Methods and apparatus for cutting a substrate

1. A method of cutting a substrate, comprising:

forming a plurality of recesses in a surface of the substrate by laser ablation; and

applying a stress to the substrate that is concentrated by the recesses to promote cutting along a cutting line via propagation of a crack through the plurality of recesses,

wherein the recess shape, defined by a boundary line of an opening of the recess at the surface of the substrate, of each of one or more of the recesses is non-circular, such that a radius of curvature of the boundary line varies along the boundary line, and the recess shape further has plural tip regions, each tip region being defined as a local minimum in the radius of curvature of the boundary line at the surface of the substrate, and

wherein the laser ablation is performed with a laser fluence controlled so that no molten flow of substrate material occurs in the tip regions.

2. The method of claim 1 , wherein the recesses are distributed non-uniformly along the cutting line.

3. The method of claim 2 , wherein the recesses are closer together in regions where deviation of a crack away from the cutting line would otherwise be more likely than in other regions.

4. The method of claim 2 , wherein:

the cutting line comprises a first portion and a second portion;

an average radius of curvature per unit length is lower in the first portion than in the second portion;

the recesses are closer together on average in the first portion than in the second portion.

5. The method of claim 2 , wherein:

the cutting line comprises a first portion and a second portion;

an average stress concentration per unit length caused by one or more structures in the substrate that do not intersect with the first portion or the second portion is higher in the first portion than in the second portion; and

the recesses are closer together on average in the first portion than in the second portion.

6. The method of claim 1 , wherein the laser is configured to form each recess by ablation using a laser beam having the same shape as the recess.

7. The method of claim 1 , wherein a smallest rectangular bounding box containing each of one or more of the recesses has an aspect ratio of 3 or more.

8. The method of claim 1 , wherein each of one or more of the recesses is elliptical.

9. The method of claim 1 , wherein two or more of the plurality of tip regions in each of one or more of the recesses lie on a straight line which is parallel or identical to a portion of the cutting line passing through the recess.

10. The method of claim 1 , wherein two or more of the plurality of tip regions in each of one or more of the recesses are configured to promote crack propagation in two or more respective non-parallel directions.

11. The method of claim 10 , wherein three or more of the cutting lines meet at the recess through a corresponding three or more of the tip regions.

12. The method of claim 1 , wherein the cutting line comprises a curved portion.

13. The method of claim 1 , wherein the forming of the plurality of recesses comprises forming at least one recess by simultaneously irradiating a portion of the substrate where the recess is to be formed with a plurality of laser beam spots, the plurality of laser beam spots comprising an ablation spot providing a fluence that is above a laser ablation threshold of the substrate and one or more further beam spots which each provide a fluence that is lower than the laser ablation threshold of the substrate, the one or more further beam spots being configured to reduce tensile stresses imparted by the ablation spot in at least a portion of the recess being formed by the ablation spot.

14. The method of claim 1 , wherein:

the laser is scanned over the substrate to produce the plurality of recesses; and

the orientation of a laser spot formed by the laser is changed as a function of position when the laser is scanned over the substrate along a curved path, thereby changing the orientation of recesses formed by the laser spot in correspondence with the curved path, wherein, optionally, the orientation of the laser spot is changed using a spatial light modulator, the spatial light modulator optionally comprising a micro-mirror array or deformable mirror.

15. The method of claim 1 , wherein the stress is applied mechanically, by bending the substrate, by driving a rigid member against a localised region of the sheet, or by the laser ablation.

16. The method of claim 1 , wherein the stress is applied by generating a mechanical resonance in the substrate, the mechanical resonance being optionally generated using periodically switched air jets, by applying acoustic waves to the substrate, or by actuating one or more electrically actuatable elements in contact with the substrate, each electrically actuatable element applying a periodic force to the substrate on actuation.

17. The method of claim 1 , wherein:

the stress is applied thermally; and either:

the substrate is mounted on or attached to an element and the element is heated, thermal expansion of the element applying the stress to the recesses; or

the stress is applied to each of one or more of the recesses by applying a laser spot on each side of the cutting line and scanning the laser spots parallel to the cutting line, thermal contraction in wakes of the laser spots applying the stress to the recesses.

18. The method of claim 1 , wherein the cutting line extends along said substrate surface and the concentration of the stress by the recesses is directed at least along the cutting line, thereby promoting cutting along the cutting line via propagation of a crack in the direction of the cutting line through the plurality of recesses.