Novel approach based on continuous trench modelling to predict focused ion beam prepared freeform surfaces
Focused Ion Beam (FIB) systems can be used to generate controlled micro- and nano-features on a solid surface. Prediction of surfaces fabricated in this way requires knowledge of the rate of removal of the target material in order to simulate the evolution of the surface. In this paper we present a continuous-time model of this process that allows us to predict the shape of trenches and freeform surfaces under the action of FIB. This type of model is appropriate when the points that describe the discrete trajectory of the beam (the line connecting consecutive dwell points) are close enough that the craters generated on the surface overlap. In the case of a straight beam path with constant dwell time, a trench of uniform depth is generated under these conditions. This simplified approach considerably reduces the computing time needed to simulate the process, without significantly reducing the accuracy of the predicted surface. Calibration of the model for a particular FIB setup and workpiece involves only a small number of experimental trials. The predictions of the model have been tested on a single crystalline Boron p-doped Si target material for several different beam paths. The depth and shape of the cross section of single and overlapping trenches with constant dwell time are predicted with high accuracy. The model was also used to predict three freeform surfaces, where the dwell time varies along each line of the beam path. Atomic force microscopy topography measurements show that the average relative error between the measured and simulated profiles is 210% depending on the complexity of the machined surface.