Hints, Tips and Solutions

Q. How do I create Circular and Cylindrical meshes in ATLAS?

A. It has been possible for some time to create meshes with circular and cylindrical symmetry using the DevEdit device building tool. This capability has been extended recently to the ATLAS command language, thus providing the ATLAS user with an alternative and more convenient way to construct devices with circular symmetry. Possible applications are nanowires and mesa-type structures. For nanowires, quantum transport models are available.

To specify a circular mesh with ATLAS2D, the user includes the parameter CIRCULAR on the MESH statement. The properties of the MESH must then be given by using a number of R.MESH and A.MESH statement. The radial mesh spacing is controlled by the R.MESH statements, and the angular mesh given by the A.MESH statements.

To conform to the new MESH shape , the parameters R.MIN, R.MAX, A.MIN, and A.MAX have been added to the REGION, ELECTRODE and DOPING statements.

These permit the use of polar coordinates in delineating the edges of REGIONS and ELECTRODES. The minimum radius is specified by R.MIN and the maximum by R.MAX , both in units of microns. A.MIN and A.MAX specify the minimum and maximum angular ranges respectively, in units of degrees between 0 and 360.

To give a first example, for illustrative purposes only, the set of ATLAS commands shown in Figure 1 results in the structure as shown in Figure 2. For best results the radial limits of the REGIONS and ELECTRODES align with R.MESH locations, and the angular limits align with the major spokes as defined by the A.MESH spacing.

Figure 1. Example ATLAS commands for the electrical capacitance tomography cell.

 

Figure 2. Circular device structure for Electrical capacitance tomography cell.

 

In some cases it may be possible to study a reduced angular range, rather than a full circle. For this reason the MAXANGLE parameter has been introduced onto the MESH statement to allow the user to specify a wedge shaped device structure. MAXANGLE should not be greater than 180 degrees. The algorithm used by MESH CIRCULAR creates a constrained Delaunay mesh. If the radial mesh spacing decreases with increasing radial position, obtuse elements can sometimes be created. The number of obtuse elements can typically be reduced by the use of the MINOBTUSE parameter, also on the MESH statement.

The R.MIN, R.MAX, A.MIN and A.MAX parameters have also been implemented for the DOPING statement. They apply to the analytic doping profiles, UNIFORM, GAUSSIAN and ERFC. For GAUSSIAN and ERFC doping profiles the principal direction is the radial direction and the lateral direction is the tangential direction. Figure 3 shows the use of these parameters.
This gives a semi-circular structure as shown in Figures 4 and 5. The doping density along with junction positions are also shown.

Figure 3. Example ATLAS commands for a semi-circular structure.

 

Figure 4. Half of a symmetrical circular structure.

 

Figure 5. Doping density in semi-circular structure showing p-n junctions.

 

Of arguably more use is the ability to create cylindrical structures in ATLAS3D.

This is effected by using the CYLINDRICAL parameter on the MESH statement in ATLAS3D. A distinction must be made between the structures produced by ATLAS2D and ATLAS3D when using the CYLINDRICAL parameter. In ATLAS2D, the Device is a body of revolution around the x=0 axis, and consequently has no angular dependence. In ATLAS3D, using the CYLINDRICAL parameter allows a device with full radial, angular and axial variations to be modelled. To achieve this both the REGION and ELECTRODE statements accept the R.MIN, R.MAX, A.MIN and A.MAX parameters as well as the Z.MIN and Z.MAX parameters. The DOPING statement also accepts these parameters for analytical doping profiles. The principal direction of the doping is in the z-direction, with the parameters CHAR, PEAK, DOSE, START and JUNCTION applying to the z-direction. The lateral fall-off in the radial and angular directions can be controlled by the LAT.CHAR or RATIO.LAT parameters. An example of a quite complicated 3d cylindrical geometry produced by the commands shown in Figure 6 is shown in Figure 7.

Figure 6. Example ATLAS commands for the cylindrical wedge structure.

 

Figure 7. Example cylindrical structure.

 

The MAXANGLE parameter has been set to 90 degrees, but the major angular spacing is 36 degrees. ATLAS requires that the actual MAXANGLE used correspond to a whole number of major angular mesh spacings. Thus the mesh spacing has been automatically corrected by ATLAS to 108 degrees. This can be seen in a cutplane of the structure.

Figure 8. Cutplane of Cylindrical structure, showing details of mesh.

 

Tip : Because the mesh is independent of position along the z-axis, the radial and angular boundaries of all the REGION’s and ELECTRODE’s are included in the R.MESH and A.MESH statements, irrespective of the z-location of the REGION. It is always recommended to have mesh points exactly co-incident with region boundaries.

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