after an intersection with a triangle. In the previous version, only horizontal and vertical layers sample were available Drouin and others, ; Hovington and others, An example of a complex sample, an integrated circuit, is shown in Figure 1A. For a multiple elements region, the mass density is calculated with this equation. Also available in this category is the truncated pyramid shape which is useful to simulate interconnect line pattern. Using the electron transport 3D feature, the beam and scanning parameters allow the simulation of realistic line scans and images. This process can be very intensive on computing power and thus time. Specifically, the Monte Carlo software should be able to build a 3D sample and track the electron trajectory in a 3D geometry. The last category is 3D shape with curved surface and contains 4 shapes. During the ray tracing of the electron trajectory, the current region is changed each time the electron intersects a triangle. The small gap is a lot smaller than the electron mean free path, i. The engine generated a new segment from the new event coordinate, see electron trajectory calculation section. The 10 triangles in the current partition are tested for interception with the new segment. C: intersection of two triangles with discontinuity in the determination of the new region. In particular, the navigation allows the user to see inside the shape to observe imbedded shape. The second aspect is the physical interaction with the matter inside the sample. As illustrated in Figure 2E , the region associated with an electron inside the Au region define by the finite plane the dash lines define the lateral limit and going out of the dimension define by the plane, either on the side or top, does not change and the electron continue his trajectory as inside a Au region. The box is often used to define a substrate. The Monte Carlo method is useful to help understand these instruments Joy, b. For complex samples, a large number of material property regions two per shape have to be specified by the user; to accelerate the sample set-up, the software can merge regions with the same chemical composition into a single region. They can even be used to manufacture integrated circuits by electron beam lithography.