Abstract: A method of transferring a pattern of a mask onto shot areas on a substrate determines two sets of parameters in a single model equation. The parameters in one of the two sets relate to arrangement of a plurality of shot areas on the substrate, and the parameters in the other set relate to the shot areas per se. The mask and the substrate are moved relatively in accordance with the determined parameters.

Abstract: A method of aligning each of a plurality of processing areas arranged on a substrate with a predetermined transfer position in a static coordinate system XY for defining a moving position of said substrate, a pattern of a mask being transferred to each of the plurality of processing areas, the method comprising the steps of: wherein each of the plurality of processing areas has a specific point and a plurality of marks for alignment arranged by a predetermined positional relationship with respect to said specific point; measuring coordinate positions of a predetermined number of marks selected from several processing areas of the plurality of processing areas on the static coordinate system XY; calculating a plurality of parameters in a model equation expressing the regularity of arrangement of the plurality of processing areas by performing a statistic calculation by use with the measured plurality of coordinate positions, arrangement coordinate values upon the design of the specific points of the several pr

Abstract: A method and apparatus for exposing an image of a pattern formed in a mask onto a sensitive substrate. The mask is irradiated with an irradiation light. Data is computed relating to the thermal expansion saturation point of the mask due to absorption of the irradiation light. The mask is expanded to the thermal expansion saturation point based on the computed data, and the image of the mask pattern is exposed onto the sensitive substrate.

Abstract: A method of aligning each of a plurality of processing areas arranged on a substrate with a predetermined transfer position in a static coordinate system XY for defining a moving position of said substrate, a pattern of a mask being transferred to each of the plurality of processing areas, the method comprising the steps of: wherein each of the plurality of processing areas has a specific point and a plurality of marks for alignment arranged by a predetermined positional relationship with respect to said specific point; measuring coordinate positions of a predetermined number of marks selected from several processing areas of the plurality of processing areas on the static coordinate system XY; calculating a plurality of parameters in a model equation expressing the regularity of arrangement of the plurality of processing areas by performing a statistic calculation by use with the measured plurality of coordinate positions, arrangement coordinate values upon the design of the specific points of the several pr

Abstract: A method of aligning each of a plurality of processing areas arranged on a substrate with a predetermined transfer position in a static coordinate system XY for defining a moving position of said substrate, a pattern of a mask being transferred to each of the plurality of processing areas, the method comprising the steps of: wherein each of the plurality of processing areas has a specific point and a plurality of marks for alignment arranged by a predetermined positional relationship with respect to said specific point; measuring coordinate positions of a predetermined number of marks selected from several processing areas of the plurality of processing areas on the static coordinate system XY; calculating a plurality of parameters in a model equation expressing the regularity of arrangement of the plurality of processing areas by performing a statistic calculation by use with the measured plurality of coordinate positions, arrangement coordinate values upon the design of the specific points of the several pr

Abstract: An error in alignment between both positions is obtained from reference position information incorporated in advance in an exposure apparatus for manufacturing a semiconductor and detection position information obtained by physically non-contact measuring a mark formed on an object to be measured such as a wafer, a mask or a wafer stage. This mark has a construction having a periodic pattern at a predetermined pitch in connection with a scanning direction. A periodic signal obtained by non-contact scanning the mark is subjected to Fourier integration processing and a phase angle including not only a fundamental wave component but a high-order component by calculation of a sine wave and a cosine component of Fourier conversion to thereby detect position information of an average center position of the mark with a correction of a mark deformation caused by wafer or process of mask added thereto. An error in alignment is corrected by relatively moving said object to a reference position.

Abstract: A measuring method comprises a first step to expose by the irradiation of a predetermined energy ray onto the resist layer of a photosensitive board a first mask pattern having at least two linear pattern portions arranged substantially in axial symmetry with respect to a straight line in a predetermined first direction and inclined at a predetermined angle to the straight line in the first direction, a second step to overlap with the first mask pattern image exposed on the resist layer a second mask pattern formed by the linear patterns which extend in a second direction substantially perpendicular to the first direction by relatively driving the second mask pattern in a predetermined amount in the first direction for exposure, and a third step to measure an interval in the second direction between at least two wedge-shaped resist images formed by the overlapped portions of the first mask pattern and the second mask pattern.

Abstract: Measured is a coordinate position, on a static coordinate system, of each of some specified areas selected from a plurality of areas on a substrate. The coordinate positions of some specified areas undergo a weighted averaging process by use of such a weight that it decreases with a larger distance between the specified areas. The coordinate position is thereby smoothed per specified area. The weight is given to each of some smoothed coordinate positions, and, thereafter, a statistic calculation is effected. The coordinate position, on the static coordinate system, of the area on the substrate is thereby obtained. The substrate is sequentially located based on the obtained coordinate position, and each area on the substrate is thus aligned to a predetermined position.

Abstract: A positioning method involving the following steps is disclosed. Measured are coordinates positions of at least three preselected exposure areas on a static coordinate system among a plurality of exposure areas two-dimensionally formed in accordance with predetermined array coordinates on a photosensitive substrate. Calculative array coordinates of the plurality of exposure areas on the static coordinate system are calculated by using a plurality of first parameters calculated by statistically calculating the plurality of measured coordinate positions. Then, the photosensitive substrate is positioned in an exposure position while being moved in accordance with the calculative array coordinates thus calculated. Specific marks formed on a mask are thus exposed on each of a plurality of predetermined positions on the photosensitive substrate.

Abstract: An exposure method for aligning a plurality of shot areas arranged on a substrate with predetermined exposure positions on a predetermined coordinate system in turn and transcribing, on the substrate, a pattern formed on a mask through a projection optical system comprises the steps of measuring, on a predetermined coordinate system, coordinates of a plurality of sample shot areas selected from a plurality of shot areas, determining weight coefficients corresponding to the coordinates of the sample shot areas, performing statistical calculation based on the coordinates and the weight coefficients of the measured sample shot areas and determining coordinates of the i-th shot area on the predetermined coordinate system, controlling the movement of the substrate according to the determined coordinates of the i-th shot area to set the i-th shot area at the exposure position, and adjusting the projection magnification of the projection optical system based on a parameter expressing deformation of the shot area amo

Abstract: An exposure method for use in an apparatus for projecting a pattern formed on a mask onto a photosensitive substrate through a projection optical system, comprises the steps of providing a mask bearing a pattern of which width gradually varies in a reference direction on the mask transferring the pattern onto the photosensitive substrate through the projection optical system measuring the length of pattern transferred onto the photosensitive substrate, in a reference direction on the substrate corresponding to the reference direction of the mask determining optimum exposure conditions for the projection exposure, from thus measured length of the pattern and controlling the exposure according to the conditions.

Abstract: An apparatus having stage means on which a substrate is placed, holding means for holding a mask formed with at least one mark, and exposing means for exposing the image of said at least one mark on the exposure surface of the substrate which is coated with photoresist includes displacing means for imparting relative displacement between the stage means and the holding means, control means for controlling the exposing means and the displacing means and executing first exposure and second exposure successively, the control means executing the first and the second exposure of exposing the image of said at least one mark on a plurality of predetermined areas of the exposure surface of the substrate placed on the stage means, and controlling the exposing means and the displacing means so that the amount of deviation between the position of the image of said at least one mark in each of the predetermined areas during the first exposure and the position of said image during the second exposure assumes a predetermin