E/I core actuator commutation formula and control method

A method for making an object including the steps of:

• providing a substrate;
• providing an illumination system that directs an illumination beam at a reticle;
• providing a stage that retains the substrate;
• coupling a first actuator to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and
• directing current with a control system to the first actuator to move the stage with a control system, wherein the amount of current directed to the first actuator is determined utilizing a first parameter and a second parameter that are added to a numerical value representative of the first gap.

A method of making a wafer including the steps of:

• providing a substrate;
• providing an illumination system that directs an illumination beam at a reticle that transferred to the substrate;
• providing a stage that retains the substrate;
• coupling a first actuator to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and irecting current with a control system to the first actuator to move the stage with a control system, wherein the amount of current directed to the first actuator is determined utilizing a first parameter and a second parameter that are added to a numerical value representative of the first gap.

A stage assembly comprising:

• a stage;
• a first actuator that is coupled to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and
• a control system that directs current to the first actuator to move the stage, wherein the amount of current directed to the first actuator is calculated using the formula:
• I
• 1
• =
• 1
• K
• D
• ⁢
• (
• g
• 1
• +
• a
• )
• ⁢
• (
• g
• 1
• +
• b
• )
• ⁢
• (
• F
• 0
• -
• Δ
• ⁢
• ⁢
• F
• D
• 2
• )
• where I1, is the current, KD is the electromagnetic constant, g1 is the first gap, a is the first parameter, b is the second parameter, FO is a bias force and ΔFD is the net force generated by the actuator pair.

A method for positioning a stage, the method comprising the steps of:

• coupling a first actuator to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and
• directing current with a control system to the first actuator to move the stage with a control system, wherein the amount of current directed to the first actuator is calculated using the formula:
• I
• 1
• =
• 1
• K
• D
• ⁢
• (
• g
• 1
• +
• a
• )
• ⁢
• (
• g
• 1
• +
• b
• )
• ⁢
• (
• F
• 0
• -
• Δ
• ⁢
• ⁢
• F
• D
• 2
• )
• where I1, is the current, KD is the electromagnetic constant, g1 is the first gap, a is the first parameter, b is the second parameter, FO is a bias force and ΔFD is the net force generated by the actuator pair.

A stage assembly comprising:

• a stage;
• a stage support that supports the stage;
• a first actuator that is coupled to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and
• a control system that directs current to the first actuator to move the stage, wherein the amount of current directed to the first actuator is determined utilizing a first parameter that is added to a numerical value representative of the first gap, wherein the value of the first parameter is adjusted to compensate for a stiffness of the stage support.

A stage assembly comprising:

• a stage;
• a first actuator that is coupled to the stage, the first actuator having a first E core and a first I core that is spaced apart a first gap from the first E core;
• and
• a control system that directs current to the first actuator to move the stage, wherein the amount of current directed to the first actuator is determined utilizing a first parameter that is added to a numerical value representative of the first gap, wherein the control system directs current to the first actuator so that a bias force generated by the first actuator is greater than a minimum force that can be generated by the first actuator but less than one half of the sum of the minimum force and a maximum force that can be generated by the first actuator.