System for analyzing mask topography and method of forming image using the system

A system for analyzing a mask topography, where an illumination system is configured to transmit light incident on a mask, wherein light passes through the mask to a projection system having a projection lens configured to transmit light to an image surface of a wafer, the system comprising a set of modules embodied in a tangible device and executable by at least one processor, the set of modules comprising:

• an initial E-field module configured to determine a first electric field on a mask surface of the mask using a Kirchhoff method, independent of a pitch formed on the mask, and to determine a second electric field on a pupil surface of the projection lens using an electromagnetic field analysis method dependent on the pitch;
• and
• a resultant E-field module configured to determine a third electric field on the image surface of the wafer as a combination of the first electric field and the second electric field,
• wherein, when an angle of incidence of the incident light is large enough to affect an amplitude and the aspect ratio of a mask thickness to a feature size is high, the initial E-field module is configured to determine the second electric field based on the assumption that the incidence is an oblique incidence, and
• wherein the initial E-field module is configured to:
• determine the second electric field based on an assumption that the oblique incidence is normal incidence;
• and
• determine the second electric field in the case of the oblique incidence by shifting the second electric field in the case of normal incidence according to a predetermined frequency.

A system for analyzing a mask topography, where an illumination system is configured to transmit light incident on a mask, wherein light passes through the mask to a projection system having a projection lens configured to transmit light to an image surface of a wafer, the system comprising a set of modules embodied in a tangible device and executable by at least one processor, the set of modules comprising:

• an initial E-field module configured to determine a first electric field on a mask surface of the mask using a Kirchhoff method, independent of a pitch formed on the mask, and to determine a second electric field on a pupil surface of the projection lens using an electromagnetic field analysis method dependent on the pitch;
• and
• a resultant E-field module configured to determine a third electric field on the image surface of the wafer as a combination of the first electric field and the second electric field,
• wherein the initial E-field module is configured to determine the second electric field for each of a plurality of pitches and to store the second electric field in a lookup table according to each pitch, and
• wherein the lookup table is corrected with respect to a critical dimension.