Simulation of Diffraction Effects Using Phase-Shifting Layers in Photolithography

Contemporary micro- and nanoelectronic production is based on projection lithography technology, which determines the possibility of forming nanosized topological features. The close proximity of elements on the photomask leads to negative diffraction effects that affect the quality and size of the resulting images. The diffraction pattern obtained when deep ultraviolet radiation passes through a photomask with 180° phase-shifting partially transparent lines with different geometric parameters of the template structure and different transparency of the lines is simulated in this study. The calculation is carried out based on Fourier optics. One-dimensional regular template structures with an even number of transparent gaps of infinite length with phase-shifting material lines between them are considered. The electromagnetic wave incident on the photomask is considered to be plane and linearly polarized. Cases of radiation with wavelengths of 193, 248, and 365 nm are considered. The type of diffraction pattern is studied and its contrast is calculated, depending on the width of the lines and gaps, their ratio, the transmission coefficient of the phase-shifting material lines, and the number of gaps and lines. It is shown that the use of phase-shifting material lines significantly increases the contrast in cases where the dimensions of the elements are much smaller than the wavelength of the incident radiation. It is found that the deviation of the phase shift from the ideal value of 180° by 15° in either direction has little effect on the contrast of the diffraction pattern. It is established that, with a large number of structural elements in the case of incident radiation in the form of a plane wave, the fundamental lower limit for the spatial period of the structure is the radiation wavelength (without taking into account the numerical aperture of the focusing system). It is demonstrated that by disrupting the regularity of the structure—reducing the width of the gaps in the extreme parts of the structure—it is possible to improve the uniformity of the distribution of the contrast in the diffraction pattern.