1. A laser processing method comprising:
irradiating an object which is fixed on a flexible sheet to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance, along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction, to form first modified regions at least within the object along the first line along which the object is intended to be cut serially, and irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second modified regions at least within the object along the second lines serially, each of the first and second modified regions having a maximum length in a thickness direction of the object, a length of each of the first modified regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut, and a length of each of the second modified regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through the flexible sheet to divide the object into a plurality of chips along the first and second lines by functioning the first and second modified regions as starting points for cutting the object.
2. The method according to claim 1, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
3. A method of manufacturing a semiconductor device formed using a laser processing method, the manufacturing method comprising:
irradiating an object which is fixed on a flexible sheet to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from surfaces of the object by a predetermined distance along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction, to form first modified regions at least within the object along the first line along which the object is intended to be cut, and irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from the surface of the object by a predetermined distance along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second modified regions at least within the object along the second lines, serially, each of the first and second modified regions having a maximum length in a thickness direction of the object, a length of each of the first modified regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first modified region in a direction parallel to the surfaces of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut, and a length of each of the second modified regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second modified region in a direction parallel to the surfaces of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through the flexible sheet to divide the object into a plurality of chips along the first and second lines by functioning the first and second modified regions as starting points for cutting the object, with such cutting thereby providing at least one manufactured semiconductor device.
4. The method according to claim 3, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
5. A laser processing method comprising:
irradiating an object having a wafer like shape, in which a plurality of electric devices are formed on a front surface of the object, to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from the front surface of the object by a predetermined distance and such that the laser light passes through an area which is located between the electronic devices, along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction and passes through the areas between the electronic devices, to form first molten processed regions at least within the object along the first line along which the object is intended to be cut, serially, and irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from the front surface of the object by a predetermined distance and such that the laser light passes through an area which is located between the electronic devices, along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second molten processed regions at least within the object along the second lines, serially, each of the first and second molten processed regions having a maximum length in a thickness direction of the object, a length of each of the first molten processed regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first molten processed region in a direction parallel to the front surface of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut, and a length of each of the second molten processed regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second molten processed region in a direction parallel to the front surface of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through a flexible sheet which is attached to a back surface of the object, to divide the object into a plurality of chips each of which has an electronic device, along the first and second lines by functioning the first and second molten processed regions as starting points for cutting the object.
6. The method according to claim 5, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
7. A method of manufacturing a semiconductor device formed using a laser processing method, the manufacturing method comprising a step of:
irradiating an object having a wafer-like shape, in which a plurality of electric devices are formed on a front surface of the object, to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from the front surface of the object by a predetermined distance and such that the laser light passes through an area which is located between the electronic devices, along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction and passes through the areas between the electronic devices, to form first molten processed regions at least within the object along the first line along which the object is intended to be cut by a predetermined distance from the surface of the object, serially, and irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from the front surface of the object by a predetermined distance and such that the laser light passes through a area which is located between the electronic devices, along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second molten processed regions at least within the object along the second lines, serially, each of the first and second molten processed regions having a maximum length in a thickness direction of the object, a length of each of the first molten processed regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first molten processed region in a direction parallel to the surface of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut, and a length of each of the second molten processed regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second molten processed region in a direction parallel to the surface of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through a flexible sheet which is attached to a back surface of the object, to divide the object into a plurality of chips each of which has an electronic device, along the first and second lines by functioning the first and second molten processed regions as starting points for cutting the object, with such cutting thereby providing at least one manufactured semiconductor device having the electronic device.
8. The method according to claim 7, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
9. A laser processing method comprising:
irradiating an object which is fixed on a flexible sheet to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance, along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction, to form first modified regions at least within the object along the first line along which the object is intended to be cut, serially, each of the first modified regions having a maximum length in a thickness direction of the object, and a length of each of the first modified regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut;
irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second modified regions at least within the object along the second lines, serially, each of the second modified regions having a maximum length in a thickness direction of the object, and a length of each of the second modified regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through the flexible sheet to expand the distance between parts of the object surrounding by the first and second lines and adjacent to each other.
10. The method according to claim 9, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
11. A method of manufacturing a semiconductor device formed using a laser processing method, the manufacturing method comprising:
irradiating an object which is fixed on a flexible sheet to be processed with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance, along each of a plurality of first lines along which the object is intended to be cut and extends along a first direction, to form first modified regions at least within the object along the first line along which the object is intended to be cut, serially, each of the first modified regions having a maximum length in a thickness direction of the object, and a length of each of the first modified regions in a direction along the first line along which the object is intended to be cut being larger than a length of the first modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the first line along which the object is intended to be cut;
irradiating the object with laser light such that a light converging point of the laser light is located at a position located within the object and spaced from a surface of the object by a predetermined distance along each of a plurality of second lines along which the object is intended to be cut and extend along a second direction crossing the first direction, to form second modified regions at least within the object along the second lines, serially, each of the second modified regions having a maximum length in a thickness direction of the object, and a length of each of the second modified regions in a direction along the second line along which the object is intended to be cut being larger than a length of the second modified region in a direction parallel to the surface of the object and perpendicular to the direction extending along the second line along which the object is intended to be cut; and
applying a stress to the object through the flexible sheet to expand the distance between parts of the object surrounding by the first and second lines and adjacent to each other, with such cuffing thereby providing at least one manufactured semiconductor device having the electronic device.
