Methods for controlling lithographic apparatus, lithographic apparatus and device manufacturing method

1. A method comprising:

obtaining a height map representing a topographical variation across a substrate; and

using the height map to control a positioning system of a lithographic apparatus for applying a product pattern at multiple locations across the substrate, wherein using the height map comprises:

decomposing the height map into a plurality of components, including a first height map component representing topographical variations associated with a device pattern and a second height map component representing other topographical variations;

using each of the first and second height map components, calculating control set-points according to a control algorithm specific to each of the first and second height map components;

combining the control set-points calculated for the first height map component and the second height map component; and

using the combined set-points to control the positioning system to apply the product pattern to the substrate.

2. The method as claimed in claim 1 , wherein the decomposing the height map comprises calculating the first component of the height map based on an average field topography and subtracting the first component from the height map to obtain the second height map component.

3. The method as claimed in claim 1 , wherein in the calculating control set-points an algorithm specific to the first height map component is less responsive to short-range topographic variations than an algorithm specific to the second height map component.

4. The method as claimed in claim 1 , wherein in the calculating control set-points one or more of the algorithms specific to the different height map components have nonlinearity, while the combining of the control set-points is performed linearly.

5. The method as claimed in claim 1 , wherein the lithographic apparatus is of a scanning type and wherein the algorithm specific to the first height map component is permitted to consider values from a different sized portion of a field than an algorithm specific to the second height map component.

6. The method as claimed in claim 1 , wherein the calculating a control set-point for at least one of the height map components includes using the height map data to generate additional height map data by extrapolation, and wherein the height map data used for extrapolation excludes the first height map component so that the extrapolated height map data is insensitive to topographical variations associated with the device pattern.

7. An apparatus comprising a data processing apparatus programmed to at least:

receive a height map of a substrate that has been subjected to lithographic processing;

decompose the height map into a plurality of components, including a first height map component representing topographical variations associated with a device pattern and a second height map component representing other topographical variations;

using each of the first and second height map components, calculate control set-points according to a control algorithm specific to each of the first and second height map components;

combine the control set-points calculated for the first height map component and the second height map component; and

provide a set-point, based on the combination of the control set-points, to control a positioning system of a lithographic apparatus configured to apply a product pattern at multiple substrate locations.

8. The apparatus as claimed in claim 7 , wherein, to decompose the height map, the data processing apparatus is arranged to calculate the first component of the height map based on an average field topography and to subtract the first component from the height map to obtain the second height map component.

9. The apparatus as claimed in claim 7 , wherein an algorithm specific to the first height map component is less responsive to short-range topographic variations than an algorithm specific to the second height map component.

10. The apparatus as claimed in claim 7 , wherein one or more of the algorithms specific to the different height map components have nonlinearity, while the combination of the control set-points is performed linearly.

11. The apparatus as claimed in claim 7 , wherein the lithographic apparatus is of a scanning type and wherein the algorithm specific to the first height map component is permitted to consider values from a different sized portion of a field than the algorithm specific to the second height map component.

12. The apparatus as claimed in claim 7 , wherein the calculation of a control set-point for at least one of the height map components includes using the height map data to generate additional height map data by extrapolation, and wherein the height map data used for extrapolation excludes the first height map component, so that the extrapolated height map data is insensitive to topographical variations associated with the device pattern.

13. A method comprising:

obtaining a height map representing a topographical variation across a substrate; and

using the height map to control a positioning system of a lithographic apparatus for applying a product pattern at multiple locations across the substrate, wherein using the height map comprises:

subtracting from the height map a first height map component representing topographical variations associated with a device pattern so as to obtain a second height map component representing other topographical variations;

using the obtained second height map component, calculating control set-points according to a control algorithm specific to the other topographical variations; and

using the calculated set-points to control the positioning system to apply the product pattern to the substrate.

14. An apparatus comprising a data processing apparatus programmed to at least:

receive a height map of a substrate that has been subjected to lithographic processing;

subtract from the height map a first height map component representing topographical variations associated with a device pattern so as to obtain a second height map component representing other topographical variations;

using the obtained second height map component, calculate control set-points according to a control algorithm specific to the other topographical variations;

combine the control set-points calculated for the first height map component and the second height map component; and

provide a set-point, based on the combination of the control set-points, to control a positioning system of a lithographic apparatus configured to apply a product pattern at multiple substrate locations.

15. A non-transitory computer program product comprising machine readable instructions therein that, when executed, are configured to cause a general purpose data processing apparatus to at least:

obtain a height map representing a topographical variation across a substrate; and

use the height map to control a positioning system of a lithographic apparatus for applying a product pattern at multiple locations across the substrate, wherein use of the height map comprises:

(a) decomposition of the height map into a plurality of components, including a first height map component representing topographical variations associated with a device pattern and a second height map component representing other topographical variations, calculation of control set-points according to a control algorithm specific to each of the first and second height map components, combination of the control set-points calculated for the first height map component and the second height map component, and use of the combined set-points to control the positioning system to apply the product pattern to the substrate, or

(b) subtraction from the height map a first height map component representing topographical variations associated with a device pattern so as to obtain a second height map component representing other topographical variations, calculation of control set-points, using the obtained second height map component, according to a control algorithm specific to the other topographical variations, and use of the calculated set-points to control the positioning system to apply the product pattern to the substrate.

16. The computer program product of claim 15 , wherein use of the height map comprises: decomposition of the height map into a plurality of components, including a first height map component representing topographical variations associated with the device pattern and a second height map component representing other topographical variations, calculation of control set-points according to a control algorithm specific to each of the first and second height map components, combination of the control set-points calculated for the first height map component and the second height map component, and use of the combined set-points to control the positioning system to apply the product pattern to the substrate.

17. The computer program product of claim 16 , wherein the decomposition of the height map comprises calculation of the first component of the height map based on an average field topography and subtraction of the first component from the height map to obtain the second height map component.

18. The computer program product of claim 15 , wherein use of the height map comprises: subtraction from the height map a first height map component representing topographical variations associated with the device pattern so as to obtain a second height map component representing other topographical variations, calculation of control set-points, using the obtained second height map component, according to a control algorithm specific to the other topographical variations, and use of the calculated set-points to control the positioning system to apply the product pattern to the substrate.

19. A lithographic apparatus comprising a projection system and a positioning system configured to position a patterning device and substrate in relation to the projection system in order to apply a pattern to a substrate, the lithographic apparatus comprising the apparatus of claim 7 to control the positioning system.

20. A lithographic apparatus comprising a projection system and a positioning system configured to position a patterning device and substrate in relation to the projection system in order to apply a pattern to a substrate, the lithographic apparatus comprising the apparatus of claim 14 to control the positioning system.