Abstract: At the boundary where the number of effective chips changes, at least three grid points of a chip grid intersect with the periphery of a wafer effective region, and a triangle connecting these three grid points together includes therein the wafer center. To design a semiconductor chip, this feature is used to determine, by an analytic process, candidate solutions including different numbers of effective chips. These candidate solutions are used to derive an advantageous solution.

Abstract: At the boundary where the number of effective chips changes, at least three grid points of a chip grid intersect with the periphery of a wafer effective region, and a triangle connecting these three grid points together includes therein the wafer center. To design a semiconductor chip, this feature is used to determine, by an analytic process, candidate solutions including different numbers of effective chips. These candidate solutions are used to derive an advantageous solution.

Abstract: An imprint apparatus for forming a pattern of an imprint material on a substrate using a mold, includes a driving unit configured to adjust a distance and a relative tilt between the mold and the substrate, an image capturing unit configured to capture a plurality of times an interference fringe formed by illuminating the substrate via the mold in a process of enlarging a contact area between the mold and the imprint material by reducing the distance between the mold and the substrate by the driving unit, and a control unit configured to control the driving unit so as to correct the relative tilt between the mold and the substrate a plurality of times in the process based on images captured by the image capturing unit a plurality of times.

Abstract: The present invention provides an exposure apparatus including a projection device including an object whose at least one of a position, an attitude and a shape is regulatable, and configured to project light from a reticle onto a substrate, a regulating device configured to regulate the at least one of the position, the attitude and the shape of the object, and a controller configured to obtain, an amount of regulation of the object by the regulating device, the amount of regulation being used for regulating a first optical characteristic value of the projection device expressed by a square root of a weighted square sum of wavefront aberration coefficients of light projected by the projection device, and to control the regulating device based on the amount of regulation.

Abstract: The present invention provides an exposure apparatus including a projection device including an object whose at least one of a position, an attitude and a shape is regulatable, and configured to project light from a reticle onto a substrate, a regulating device configured to regulate the at least one of the position, the attitude and the shape of the object, and a controller configured to obtain, an amount of regulation of the object by the regulating device, the amount of regulation being used for regulating a first optical characteristic value of the projection device expressed by a square root of a weighted square sum of wavefront aberration coefficients of light projected by the projection device, and to control the regulating device based on the amount of regulation.

Abstract: The present invention provides a determination method of determining a light intensity distribution to be formed on a pupil plane of an illumination optical system in an exposure apparatus, the method including a step of setting a cutline used to evaluate an image of a pattern of a mask, which is formed on an image plane of a projection optical system, and a target position of the image, and a step of determining an intensity of an element light source such that the position of a midpoint between edges of the image of the pattern of the mask on the cutline from a calculated image comes close to the target position, thereby determining the light intensity distribution.

Abstract: A scanning exposure apparatus includes a first feedback loop including a first controlled object including an original stage and controlling a position of the original stage, a second feedback loop including a second controlled object including a substrate stage and controlling a position of the substrate stage, and a feedback unit including a first calculator and feed backing a synchronization error between the original stage and the substrate stage to the first feedback loop and the second feedback loop via the first calculator, wherein a transfer function from a first target value for the first controlled object to a first controlled value of the first controlled object and that from a second target value for the second controlled object to a second controlled value of the second controlled object are equal, and the exposure is performed at least during a period in which the original and the substrate are accelerated.

Abstract: The present invention provides a determination method of determining a light intensity distribution to be formed on a pupil plane of an illumination optical system in an exposure apparatus, the method including a step of setting a cut line used to evaluate an image of a pattern of a mask, which is formed on an image plane of a projection optical system, and a target value of a dimension of the image, and a step of obtaining the dimension of the image of the pattern on the cut line, and determining a weight to be applied to each of a plurality of element light sources such that the obtained dimension comes close to the target value of the dimension, thereby determining, as the light intensity distribution, light sources obtained by combining the plurality of element light sources applied with the weights.

Abstract: The present invention provides a determination method of determining a light intensity distribution to be formed on a pupil plane of an illumination optical system in an exposure apparatus, the method including a step of setting a cutline used to evaluate an image of a pattern of a mask, which is formed on an image plane of a projection optical system, and a target position of the image, and a step of determining an intensity of an element light source such that the position of a midpoint between edges of the image of the pattern of the mask on the cutline from a calculated image comes close to the target position, thereby determining the light intensity distribution.

