4.4.3 Pattern Transfer

Boolean operations can also be used to transfer a pattern defined by a given mask onto a structure. It is assumed that the initial geometry is a two-layer structure like that shown in (Figure 4.6a). The geometry can be alternatively described by two LS functions (Figure 4.6b). The first LS function ${\Phi}_1$ represents the interface between the two layers and the second ${\Phi}_2$ describes the surface. To transfer the mask pattern to the structure the top layer needs to be selectively removed. This can be expressed by the following Boolean operation

$${\Phi}'_2=\min({\Phi}_1,\max({\Phi}_2, {\Phi}_{\text{mask}})).$$ (4.16)

Here the LS function ${\Phi}_{\text{mask}}$ represents the mask, if it is extruded to the third dimension (Figure 4.6c). The final minimum and maximum coordinates of the extruded mask must be at least smaller and larger than the minimum and maximum coordinates of the LSs representing the initial structure, respectively. The final structure is shown in Figure 4.6d.

Figure 4.6: Boolean operations using level sets can be applied to describe pattern transfer.