Doping for a cylindrical structure
The constant doping object in CHARGE allows users to apply constant doping to a semiconductor region. This works fine with most structures. However, in some cases, the doping profile needs to be radial (e.g. devices with nanotubes or nanopillars). The import doping object in DEVICE can be used in such cases. The users can use the script environment to create a rectangular grid (\(x, y, z\)) and then use the script to generate a matrix (\(N\)) that keeps an undoped circular core (value = 0) and applies constant doping everywhere else (value = doping concentration). The matrices can then be saved in a .mat file and loaded into an import doping object to create the desired doping.
The attached script, [[radial_doping_cylinder.lsf]], creates a matrix \(N\) for a rectangular grid \(x, y, z\). It initializes \(N\) to have the desired doping value at all points and then for the points that fall inside the inner core, sets the value to zero. The resulting profile is shown below.
Doping for a truncated cone
If the structure has variation along the \(z\)-axis, i.e. if it is like a truncated cone rather than a cylinder then the doping is no longer uniform along \(z\)-direction and so to create a radial doping profile for such a structure, we need to define the doping at different cross-sections along \(z\). We can divide the 3D profile into \(N\) number of slices and calculate the doping profile at each slice in a manner similar to what is done in the above-mentioned post. The attached script, [[radial_doping_truncated_cone.lsf]], assumes that the dopants penetrate the surface of the cone by the same distance (0.5 um) at each slice at different \(z\) and calculates the 2D profile of each slice.
2D profile at three locations
3D profile after import
If the doping profile takes a ring shape, the attached script, [[radial_doping_ring.lsf]] can be used. In this example, the core is \(n\)-type and the shell is \(p\)-type. The number in the following plot corresponds to the net doping which is positive for \(n\)-type and negative for \(p\)-type doping.