Displacement devices, moveable stages for displacement devices and methods for fabrication, use and control of same

1. A displacement device for moving a moveable stage relative to a stator, the displacement device comprising:

a stator comprising:

an x-trace layer comprising a plurality of electrically conductive x-traces which extend generally linearly in a stator-x direction across an excitation region;

a y-trace layer comprising a plurality of electrically conductive y-traces which extend generally linearly in a stator-y direction across the excitation region;

the x-trace layer and the y-trace layer overlapping one another in a stator-z direction over the excitation region;

the stator-x direction and the stator-y direction non-parallel to one another and the stator-z direction generally orthogonal to both the stator-x and stator-y directions;

a moveable stage comprising:

a first magnet array comprising a plurality of first magnetization segments linearly elongated in a stage-x direction, each first magnetization segment having a corresponding magnetization direction generally orthogonal to the stage-x direction; and

wherein the first magnet array comprises one or more first pairs of adjacent first magnetization segments, each first pair of adjacent first magnetization segments comprising two first magnetization segments adjacent to one another in a stage-y direction non-parallel to the stage-x direction and wherein, for each first pair of adjacent first magnetization segments:

each first magnetization segment in the first pair has a corresponding magnetization direction that is oriented at a corresponding angle αn about a corresponding stage-x axis aligned with the stage-x direction as measured from a positive stage-z direction that is generally orthogonal to both the stator-x and stator-y directions and wherein the corresponding angle αn is one of 45°+n90° where n is any integer; and

each first magnetization segment in the first pair has a different magnetization direction; and

a controller connected to one or more amplifiers, the controller and the one or more amplifiers configured to drive currents in at least one of the x-traces and at least one of the y-traces to move the moveable stage relative to the stator.

2. A displacement device according to claim 1 wherein, for at least one of the one or more first pairs of adjacent first magnetization segments, the two first magnetization segments of the first pair have corresponding magnetization directions which are generally orthogonal to one another.

3. A displacement device according to claim 2 wherein for each of the one or more first pairs of adjacent first magnetization segments, the two first magnetization segments of the first pair have corresponding magnetization directions which are generally orthogonal to one another.

4. A displacement device according to claim 1 wherein the corresponding magnetization direction of each of the plurality of first magnetization segments is oriented at a corresponding angle α n about a corresponding stage-x axis aligned with the stage-x direction as measured from the positive stage-z direction and wherein the corresponding angle α n is one of 45°+n90° where n is any integer.

5. A displacement device according to claim 4 wherein the corresponding magnetization direction of each of the plurality of first magnetization segments is different from the other corresponding magnetization directions of the plurality of first magnetization segments.

6. A displacement device according to claim 4 wherein starting at a first one of the plurality first magnetization segments at a first stage-x oriented edge of the first magnet array and moving in the stage-y direction across the first magnet array, the integer n associated with the corresponding angle α n for each of the plurality of first magnetization segments increases by unity for each successive adjacent one of the first magnetization segments in the stage-y direction.

7. A displacement device according to claim 4 wherein the first magnet array consists exclusively of the plurality of first magnetization segments.

8. A displacement device according to claim 1 wherein the first magnet array further comprises one or more axial first magnetization segments, each axial first magnetization segment having a corresponding magnetization direction generally orthogonal to the stage-x direction and oriented in one of: a positive stage-y direction; a negative stage-y direction; a positive stage-z direction; and a negative stage-z direction.

9. A displacement device according to claim 1 wherein the plurality of first magnetization segments comprises a number N tx =4 different corresponding magnetization directions.

10. A displacement device according to claim 1 wherein the first magnet array comprises a pair of first sub-arrays separated from one another in the stage-y direction by a non-magnetic gap.

11. A displacement device according to claim 10 wherein each of the first sub-arrays comprises a corresponding sub-array plurality of first magnetization segments and each sub-array plurality of first magnetization segments has features of the plurality of first magnetization segments.

12. A displacement device according to claim 1 wherein a width W my of the first magnet array in the stage-y direction is given by W my =nλ 1 /4 where n is a positive integer and λ 1 is a first spatial period.

13. A displacement device according to claim 12 wherein the first spatial period λ 1 is a spatial period associated with a variation of the magnetization directions of the plurality of first magnetization segments across the stage-y direction of the first magnet array.

