Method for producing a mirror element

1. A method for producing a mirror element, comprising:

a) providing a substrate; and

b) forming a layer stack on the substrate, wherein the layer stack has at least one reflection layer system;

wherein the layer stack is formed such that a setpoint curvature of the mirror element for a predetermined operating temperature is generated by a bending force exerted by the layer stack,

wherein the substrate has an actual curvature deviating from the setpoint curvature of the mirror element prior to said forming of the layer stack,

wherein the bending force exerted by the layer stack is at least partly generated by performing a post-treatment for changing a layer tension of the layer stack, and

wherein the post-treatment for changing the layer tension of the layer stack produces an irreversible change in the actual curvature of the substrate.

2. The method as claimed in claim 1 , wherein the post-treatment comprises a thermal post-treatment by heat irradiation, laser irradiation or annealing.

3. The method as claimed in claim 1 , wherein the post-treatment comprises ion irradiation or electron irradiation.

4. The method as claimed in claim 1 , wherein the post-treatment is locally restricted to at least one portion of the layer stack.

5. The method as claimed in claim 1 , wherein the substrate is plane or has a convex curvature prior to said forming of the layer stack.

6. The method as claimed in claim 1 , wherein the substrate has a locally varying rigidity selected such that the setpoint curvature of the mirror element for the predetermined operating temperature is obtained after said forming of the layer stack.

7. The method as claimed in claim 1 , further comprising:

installing the mirror element in a microlithographic projection exposure apparatus; and

correcting the curvature by setting the temperature of the mirror element during operation of the microlithographic projection exposure apparatus.

8. A method, comprising:

producing the mirror element as claimed in claim 1 , wherein the setpoint curvature is a first setpoint curvature, the layer stack is a first layer stack, the bending force is a first bending force, and the mirror element is a first mirror element; and

providing a further substrate, and forming a further layer stack on the further substrate, wherein the further layer stack has at least one further reflection layer system to produce a second mirror element;

wherein the further layer stack is formed such that a second setpoint curvature of the second mirror element is generated by a second bending force exerted by the further layer stack, wherein the further substrate has a further actual curvature deviating from the second setpoint curvature of the second mirror element prior to said forming of the further layer stack, wherein the second bending force exerted by the further layer stack is a least partly generated by performing a further post-treatment for changing a layer tension of the further layer stack, and wherein the first setpoint curvature differs from the second setpoint curvature.

9. The method as claimed in claim 8 , wherein the first setpoint curvature differs from the second setpoint curvature due to mutually differing thicknesses of the first layer stack and of the further layer stack, even though the first bending force equals the second bending force.

10. The method as claimed in claim 8 , wherein the first setpoint curvature differs from the second setpoint curvature, even though the first layer stack and the second layer stack have mutually same thicknesses, due to the first bending force differing from the second bending force.