Stage driving exposure apparatus wherein the number of driving devices exceeds the degrees of freedom of the stage

An exposure apparatus for transferring a pattern formed on a mask onto a photosensitive substrate through a projection optical system, comprising:

• an illuminating optical system for illuminating the mask;
• a mask stage for placing the mask thereon;
• and
• a substrate stage for holding the photosensitive substrate and movable in two-dimensional directions, wherein at least one of the mask stage and the substrate stage is a stage apparatus, the stage apparatus comprising:
• stage driving devices of a number larger than degrees of freedom of the stage;
• position detectors for detecting positions of the stage;
• a first converting means for converting information detected by the position detectors into information on at least one of a position and a velocity of a center of gravity of the stage concerning each of the degrees of freedom;
• control means provided for each of the degrees of freedom for determining control amounts for each of the degrees of freedom necessary for movement of the center of gravity by means of proportional operation or (proportional+integral) operation on the basis of at least one of a positional deviation for each of the degrees of freedom obtained as a difference between a target position of the center of gravity for each of the degrees of freedom and the position of the center of gravity for each of the degrees of freedom converted by the first converting means and a velocity deviation for each of the degrees of freedom obtained as a difference between a target velocity of the center of gravity for each of the degrees of freedom and the velocity of the center of gravity for each of the degrees of freedom converted by the first converting means;
• and
• a second converting means for converting the control amounts for each of the degrees of freedom determined by the control means into control amounts for controlling the driving devices.

A stage apparatus comprising:

• stage driving devices of a number larger than degrees of freedom of a stage;
• a position detector which detects a position of the stage by illuminating a measuring light to the stage;
• an arithmetic circuit which determines control amounts of the stage for each of the degrees of freedom on the basis of information detected by the position detector, the arithmetic circuit being connected with the position detector;
• and
• a converting circuit which converts the control amounts of the stage for each of the degrees of freedom into driving amounts for each of the stage driving devices, the converting circuit being connected with the arithmetic circuit.

An exposure apparatus for transforming a pattern formed on a mask onto a photosensitive substrate through a projection optical system, comprising:

• a mask stage;
• a substrate stage;
• stage driving devices of a number larger than degrees of freedom of at least one of the mask stage and the substrate stage;
• a position detector which detects a position of the at least one of the mask stage and the substrate stage by illuminating a measuring light to the at least one of the mask stage and the substrate stage;
• an arithmetic circuit which determines control amounts for each of the degrees of freedom on the basis of the information detected by the position detector, the arithmetic circuit being connected with the position detector;
• and
• a converting circuit which converts the control amounts for each of the degrees of freedom into driving amounts for each of the stage driving devices, the converting circuit being connected with the arithmetic circuit.