Fig. 3.8 shows the situation when such a sphere is applied to only one surface cell, similar to the etchant attack by a small drop of an etching liquid. The isotropic behavior of the wet etching removes the silicon downwards and sidewards, etching a spherical cavity into the substrate. If the wafer surface is partially covered by an oxide or a resist mask, the etchant attacks the wafer surface at the areas not protected by the mask. This is modeled by applying the structuring element to all silicon surface cells (green in Fig. 3.8) After updating the material indices, the outer contour of all structuring elements forms the new surface evolving after some time of etching attack. If the selectivity of the etchant inhibits the attack of the resist, a significant underetching of the mask is observable. The right hand side of Fig. 3.8 shows the resulting contour of the surface moving downwards into the substrate for a mask with a square opening.
Chemical wet etching used for removing masks and sacrificial layers is a common application of such an isotropic step which causes strong underetching and lateral broadening of the features. Due to the underetching wet etching is scarcely used for pattern transfer, where more directional dry etching processes are predominant.
The same algorithmic concept can be applied to isotropic deposition. For the explanation the deposition of material at a single surface site is considered. If a small particle of the deposited material is nucleated on the wafer surface it forms new deposition sites at its surface. If we assume that deposited particles only stick at the sites of this nucleus, a spherical bulb will be formed. In order to illustrate this effect, the left hand side of Fig. 3.9 shows the structuring element applied to a single surface cell. For the complete process step, we assume simultaneous nucleation at all surface sites. This means that the structuring element has to be applied at all surface positions including the surface of the resist mask. This is contrary to the etching process described above, where the application of structuring elements was restricted to the unprotected silicon surface, since only the etch rate of the silicon was assumed to be larger than zero. How the ensemble of all structuring elements finally forms the contour of the deposited film is shown on the right hand side of Fig. 3.9. The figure demonstrates, that an isotropic deposition process drastically reduces the width of the mask opening. This effect is used in order to fill vias and to form contact plugs to gates and doped regions in the silicon substrate, or to underlying metal lines, if the contact resides in the interconnect levels.
Next a case will be investigated, where the velocity of the surface movement depends on the growth or etching direction, but still is the same for all surface positions.
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