14. A displacement device according to claim 12 wherein the first spatial period λ 1 is a spatial period of a first Hallbach array having a plurality of first Hallbach magnetization segments with identical widths, magnetization directions and relative spatial order to those of the plurality of first magnetization segments.

15. A displacement device according to claim 12 wherein, for each of the plurality of first magnetization segments, the width of the first magnetization segment in stage-y direction is λ 1 /N where N is equal to any one of 4, 8 and 16.

16. A displacement device according to claim 1 wherein, for at least one of the one or more first pairs of adjacent first magnetization segments, the two adjacent first magnetization segments of the at least one of the one or more first pairs abut against each other in the stage-y direction.

17. A displacement device for moving a moveable stage relative to a stator, the displacement device comprising:

a stator comprising:

an x-trace layer comprising a plurality of electrically conductive x-traces which extend generally linearly in a stator-x direction across an excitation region;

a y-trace layer comprising a plurality of electrically conductive y-traces which extend generally linearly in a stator-y direction across the excitation region;

the x-trace layer and the y-trace layer overlapping one another in a stator-z direction over the excitation region;

the stator-x direction and the stator-y direction non-parallel to one another and the stator-z direction generally orthogonal to both the stator-x and stator-y directions;

a moveable stage comprising:

a first magnet array comprising a plurality of first magnetization segments linearly elongated in a stage-x direction, each first magnetization segment having a corresponding magnetization direction generally orthogonal to the stage-x direction and at least two of the first magnetization segments having magnetization directions that are different from one another; and

a second magnet array comprising a plurality of second magnetization segments linearly elongated in the stage-x direction, each second magnetization segment having a corresponding magnetization direction generally orthogonal to the stage-x direction and at least two of the second magnetization segments having magnetization directions that are different from one another; and

wherein corresponding edges of the first and second magnet arrays elongated in the stage-x direction are spaced apart from one another in a stage-y direction generally orthogonal with the stage-x direction by a spacing parameter S m given by

S

m

=

N

S

⁢

λ

2

+

λ

4

,

where N S is a positive integer and λ is a spatial period; and

a controller connected to one or more amplifiers, the controller and the one or more amplifiers configured to drive currents in at least one of the x-traces and at least one of the y-traces to move the moveable stage relative to the stator.

18. A method for moving a moveable stage relative to a stator, the method comprising:

providing a stator comprising:

an x-trace layer comprising a plurality of electrically conductive x-traces which extend generally linearly in a stator-x direction across an excitation region;

a y-trace layer comprising a plurality of electrically conductive y-traces which extend generally linearly in a stator-y direction across the excitation region;

the x-trace layer and the y-trace layer overlapping one another in a stator-z direction over the excitation region;

the stator-x direction and the stator-y direction non-parallel to one another and the stator-z direction generally orthogonal to both the stator-x and stator-y directions;

providing a moveable stage comprising:

a first magnet array comprising a plurality of first magnetization segments linearly elongated in a stage-x direction, each first magnetization segment having a corresponding magnetization direction generally orthogonal to the stage-x direction; and

wherein the first magnet array comprises one or more first pairs of adjacent first magnetization segments, each first pair of adjacent first magnetization segments comprising two first magnetization segments adjacent to one another in a stage-y direction non-parallel to the stage-x direction and wherein, for each first pair of adjacent first magnetization segments:

each first magnetization segment in the first pair has a corresponding magnetization direction that is oriented at a corresponding angle α n about a corresponding stage-x axis aligned with the stage-x direction as measured from a positive stage-z direction that is generally orthogonal to both the stator-x and stator-y directions and wherein the corresponding angle α n is one of 45°+n90° where n is any integer; and

each first magnetization segment in the first pair has a different magnetization direction; and

driving currents in at least one of the x-traces and at least one of the y-traces to move the moveable stage relative to the stator.

19. A method according to claim 18 wherein, for at least one of the one or more first pairs of adjacent first magnetization segments, the two first magnetization segments of the first pair have corresponding magnetization directions which are generally orthogonal to one another.

20. A method according to claim 18 wherein for each of the one or more first pairs of adjacent first magnetization segments, the two first magnetization segments of the first pair have corresponding magnetization directions which are generally orthogonal to one another.