Method and system for constrained pixel graytones interpolation for pattern rasterization

• US 20060192789A1
• Filed: 02/28/2005
• Published: 08/31/2006
• Est. Priority Date: 02/28/2005
• Status: Active Grant

• Current Assignee: ASML Holding NV
• Original Assignee: ASML Holding NV
• Inventors: Baba-Ali, Nabila
• Granted Patent: US 7,286,137 B2
• Time in Patent Office: Days
• US Class Current: 345/606
• CPC Class Codes: G03F 7/70291 Addressable masks, e.g. spatial light modulators [SLMs], digital micro-mirror devices [DMDs] or liquid crystal display [LCD] patterning devices

Abstract

A method and system for preparing data to be used by a patterning device. The method including the following steps: a first set of graytones for a set of pixels is calculated, the first set of graytones corresponding to a center of a pattern being located at a first grid position, and a second set of graytones for the set of pixels is calculated, the second set of graytones corresponding to the center of the pattern being located at a second grid position. A plurality of sets of graytones for the set of pixels is linearly interpolated with constraints, from the first and second set of graytones, the plurality of sets of graytones corresponding to the pattern being shifted by a continuous shift-amount between the first grid position and the second grid position.

Claims

1. A rasterization method, comprising:

(a) calculating a first set of graytones for a set of pixels, the first set of graytones corresponding to a center of a pattern being located at a first grid position;

(b) calculating a second set of graytones for the set of pixels, the second set of graytones corresponding to the center of the pattern being located at a second grid position; and

(c) linearly interpolating with constraints, from the first and second set of graytones, a plurality of sets of graytones for the set of pixels, the plurality of sets of graytones corresponding to the pattern being shifted by a continuous shift-amount between the first grid position and the second grid position.

2. The method of claim 1, wherein the constraints of step (c) comprise:

setting a slope of each respective pixel in the set of pixels equal to one of zero and alpha, wherein alpha is equal to (1−

Att)/Wp, with Att being a maximum negative graytone amplitude and Wp being a width of each pixel in the set of pixels as projected on a target.

3. The method of claim 2, further comprising:

determining a first range of the shift-amounts and a second range of the shift-amounts for each respective pixel based on the first graytone of the respective pixel, alpha, and the second graytone in the second set of graytones corresponding to the respective pixel.

4. The method of claim 2, wherein the constraints of step (c) further comprise:

setting the slope of each respective pixel in the set of pixels equal to zero over a first range of the shift-amounts and alpha over a second range of the shift-amounts, if at least one of the following is true,

(i) a first graytone in the first set of graytones corresponding to the respective pixel is equal to one and a second graytone in the second set of graytones corresponding to the respective pixel is greater than (1−

Att)/2, and

(ii) the first graytone in the first set of graytones corresponding to the respective pixel is equal to Att and the second graytone in the second set of graytones corresponding to the respective pixel is less than (1−

Att)/2.

5. The method of claim 2, wherein the constraints of step (c) further comprise:

setting the slope of each respective pixel in the set of pixels equal to alpha over the first range of the shift-amounts and zero over the second range of the shift-amounts, if at least one of the following is true,

(i) the first graytone in the first set of graytones corresponding to the respective pixel is equal to one and the second graytone in the second set of graytones corresponding to the respective pixel is less than (1−

Att)/2,

(ii) the first graytone in the first set of graytones corresponding to the respective pixel is equal to Att and the second graytone in the second set of graytones corresponding to the respective pixel is greater than (1−

Att)/2, and

(iii) the first graytone in the first set of graytones corresponding to the respective pixel is different than one of one and Att.

6. The method of claim 1, further comprising:

(d) generating control signals based on at least one of the first set of graytones, the second set of graytones, and the plurality of sets of graytones, the control signals being used to control an actuation device.

7. The method of claim 6, wherein step (d) comprises:

using the control signals to control at least one of a tilt angle, a phase angle, and a voltage.

8. The method of claim 6, wherein step (d) further comprises:

actuating one of tilting mirrors, phase-tilting mirrors, pistoning mirrors, and grating light valves using the actuation device.

9. A system, comprising:

a computing module that computes a first and second set of graytones for a set of pixels, the first and second set of graytones corresponding to a center of a pattern being located at a first and second grid position, respectively; and

an interpolator that linearly interpolates with constraints, from the first and second set of graytones, a plurality of sets of graytones for the set of pixels, the plurality of sets of graytones corresponding to the pattern being shifted by a continuous shift-amount between the first grid position and the second grid position.

10. The system of claim 9, wherein the interpolator linearly interpolates with constraints a plurality of sets of graytones for the set of pixels, the constraints comprising:

a slope of each respective pixel in the set of pixels is set equal to one of zero and alpha, wherein alpha is equal to (1−

Att)/Wp, with Att being a maximum negative amplitude and Wp being a width of each pixel in the set of pixels as projected on a target.

11. The system of claim 10, wherein the interpolator determines a first range of the shift-amounts and a second range of the shift-amounts for each respective pixel based on the first graytone of the respective pixel, alpha, and the second graytone in the second set of graytones corresponding to the respective pixel.

12. The system of claim 10, wherein the interpolator linearly interpolates with constraints a plurality of sets of graytones for the set of pixels, the constraints further comprising:

the slope of each respective pixel in the set of pixels is set equal to zero over a first range of the shift-amounts and alpha over a second range of the shift-amounts, if at least one of the following is true,

(i) a first graytone in the first set of graytones corresponding to the respective pixel is equal to one and a second graytone in the second set of graytones corresponding to the respective pixel is greater than (1−

Att)/2, and

(ii) the first graytone in the first set of graytones corresponding to the respective pixel is equal to Att and the second graytone in the second set of graytones corresponding to the respective pixel is less than (1−

Att)/2.

13. The system of claim 10, wherein the interpolator linearly interpolates with constraints a plurality of sets of graytones for the set of pixels, the constraints further comprising:

the slope of each respective pixel in the set of pixels is set equal to alpha over the first range of the shift-amounts and zero over the second range of the shift-amounts, if at least one of the following is true,

(i) the first graytone in the first set of graytones corresponding to the respective pixel is equal to one and the second graytone in the second set of graytones corresponding to the respective pixel is less than (1−

Att)/2,

(ii) the first graytone in the first set of graytones corresponding to the respective pixel is equal to Att and the second graytone in the second set of graytones corresponding to the respective pixel is greater than (1−

Att)/2, and

(iii) the first graytone in the first set of graytones corresponding to the respective pixel is different than one of one and Att.

14. The system of claim 9, further comprising:

a converter that converts at least one of the first set of graytones, the second set of graytones, and the plurality of sets of graytones into control signals that are used to actuate an actuation device.

15. The system of claim 14, wherein the control signals control at least one of a tilt angle, a phase angle, and a voltage.

16. The system of claim 14, further comprising:

an illumination system that supplies a beam of radiation;

a pattern generator that includes an array of individually controllable elements that are controlled using the actuation device, the pattern generator patterning the beam of radiation; and

a projector that projects the patterned beam onto a target portion of an object.

17. The system of claim 16, wherein the object is one of a semiconductor wafer, a flat panel display glass substrate, or a display of a projection device.

18. The system of claim 16, wherein the pattern generator comprises one of tilting mirrors, phase-tilting mirrors, pistoning mirrors, and grating light valves.