The positive phase shift corresponds to giving positive detuning to the electron energy, and the FEL field is amplified regardless of the dimensionless current when the initial electron energy is resonant.
The interaction between unbunched electrons and the FEL field with uniform amplitude and phase is considered in the time domain. The positive phase shift connects the zero small signal gain in low gain regime for resonant electrons to the exponential growth in high gain regime. The positive phase shift corresponds to giving electrons positive energy detuning and results in the FEL amplification. An FEL interaction with unbunched electrons at resonant energy induces a positive phase shift of the FEL field relative to the input phase. This chapter discusses phase shift induced by a free-electron laser (FEL) interaction. Nagai, in Free Electron Lasers 2003, 2004 Publisher Summary Specifications related to half-tone and EAPSMs can be found in SEMI P29-0997: Guideline for description of characteristics specific to Halftone Attenuated Phase Shift Masks and Mask Blanks. Usually 6% transmittance is used for leading edge masks a higher transmittance allows one to achieve better contrast, due to a greater phase interaction, but is practically unusable due to the risk of unwanted side-lobe printing. The improved image quality allows one to achieve a larger process latitude and depth of focus leading to a robust lithographic process. The destructive interference between clear areas and a partially transmitting background enhances the image contrast of the bright region. In the case of EAPSMs, the opaque region of the binary mask is substituted by a partially transmitting material that induces a 180° phase variation with respect to the bright regions. PSMs can be separated in two categories: “weak PSMs,” that include half-tone and embedded attenuated phase shift masks (EAPSMs), and “strong PSMs” that include alternating phase shift masks (APSMs). The principle of this method consists in taking advantage of phase differences caused by different areas on the mask to obtain destructive interference and achieve better image contrast.
PSMs were introduced in 1982 to improve the ultimate resolution achievable with wafer scanner exposure tools. Cantù, in Encyclopedia of Condensed Matter Physics, 2005 Phase-Shift Masks
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