Abstract: The present invention provides a determination method of determining a light intensity distribution to be formed on a pupil plane of an illumination optical system in an exposure apparatus, the method including a step of setting a cut line used to evaluate an image of a pattern of a mask, which is formed on an image plane of a projection optical system, and a target value of a dimension of the image, and a step of obtaining the dimension of the image of the pattern on the cut line, and determining a weight to be applied to each of a plurality of element light sources such that the obtained dimension comes close to the target value of the dimension, thereby determining, as the light intensity distribution, light sources obtained by combining the plurality of element light sources applied with the weights.

Abstract: A scanning exposure apparatus includes a first feedback loop including a first controlled object including an original stage and controlling a position of the original stage, a second feedback loop including a second controlled object including a substrate stage and controlling a position of the substrate stage, and a feedback unit including a first calculator and feed backing a synchronization error between the original stage and the substrate stage to the first feedback loop and the second feedback loop via the first calculator, wherein a transfer function from a first target value for the first controlled object to a first controlled value of the first controlled object and that from a second target value for the second controlled object to a second controlled value of the second controlled object are equal, and the exposure is performed at least during a period in which the original and the substrate are accelerated.

Abstract: An exposure apparatus for exposing a substrate to light. A substrate stage holds the substrate and is to be moved. A measuring device measures a positional deviation amount of a mark on the substrate held by the substrate stage. A computing device determines a coefficient of a linear expression that approximates the measured positional deviation amount of each mark and is linear with respect to a term including at least one of an X coordinate to the Nth power and a Y coordinate to the Nth power, where N is an integer not less than zero, and a control device controls a position of the substrate stage in accordance with a target position determined based on the linear expression to expose a shot to the light.

Abstract: An apparatus includes a control unit configured to control an exposure unit and a driving unit such that exposure of a first region of a substrate starts and ends while a substrate stage is accelerated in a first direction parallel to a scanning direction, an absolute value of maximum acceleration of the substrate stage during a deceleration period is greater than an absolute value during a first approach run period, and a distance by which the substrate stage moves during the first approach run period is approximately equal to a distance by which the substrate stage moves during the deceleration period.

Abstract: In determining a relative position between a chip lattice including rectangular cells, each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.

Abstract: An optical apparatus which includes an image forming optical system having a movable optical element, and a driving mechanism configured to move the optical element. The apparatus includes a first block which measures a wavefront aberration of the optical system. A second block obtains a linear evaluation value of an aberration expressed by a linear function of a position of the movable optical element out of aberrations of the optical system, and a quadratic evaluation value of a square of a root mean square of the wavefront aberration measured by the first block expressed by a quadratic function of the position. A third block uses a dummy variable as an upper limit value of the linear evaluation value and obtains a minimum value of the dummy variable by a linear programming. A fourth block determines a position of the optical element to be moved by the driving mechanism.

Abstract: An exposure apparatus for exposing a substrate, includes a substrate stage configured to hold the substrate and to move, a measuring device configured to measure a positional deviation amount of a mark on the substrate held by the substrate stage, a computing device configured to determine a linear expression for approximating positional deviation amounts measured by using the measuring device, and a control device configured to control a position of the substrate stage in accordance with a target position based on the linear expression, for exposure of an exposure region on the substrate, wherein the computing device is configured to determine the linear expression in accordance with an integer programming method so as to minimize the number of marks having a difference between a mark positional deviation amount as measured by the measuring device and a mark positional deviation amount as approximated in accordance with the linear expression, which difference is out of a predetermined allowable range.

Abstract: An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism. A first block obtains a linear evaluation value by normalizing, by a first tolerance, an aberration expressed by a linear function of a position of the movable optical element and normalizing, by a second tolerance, an aberration expressed by a quadratic function of the position out of the aberrations of the optical system. A second block obtains a minimum value of a dummy variable by linear programming. A third block determines a position of the optical element to be moved by the driving mechanism using a value prepared by adding a relaxation amount to the minimum value obtained by the second block and minimizes the weighted sum of the quadratic evaluation values by adjusting the weights assigned to the quadratic evaluation values and a relaxation amount.

Abstract: An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism which moves the optical element is disclosed.

Abstract: An exposure apparatus for exposing a substrate to light via a pattern of an original while the original and the substrate are scanned. The apparatus includes a stage configured to hold the substrate and to move, a projection optical system configured to project the pattern of the original onto the substrate, a measurement unit configured to measure a positional deviation between superposition marks formed on the substrate, and a controller configured to control operation of projection of a slit shot pattern of an original onto plural areas of a substrate, with each area partially overlapping four of the plural areas adjacent to each other. The projection is performed by keeping the original stand still and moving the stage, to cause the measurement unit to perform measurement of a positional deviation between superposition marks in each of the overlapping areas formed through the projection, and to control movement of the stage based on the measurement.

Abstract: In determining a relative position between a chip lattice comprised of rectangular cells each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.