Lithographic apparatus and device manufacturing method

1. A lithographic apparatus comprising:

an illumination system configured to condition a radiation beam;

a support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam;

a substrate table constructed to hold a substrate;

a projection system configured to project the patterned radiation beam onto a target portion of the substrate; and

a control system configured to at least:

obtain a density distribution of the pattern,

receive radiation data characterizing the radiation beam,

receive measurement data representative of a temperature of the patterning device and set a parameter of a thermo-mechanical model of the patterning device based on the measurement data, the thermo-mechanical model further comprising one or more variables in addition to the parameter and the thermo-mechanical model comprising a three-dimensional finite element model of the patterning device,

determine a spatial distribution of dissipation of the pattern based on the radiation data and the density distribution of the pattern,

determine a deformation of the pattern by applying the dissipation distribution in the thermo-mechanical model of the patterning device, and

determine a control signal to control a component of the lithographic apparatus based on the deformation of the pattern.

2. The apparatus of claim 1 , wherein the control system is configured to determine an optical control signal, as the control signal, to adjust a setting of the illumination system or the projection system, based on the deformation of the pattern.

3. The apparatus of claim 1 , wherein the control system is configured to determine a position control signal, as the control signal, to control a position of the substrate table relative to the support, based on the deformation of the pattern.

4. The apparatus of claim 1 , further comprising an image sensor configured to capture an image of the pattern and wherein the control system is configured to receive the image as pattern data and determine the density distribution of the pattern based on the pattern data.

5. The apparatus of claim 1 , wherein the radiation data comprises radiation beam intensity, radiation beam power, radiation beam duty cycle, or any combination selected from the foregoing.

6. The apparatus of claim 1 , further comprising a temperature sensor configured to provide the measurement data.

7. The apparatus of claim 6 , wherein the temperature sensor comprises an array of infrared temperature sensors, configured to measure a temperature of a surface of the patterning device and provide the measurements of the temperature of the surface to the control system as the measurement data.

8. The apparatus of claim 7 , wherein the array of infrared temperature sensors is configured to measure a temperature of a front surface of the patterning device, the pattern being provided on a back surface of the patterning device opposing the front surface.

9. A method of controlling a lithographic apparatus, the method comprising:

obtaining a density distribution of a pattern on a patterning device for use in the lithographic apparatus;

receiving radiation data characterizing a radiation beam to be applied by the lithographic apparatus;

receiving measurement data representative of a temperature of the patterning device and setting a parameter of a thermo-mechanical model of the patterning device based on the measurement data, the thermo-mechanical model further comprising one or more variables in addition to the parameter and wherein the thermo-mechanical model comprises a three-dimensional finite element model of the patterning device;

determining a spatial distribution of dissipation of the pattern based on the density distribution of the pattern and the received radiation data;

determining a deformation of the pattern by applying the dissipation distribution in the thermo-mechanical model of the patterning device; and

determining a control signal to control a component of the lithographic apparatus based on the deformation of the pattern.

10. A device manufacturing method comprising projecting, using a lithographic apparatus, a patterned beam of radiation onto a substrate, wherein projecting the patterned beam of radiation is preceded by controlling the apparatus in accordance with claim 9 .

11. A computer program product comprising a set of computer readable instructions stored on a non-transitory computer readable medium, the set of instructions configured to, when run on a computer system, enable the computer system to at least:

obtain a density distribution of the pattern of a pattern on a patterning device for use in a lithographic apparatus;

receive radiation data characterizing a radiation beam to be applied by the lithographic apparatus;

receive measurement data representative of a temperature of the patterning device and set a parameter of a thermo-mechanical model of the patterning device based on the measurement data, the thermo-mechanical model further comprising one or more variables in addition to the parameter and the thermo-mechanical model comprising a three-dimensional finite element model of the patterning device;

determine a spatial distribution of dissipation of the pattern based on the density distribution of the pattern and the received radiation data;

determine a deformation of the pattern by applying the dissipation distribution in the thermo-mechanical model of the patterning device; and

determine a control signal to control a component of the lithographic apparatus based on the deformation of the pattern.

12. The computer program product of claim 11 , wherein the instructions are configured to determine an optical control signal, as the control signal, to adjust a setting of an illumination system of the lithographic apparatus or of a projection system of the lithographic apparatus, based on the deformation of the pattern.

13. The computer program product of claim 11 , wherein the instructions are configured to determine a position control signal, as the control signal, to control a position of a substrate table of the lithographic apparatus, based on the deformation of the pattern.

14. The computer program product of claim 11 , wherein the radiation data comprises radiation beam intensity, radiation beam power, radiation beam duty cycle, or any combination selected from the foregoing.

15. A computer program product comprising a set of computer readable instructions stored on a non-transitory computer readable medium, the set of instructions configured to, when run on a computer system, enable the computer system to at least:

obtain a density distribution of a pattern on a patterning device for use in a lithographic apparatus;

receive radiation data characterizing a radiation beam to be applied by the lithographic apparatus;

determine a spatial distribution of dissipation of the pattern based on the density distribution of the pattern and the received radiation data;

determine a deformation of the pattern by applying the dissipation distribution as in a thermo-mechanical model of the patterning device, wherein the thermo-mechanical model is configured to determine deformation in each of at least three orthogonal dimensions; and

determine a control signal to control a component of the lithographic apparatus based on the deformation of the pattern.

16. The computer program product of claim 15 , wherein the instructions are further configured to cause the computer system to:

receive measurement data representative of a temperature of the patterning device, and

set a parameter of a thermo-mechanical model of the patterning device based on the measurement data.

17. The computer program product of claim 15 , wherein the instructions are configured to determine a position control signal, as the control signal, to control a position of a table of the lithographic apparatus, based on the deformation of the pattern.