Command trajectory for driving a stage with minimal vibration

A method of driving a stage to change a velocity of said stage from a first velocity to a second velocity that differs from said first velocity, said method comprising the steps of:

• changing a jerk of said stage continuously with a positive jerk over a first period of time;
• changing a jerk of said stage continuously with a negative jerk over a second period of time;
• and
• adjusting a first ratio between said second period of time and said first period of time to a desired value.

A method of driving a stage, said method comprising the steps of:

• changing the position of said stage to produce an acceleration on the stage during an acceleration period until said stage reaches a desired velocity;
• changing the position of said stage to produce a desired velocity for a desired period of time;
• and
• changing the position of said stage to produce a deceleration on the stage during a deceleration period until said stage is stationary;
• wherin a third derivative with respect to time of said changing the position of said stage to produce an acceleration on said stage is continuous and equal to zero at the start and finish of said acceleration period.

A scanning exposure apparatus comprising:

• a first stage that holds a substrate, said first stage being movable in a scanning direction;
• a second stage that holds a mask;
• a projection optical system disposed between said first stage and second stage, said projection optical system projecting an image formed on said mask on said substrate;
• an actuator connected with said first stage;
• and
• a controller connected with said actuator, said controller being programmed to provide a motion trajectory signal to said actuator;
• wherein
• said actuator accelerates said first stage from a first velocity to a second velocity in response to said motion trajectory signal, said motion trajectory signal controls said actuator to produce an acceleration of said first stage based on a derivative with respect to time of said acceleration, said derivative of said acceleration is continuous and equal to zero at the start and finish of said acceleration.

A stage system comprising:

• an actuator;
• a movable stage coupled to said actuator;
• a position control circuit connected with said actuator, said position control circuit being programmed to provide a motion trajectory signal to said actuator;
• and
• wherein said actuator accelerates said movable stage from a first velocity to a second velocity in response to said motion trajectory signal;
• and
• said motion trajectory signal controls said actuator to produce an acceleration of said movable stage based on a derivative with respect time of said acceleration, said derivative of said acceleration being continuous having a positive segment and a negative segment, said position control circuit adjustably controlling a ratio between said positive and negative segment.

A stage system comprising:

• an actuator;
• a controller connected with said actuator, said controller being programmed to provide a motion trajectory signal to said actuator, and
• a movable stage connected with said actuator,
• wherein said actuator changes a velocity of said movable stage from a first velocity to a second velocity that differs from said first velocity in response to said motion trajectory signal;
• and
• said motion trajectory signal controls said actuator so that a jerk of said movable stage changes continuously with a positive jerk over a first period of time and changes continuously with a negative jerk over a second period of time, and a first ratio between said second period of time and said first period of time is adjustable.

An exposure apparatus comprising:

• an optical system that forms an image on a substrate;
• a substrate stage that supports said substrate;
• an actuator connected with said substrate stage;
• and
• a controller connected with said actuator, said controller being progmmmed to provide a motion trajectory signal to said actuator,
• wherein said actuator changes a velocity of said substrate stage from a first velocity to a second velocity that differs from said first velocity in response to said motion trajectory signal;
• and
• said motion trajectory signal controls said actuator so that a jerk of said substrate stage changes continuously with a positive jerk over a first period of time and changes continuously with a negative jerk over a second period of time, and a first ratio between said second period of time and said first period of time is adjustable.

An exposure apparatus comprising:

• an optical system that images a pattern formed in a mask onto a substrate;
• a mask stage that supports said mask;
• an actuator connected with said mask stage;
• and
• a controller connected with said actuator, said controller being programmed to provide a motion trajectory signal to said actuator,
• wherein said actuator changes a velocity of said mask stage from a first velocity to a second velocity that differs from said first velocity in response to said motion trajectory signal;
• and
• said motion trajectory signal controls said actuator so that a jerk of said mask stage changes continuously with a positive jerk over a first period of time and changes continuously with a negative jerk over a second period of time, and a first ratio between said second period of time and said first period of time is adjustable.