A method for designing a phase shift mask, said phase shift mask having a substrate with a transparent property and an opaque layer having an opaque property formed on the substrate, wherein a plurality of rectangular apertures are formed in said opaque layer, a two-dimensional layout pattern is formed by opaque parts comprising regions at which said opaque layer is formed and transparent parts comprising regions at which said apertures are formed, and for a pair of adjacently disposed apertures, a trench having a predetermined depth and an outline greater than an outline of an aperture is formed at a portion of the substrate at which a first aperture is formed so that a phase of light transmitted through the first aperture will be shifted by 180 degrees with respect to a phase of light transmitted through a second aperture:
- said phase shift mask designing method comprising a preparation step for preparing a function necessary for designing and a designing step in which designing is actually carried out using said function;
- said preparation step comprising:
- an exposure condition setting step for setting an exposure condition for use of the phase shift mask to be designed;
- a two-dimensional dimension condition setting step for defining an X-Y plane having an X-axis and a Y-axis on a surface of said substrate and setting a two-dimensional dimension condition M that determines specific dimension values for a width Wx in the X-axis direction and a width Wy in the Y-axis direction of each aperture and a width Ws of each opaque part;
- an undercut amount setting step for setting an undercut amount Uc that indicates a distance between a position of an outline of the trench and a position of an outline of the aperture;
- a bias correction amount setting step for setting a bias correction amount δ that indicates an amount of increase or decrease of an aperture width that is set by said two-dimensional dimension condition M;
- a three-dimensional analysis step for executing, on each of a plurality of cases in which said two-dimensional dimension condition M, said undercut amount Uc, and said bias correction amount δ are changed in a plurality of ways, a three-dimensional analysis of defining a two-dimensional layout, in which a plurality of apertures of the same size are disposed along the X-axis on said X-Y plane based on a dimension condition obtained by applying a correction in accordance with a predetermined bias correction amount δ on the predetermined dimension condition M, defining a three-dimensional structure for an aperture with which phase shifting is to be performed based on a predetermined undercut amount Uc and a trench depth d that is determined based on said exposure condition, and determining a light intensity deviation D, which indicates, for a case where light is transmitted under said exposure condition through a pair of adjacent apertures that have been designed using a three-dimensional structural body that is defined by said two-dimensional layout and said three-dimensional structure, a difference in intensities of light that has been transmitted through said pair of adjacent apertures;
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- an optimal function defining step for comparing a plurality of light intensity deviations D, which have been determined under a specific two-dimensional dimension condition M in said three-dimensional analysis step, with each other, determining, for each of a plurality of undercut amounts Uc, a bias correction amount δ by which the light intensity deviation D is minimized as an optimal value for said specific two-dimensional dimension condition M, and determining, for each of a plurality of two-dimensional dimension conditions M, an optimal function that indicates an optimal value of a bias correction amount δ with respect to an undercut amount Uc;
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- said designing step comprising:
- a two-dimensional layout pattern designing step for designing a two-dimensional layout pattern, wherein a plurality of apertures are disposed on a two-dimensional plane, and determining for each aperture, whether or not phase shifting is to be performed;
- an optimal function extracting step for selecting, from among a plurality of two-dimensional dimension conditions M for which the optimal functions are determined, a condition that can be applied to said two-dimensional layout pattern and extracting an optimal function determined for the selected two-dimensional dimension condition M;
- an optimal value determination step for determining optimal values of an undercut amount Uc and a bias correction amount δ based on the extracted optimal function;
- a layout correction step for correcting said two-dimensional layout pattern based on said optimal value of the bias correction amount δ;
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- a three-dimensional structure determination step for determining a three-dimensional structure for an aperture with which phase shifting is to be performed based on said optimal value of the undercut amount Uc and a trench depth d that is determined based on the exposure condition.