Particle beam system and method for operating a particle optical unit

1. A method of operating a multi-beam particle optical unit, the multi-beam particle optical unit comprising at least two particle-optical components through which a plurality of particle beams pass, the at least two particle-optical components having a settable effect on the plurality of particle beams, the method comprising:

(1) providing a first setting of effects of the at least two particle-optical components so that the particle beams are used to image a first plane into a second plane, the imaging of the first plane onto the second plane being characterizable by at least two parameters;

(2) determining a matrix A so that:

{right arrow over (Δ p 1 )}= A ·{right arrow over (Δ w 1 )};

{right arrow over (Δ w 1 )}={right arrow over ( w 1 )}−{right arrow over ( w 1 )};

{right arrow over (Δ p 1 )}={right arrow over (Δ p 1 )}−{right arrow over ( p )},

wherein:

{right arrow over (w 1 )} is a vector having components w 1 1 , w 2 1 , . . . , w n 1 ;

n is the number of particle-optical components and each of the components w l 1 represents a value of an effect of one of the particle-optical components in the case of the first setting;

{right arrow over (w)} is a vector having components w 1 , w 2 , . . . , w n representing the values of the effects of the particle-optical components in the case of a setting different from the first setting;

{right arrow over (p 1 )} is a vector having components p 1 1 , p 2 1 , . . . , p m 1 ;

m is the number of parameters characterizing the particle optical imaging of the first plane onto the second plane, and each of the components p i 1 represents a value of one of the parameters in the case of the first setting; and

{right arrow over (p)} is a vector having components p 1 , p 2 , . . . , p m representing the values of the parameters in the case of the setting different from the first setting;

(3) determining a matrix S so that S·A=D A , D A being a diagonal matrix;

(4) defining values of parameters which characterize a desired imaging of the first plane onto the second plane; and

(5) providing a second setting of the effects of the particle-optical components so that the imaging of the first plane onto the second plane is characterizable by the parameters having the defined values, the effects required for the second setting being determined in accordance with:

{right arrow over (Δ w 2 )}= S ·{right arrow over (Δ p 2 )} with

{right arrow over (Δ w 2 )}={right arrow over ( w 2 )}−{right arrow over ( w 1 )} and

{right arrow over (Δ p 2 )}={right arrow over ( p 2 )}−{right arrow over ( p 1 )}

{right arrow over (w 2 )} is a vector having components w 1 2 , w 2 2 , . . . , w n 2 representing the values of the effects of the particle-optical components in the case of the second setting; and

{right arrow over (p 2 )} is a vector having components p 1 2 , p 2 2 , . . . , p m 2 representing the defined values of the parameters.

2. The method of claim 1 , wherein the at least two parameters comprise parameters selected from the group consisting of an imaging scale, a rotation, a convergence of the beam path, and a distance along the beam path between the first plane and the second plane.

3. The method of claim 1 , wherein determining the matrix A comprises:

generating the setting different from the first setting so that only one of the components Δw 1 1 , Δw 2 1 , . . . , Δw n 1 of the vector {right arrow over (Δw 1 )} is different from zero;

analyzing the imaging of the first plane onto the second plane that arises in the case of the setting of the particle-optical components that is different from the first setting; and

determining the parameters characterizing the imaging of the first plane onto the second plane.

4. The method of claim 3 , further comprising repeating the process of generating the setting different from the first setting, wherein each time a different one of the components Δw 1 1 , Δw 2 1 , . . . , Δw n 1 of the vector {right arrow over (Δw 1 )} is different from zero.

5. The method of claim 1 , wherein determining the matrix A comprises numerically simulating the imaging of the first plane onto the second plane.

6. The method of claim 1 , wherein the at least two particle-optical components comprise a particle-optical lens, and the settable effect of the particle-optical lens is a focusing effect of the particle-optical lens.

7. The method of claim 1 , wherein the at least two particle-optical components comprise a least one stigmator, and the settable effect is an astigmatic effect of the stigmator.

8. A method of operating a multi-beam particle optical unit, the multi-beam particle optical unit comprising at least two particle-optical components through which a plurality of particle beams pass, the at least two particle-optical components having a settable effect on the plurality of particle beams, the method comprising:

(1) determining a matrix A so that:

{right arrow over (Δ p 1 )}= A ·{right arrow over (Δ w 1 )};

{right arrow over (Δ w 1 )}={right arrow over (Δ w 1 )}−{right arrow over ( w )}; and

{right arrow over (Δ p 1 )}={right arrow over (Δ p 1 )}−{right arrow over ( p )},

wherein:

{right arrow over (w 1 )} is a vector having components w 1 1 , w 2 1 , . . . , w n 1 ;

n is the number of particle-optical components and each of the components w i 1 represents a value of an effect of one of the particle-optical components in the case of a first setting of the effects of the at least two particle-optical components;

{right arrow over (w)} is a vector having components w 1 , w 2 , . . . , w n representing the values of the effects of the particle-optical components in the case of a setting different from the first setting;

{right arrow over (p 1 )} is a vector having components p 1 1 , p 2 1 , . . . , p m 1 ;

m is the number of parameters characterizing the imaging and each of the components p i 1 represents a value of one of the parameters in the case of the first setting; and

{right arrow over (p)} is a vector having components p 1 , p 2 , . . . , p m representing the values of the parameters in the case of the setting different from the first setting; and

(2) providing a second setting of the effects of the particle-optical components so that the imaging of the first plane onto the second plane is characterizable by parameters characterizing a desired imaging of the first plane onto the second plane, the effects required for the second setting being determined in accordance with:

{right arrow over (Δ w 2 )}= S ·{right arrow over (Δ p 2 )} with

{right arrow over (Δ w 2 )}={right arrow over ( w 2 )}−{right arrow over ( w 1 )} and

{right arrow over (Δ p 2 )}={right arrow over ( p 2 )}−{right arrow over ( p 1 )}

wherein:

S is a matrix;

S·A=D A ;

D A is a diagonal matrix;

{right arrow over (w 2 )} is a vector having components w 1 2 , w 2 2 , . . . , w n 2 representing the values of the effects of the particle-optical components in the case of the second setting; and

{right arrow over (p 2 )} is a vector having components p 1 2 , p 2 2 , . . . , p m 2 representing the defined values of the parameters.

9. The method of claim 8 , wherein the at least two parameters comprise parameters selected from the group consisting of an imaging scale, a rotation, a convergence of the beam path, and a distance along the beam path between the first plane and the second plane.

10. The method of claim 8 , further comprising determining the matrix A by a method that comprises:

generating the setting different from the first setting so that only one of the components Δw 1 1 , Δw 2 1 , . . . , Δw n 1 of the vector {right arrow over (Δw 1 )} is different from zero;

analyzing the imaging of the first plane onto the second plane that arises in the case of the setting of the particle-optical components that is different from the first setting; and

determining the parameters characterizing said imaging of the first plane onto the second plane.