Triangle and tetrahedron mesh generation method

Claim 1

A method for analyzing a semiconductor device, the method comprising steps of; receiving as an input a digital representation of the semiconductor device; generating a triangular mesh from the digital representation of the semiconductor device, the triangular mesh satisfying a condition of Delaunay partition; searching for triangles which are included in the triangle mesh and intersect a substance boundary, the substance boundary representing an interface between areas in the semiconductor device; selecting one of the vertices of any of the triangles intersecting with the substance boundary as a moving node, one of the vertices not being on the substance boundary, and projecting the moving node on the substance boundary to obtain a projected point; listing triangles which commonly have the moving node as processing object triangles and listing those triangles which are positioned around the processing object triangles as peripheral triangles; and checking to detect whether or not the projected point is included in a circumscribed circle about any of the peripheral triangles and, when the projected point is included in a circumscribed circle, adding a node at the projected point and producing triangles using the node, but when the projected point is not included in a circumscribed circle about any one of the peripheral triangles, deleting all of the processing object triangles, shifting the moving node to the projected point and re-constructing triangles in a region, from which the processing object triangles have been removed, using a maximum included angle method.

Claim 2

A method for analyzing a semiconductor device, the method comprising steps of; receiving as an input a digital representation of the semiconductor device; generating a triangular mesh from the digital representation of the semiconductor device, the triangular mesh satisfying a condition of Delaunay partition; searching for triangles which are included in the triangle mesh and intersect a substance boundary, the substance boundary representing an interface between areas in the semiconductor device; selecting one of the vertices of any of the triangles intersecting with the substance boundary as a moving node, one of the vertices not being on the substance boundary, and projecting the moving node on the substance boundary to obtain a projected point; listing triangles which commonly have the moving node as processing object triangles and listing those triangles which are positioned around the processing object triangles as peripheral triangles; and checking to detect whether or not the projected point is included in a circumscribed circle about any of the peripheral triangles and, when the projected point is included in a circumscribed circle, adding a node at the projected point and producing triangles using the node, but when the projected point is not included in a circumscribed circle about any one of the peripheral triangles, deleting all of the processing object triangles, shifting the moving node to the projected point and re-constructing triangles in a region, from which the processing object triangles have been removed, using a maximum included angle method.

Claim 6

A method for analyzing a semiconductor device, the method comprising steps of: receiving as an input a digital representation of the semiconductor device; generating a tetrahedral mesh from the digital representation of the semiconductor device, the tetrahedral mesh satisfying a condition of Delaunay partition; searching for tetrahedra which are included in the tetrahedron mesh and intersect with a substance boundary the substance boundary representing an interface between areas in the semiconductor device; selecting one of the vertices of any of the tetrahedra intersecting with the substance boundary as a moving node, one of the vertices not being on the substance boundary, and projecting the moving node on the substance boundary to obtain a projected point; listing tetrahedra which commonly have the moving node as processing object tetrahedra and listing tetrahedra which are positioned around the processing object tetrahedra as peripheral tetrahedra; and checking to detect whether or not the projected point is included in a circumscribed sphere about any of the peripheral tetrahedra and, when the projected point is included in a circumscribed sphere, adding a node at the projected point and producing tetrahedra using the node, but when the projected point is not included in a circumscribed sphere about any one of the peripheral tetrahedra, deleting all of the processing object tetrahedra, shifting the moving node to the projected point and re-constructing tetrahedra in a region, from which the processing object tetrahedra have been removed, using a minimum circumscribed circle method.

Claim 7

A method for analyzing a semiconductor device, the method comprising steps of: receiving as an input a digital representation of the semiconductor device; generating a tetrahedral mesh from the digital representation of the semiconductor device, the tetrahedral mesh satisfying a condition of Delaunay partition; searching for tetrahedra which are included in the tetrahedron mesh and intersect with a substance boundary the substance boundary representing an interface between areas in the semiconductor device; selecting one of the vertices of any of the tetrahedra intersecting with the substance boundary as a moving node, one of the vertices not being on the substance boundary, and projecting the moving node on the substance boundary to obtain a projected point; listing tetrahedra which commonly have the moving node as processing object tetrahedra and listing tetrahedra which are positioned around the processing object tetrahedra as peripheral tetrahedra; and checking to detect whether or not the projected point is included in a circumscribed sphere about any of the peripheral tetrahedra and, when the projected point is included in a circumscribed sphere, adding a node at the projected point and producing tetrahedra using the node, but when the projected point is not included in a circumscribed sphere about any one of the peripheral tetrahedra, deleting all of the processing object tetrahedra, shifting the moving node to the projected point and re-constructing tetrahedra in a region, from which the processing object tetrahedra have been removed, using a minimum circumscribed circle method.