This paper reports the simulation study of a new phase-shifting mask (PSM), quartz-etch halftone-rim, applied on one and two dimensional patterns, such as contact hole, line/space and polylayer using positive- tone resist (optical parameters focused mainly on (lambda) equals 365 nm, NA equals 0.5, sigma equals 0.6, halftone chrome T equals 4%). When apply this halftone-rim PSM on 0.35 micrometers dense contact holes, the simulations indicated that optimized rim width is 0.15 (lambda) /NA (0.11 micrometers ). Optimized single side width for biased contact is 0.1 micrometers (0.9 X optimized rim width). Optimized biased contact is 0.55 micrometers (0.35 + 0.1 + 0.1 micrometers ) which is 1.57 times larger of 0.35 micrometers design rule. Exposure latitude is 9.9%. Total depth of focus (DOF) is about 1.2 micrometers . Compared with sized-rim PSM (chrome T equals 0%), this halftone-rim PSM has lower operation exposure dose; higher exposure latitude and larger DOF. When apply it on the 0.35 micrometers dense and isolated line/space, optimized rim width is 0.12 (lambda) /NA (0.09 micrometers ). Optimized single side width for biased space is 0.08 micrometers (0.9 X optimized rim width). The total DOF is about 1.0 micrometers for line/space. By using combination of halftone-rim PSM and off-axis illumination (OAI), the total DOF will reach 1.2-1.5 micrometers for 0.35 micrometers dense line/space. However, the improvement for line/space is insignificant if compared with sized-rim PSM. Halftone-rim PSM has advantages on patterning of contact holes but not on line/space in this study.