Method of performing dose modulation, in particular for electron beam lithography

1. A method for transferring a pattern onto a substrate by direct writing by means of a particle or photon beam, the method comprising:

a step of producing a dose map, associating a dose to each of a plurality of elementary shapes of said pattern; and

a step of exposing the substrate according to the pattern with a spatially-dependent emitted dose depending on said dose map;

wherein said step of producing a dose map includes:

computing at least a first and a second metrics of the pattern for each of said elementary shapes, said first metric being representative of features of the pattern within a first range from the elementary shape and said second metric being representative of features of the pattern within a second range, larger than the first range, from the elementary shape, wherein said first metric is a critical dimension of the pattern and said second metric is a pattern density;

computing the critical dimension from an overlap factor between the pattern and a disk centered on geometrical center of the elementary shape, a diameter of the disk being such that it partially extends beyond an edge of the pattern; and

determining the emitted dose associated to each of said elementary shapes of the pattern as a function of said metrics.

2. The method according to claim 1 wherein the disk is the smallest of a predetermined finite set of disks centered on the geometrical center of the elementary shape to partially extend beyond said edge of the pattern.

3. The method according to claim 1 comprising computing the density value of each elementary shape by convolving the pattern with a point spread function of the particle or photon beam.

4. The method according to claim 1 wherein the first metric is a density value computed by convolving the pattern with a point spread function of the particle or photon beam characterized by a first radius and the second metric is a density value computed by convolving the pattern with a point spread function of the particle or photon beam characterized by a second radius, larger than the first radius.

5. The method according to claim 1 wherein said step of exposing the substrate is performed by projecting shaped particle or photon shots onto said substrate, each shot corresponding to an elementary shape of the pattern, and wherein said dose map associates a dose to each of said shots.

6. The method according to claim 1 wherein said step of determining the emitted dose associated to each of said elementary shapes of the pattern as a function of said metrics is carried out by using a pre-computed look-up table.

7. The method according to claim 6 wherein said step of producing a dose map includes directly reading the dose associated to each of said elementary shapes from the look-up table.

8. The method according to claim 6 wherein said step of producing a dose map includes obtaining the dose associated to each of said elementary shapes by interpolating between two values read from the look-up table.

9. The method according to claim 1 further comprising a preliminary calibration step of determining a relation between said metrics and an emitted dose by using numerical simulations or experimental tests to find optimal doses for a plurality of reference patterns, each being representative of a different set of values of said metrics, according to a predetermined optimality criterion.

10. The method according to claim 9 wherein at least some of said reference patterns include a one- or two-dimensional grating.

11. The method according to claim 9 wherein said optimal criterion consists in maximizing similarity between the reference pattern and the corresponding pattern transferred onto the substrate.

12. The method according to claim 1 wherein said beam is an electron beam.

13. The method according to claim 1 further comprising:

before said exposing the substrate, a step of depositing a resist layer on it; and

after said exposing the substrate, a step of developing the resist layer.

14. A computer program product comprising:

computer-executable code for causing a computer to produce a dose map, associating an emitted dose to each of a plurality of elementary shapes of a pattern to be transferred onto a substrate by direct writing by means of a particle or photon beam, by: computing at least a first and a second metrics of the pattern for each of said elementary shapes, said first metric being representative of features of the pattern within a first range from the elementary shape and said second metric being representative of features of the pattern within a second range, larger than the first range, from the elementary shape, wherein said first metric is a critical dimension of the pattern and said second metric is a pattern density; computing the critical dimension from an overlap factor between the pattern and a disk centered on geometrical center of the elementary shape, a diameter of the disk being such that it partially extends beyond an edge of the pattern; and determining the emitted dose associated to each of said elementary shapes of the pattern as a function of said metrics.

15. The computer program product according to claim 14 , further comprising computer-executable code for causing a computer to determine a relation between said metrics and an emitted dose by using numerical simulations or experimental tests to find optimal doses for a plurality of reference patterns, each being representative of a different set of values of said metrics, according to a predetermined optimality criterion.

16. A computer program product comprising computer-executable code for causing a computer to produce a dose map, associating an emitted dose to each of a plurality of elementary shapes of a pattern to be transferred onto a substrate by direct writing by means of a particle or photon beam, by computing at least two metrics for each of said elementary shapes of the pattern, and determining the emitted dose associated to each of said elementary shapes of the pattern as a function of said metrics, further comprising computer-executable code for carrying out a method according to claim 1 by causing a computer to drive a source of said particle or photon beam in order to expose said substrate according to said pattern with a spatially-dependent dose depending on said dose map.