Gray-tone electron-beam lithography

1. A method of fabricating an optical device using electron-beam lithography, the method comprising:

receiving instructions for varying a characteristic of a beam of electrons as a function of displacement of a substrate in relation to the beam of electrons, wherein the function is a monotonic function;

generating the beam of electrons using an electron source;

securing the substrate to a platform;

controlling the platform to move in relation to the electron source;

varying the characteristic of the beam of electrons according to the function of displacement of the substrate in relation to the beam of electrons, wherein:

the optical device is configured to couple light out of a waveguide of an artificial-reality display; and

varying the beam of electrons comprises modifying the beam of electrons to expose one or more portions of a photoresist on the substrate; and

etching the substrate and/or the photoresist to form one or more elements in the substrate based on the one or more portions of the photoresist that are exposed, wherein the one or more elements include an element with varying height repeated in two dimensions.

2. The method of claim 1 , further comprising executing the instructions multiple times to expose a photoresist on the substrate to define an array of elements in the photoresist.

3. The method of claim 1 , wherein the characteristic of the beam of electrons comprises a dwell time of the beam of electrons, which changes a dose of electrons exposing a photoresist on the substrate.

4. The method of claim 1 , wherein:

the characteristic of the beam of electrons is a sequence of start times and stop times of the beam of electrons in relation to movement of the platform.

5. The method of claim 4 , wherein durations of intervals between start times and/or stop times of the sequence change while the platform maintains constant velocity.

6. The method of claim 4 , wherein the start times and/or stop times of the sequence have consistent intervals while the platform changes velocity.

7. The method of claim 1 , wherein the one or more elements include circles with varying diameters and varying blaze direction.

8. The method of claim 1 , wherein the one or more elements include grating ridges of varying heights and varying blaze angle.

9. The method of claim 1 , wherein:

the optical device is a grating, and

the grating is a chirped grating.

10. The method of claim 1 , wherein the characteristic of the beam of electrons is an intensity of the beam of electrons.

11. The method of claim 1 , wherein:

a writing field of the beam of electrons on the platform is defined by an area of the platform that can be exposed by the beam of electrons without field stitching, and

the writing field is equal to or greater than 0.36 square millimeters and equal to or less than 3600 square millimeters.

12. The method of claim 1 , wherein the characteristic of the beam of electrons is a width of the beam of electrons.

13. A system used in electron-beam lithography for fabricating an optical device, the system comprising:

an electron source, wherein the electron source produces a beam of electrons;

a platform configured to:

hold a substrate, and

move in relation to the electron source; and

a controller configured to:

control movement of the platform in relation to the electron source, and

vary a characteristic of the beam of electrons as a function of substrate displacement in relation to the beam of electrons, wherein:

the function is a monotonic function,

the optical device is configured to couple light out of a waveguide of an artificial-reality display, and

varying the beam of electrons is configured to expose one or more portions of a photoresist on the substrate so that one or more elements can be formed in the substrate based on the one or more portions of the photoresist that are exposed, and

the one or more elements include an element with varying height repeated in two dimensions.

14. The system as recited in claim 13 , further comprising a photoresist covering at least a portion of a surface of the substrate, wherein the beam of electrons forms a feature in the photoresist by exposing the photoresist.

15. The system as recited in claim 13 , wherein:

a writing field of the beam of electrons on the platform is defined by an area of the platform that can be exposed by the beam of electrons without field stitching, and

the writing field is equal to or greater than 0.36 square millimeters and equal to or less than 3600 square millimeters.

16. The system as recited in claim 13 , wherein movement of the platform in relation to the electron source is along only one axis of a three-dimensional coordinate system.

17. The system as recited in claim 13 , wherein movement of the platform in relation to the electron source is along two dimensions of a three-dimensional coordinate system.

18. The system as recited in claim 13 , wherein the characteristic of the beam of electrons comprises a width of the beam of electrons.

19. The system as recited in claim 13 , wherein:

the platform is configured to move in a first direction,

the electron source is configured to move the beam of electrons in a second direction, and

the characteristic of the beam of electrons is varied start times and/or stop times of the beam of electrons.

20. The system of claim 13 , wherein the one or more elements includes circles with varying blaze directions.