12. The method according to claim 11, wherein the laser light is a pulsed laser and is irradiated under a condition with a peak power density of at least 1\xd7108(Wcm2) at the light-converging point.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A computer-implemented method comprising:
determining, using one or more computing devices, a set of first nodes in a social graph of a social network, the first nodes representing users of the social network;
generating, using the one or more computing devices, a neighbor list including sets of neighboring nodes for each of the first nodes;
transforming, using the one or more computing devices, the neighbor list to identify trivial neighboring nodes and non-trivial neighboring nodes;
comparing, using the one or more computing devices, the first nodes that are associated with each of the non-trivial neighboring nodes to produce a similarity matrix; and
clustering, using the one or more computing devices, similar nodes from set of first nodes using the similarity matrix.
2. The computer-implemented method of claim 1, wherein the trivial neighboring nodes are associated with a single node from among the set of first nodes and the non-trivial neighboring nodes are associated with two or more nodes from among the set of first nodes.
3. The computer-implemented method of claim 1, wherein transforming the neighbor list includes transforming the sets of neighboring nodes into sets that are indexed by neighboring node and that include the first nodes that the neighboring node corresponds to.
4. The computer-implemented method of claim 1, wherein transforming the neighbor list includes converting the neighbor list into an inverted index.
5. The computer-implemented method of claim 1, wherein comparing the first nodes that are associated with each of the non-trivial neighboring nodes to produce the similarity matrix includes determining a number of intersecting first nodes between the sets of neighboring nodes.
6. The computer-implemented method of claim 1, wherein clustering the similar nodes from the set of first nodes using the similarity matrix includes processing the similarity matrix to cluster the first nodes into clusters based on a predetermined similarity metric.
7. The computer-implemented method of claim 6, further comprising merging two or more of the clusters based on a predetermined cluster-to-cluster level of similarity.
8. A computer program product comprising a non-transitory computer-readable medium storing a computer-readable program, wherein the computer-readable program, when executed on a computer, causes the computer to perform operations comprising:
determining a set of first nodes in a social graph of a social network, the first nodes representing users of the social network;
generating a neighbor list including sets of neighboring nodes for each of the first nodes;
transforming the neighbor list to identify trivial neighboring nodes and non-trivial neighboring nodes;
comparing the first nodes that are associated with each of the non-trivial neighboring nodes to produce a similarity matrix; and
clustering similar nodes from set of first nodes using the similarity matrix.
9. The computer program product of claim 8, wherein the trivial neighboring nodes are associated with a single node from among the set of first nodes and the non-trivial neighboring nodes are associated with two or more nodes from among the set of first nodes.
10. The computer program product of claim 8, wherein transforming the neighbor list includes transforming the sets of neighboring nodes into sets that are indexed by neighboring node and that include the first nodes that the neighboring node corresponds to.
11. The computer program product of claim 8, wherein transforming the neighbor list includes converting the neighbor list into an inverted index.
12. The computer program product of claim 8, wherein comparing the first nodes that are associated with each of the non-trivial neighboring nodes to produce the similarity matrix includes determining a number of intersecting first nodes between the sets of neighboring nodes.
13. The computer program product of claim 8, wherein clustering the similar nodes from the set of first nodes using the similarity matrix includes processing the similarity matrix to cluster the first nodes into clusters based on a predetermined similarity metric.
14. The computer program product of claim 8, wherein the computer-readable program, when executed on a computer, further causes the computer to perform operations of:
merging two or more of the clusters based on a predetermined cluster-to-cluster level of similarity.
15. A system comprising:
one or more processors;
one or more memories storing instructions that, when executed by the one or more processors, cause the system to perform operations including:
determining a set of first nodes in a social graph of a social network, the first nodes representing users of the social network;
generating a neighbor list including sets of neighboring nodes for each of the first nodes;
transforming the neighbor list to identify trivial neighboring nodes and non-trivial neighboring nodes;
comparing the first nodes that are associated with each of the non-trivial neighboring nodes to produce a similarity matrix; and
clustering similar nodes from set of first nodes using the similarity.
16. The system of claim 15, wherein the trivial neighboring nodes are associated with a single node from among the set of first nodes and the non-trivial neighboring nodes are associated with two or more nodes from among the set of first nodes.
17. The system of claim 15, wherein transforming the neighbor list includes transforming the sets of neighboring nodes into sets that are indexed by neighboring node and that include the first nodes that the neighboring node corresponds to.
18. The system of claim 15, wherein transforming the neighbor list includes converting the neighbor list into an inverted index.
19. The system of claim 15, wherein comparing the first nodes that are associated with each of the non-trivial neighboring nodes to produce the similarity matrix includes determining a number of intersecting first nodes between the sets of neighboring nodes.
20. The system of claim 15, wherein clustering the similar nodes from the set of first nodes using the similarity matrix includes processing the similarity matrix to cluster the first nodes into clusters based on a predetermined similarity metric.
21. The system of claim 15, wherein the instructions, when executed by the one or more processors, further cause the system to perform operations including:
merging two or more of the clusters based on a predetermined cluster-to-cluster level of similarity.