In this study, the known optical alternating phase shift mask (APSM) issues, such as imaging imbalance, phase error, and EUVL APSM fabrication specific issues are explored in the case of extreme ultra-violet lithograph (EUVL). EUVL APSM fabrication starts with a phase step in the substrate followed by Mo/Si multi-layer (ML) deposition. This phase step can be created either by directly etching the step into the substrate or by depositing a thin film layer and then patterning the thin film layer. The advantage of depositing thin film layer is that the step control can be obtained via thin film deposition thickness control and the thin film high etch selectivity to the substrate. The first few orders of phase steps, which is determined by [λ/(4cosθ)](2m+1), with m=0, 1, 2, -, are viable in EUVL APSM fabrication. The smallest phase step needed to induce a 180-degree phase shift is λ/(4conθ), or 3.37nm, for λ=13.4nm. In most of cases, the thin film quality or smoothness increases as the film thickness increases. In other word, using the minimum step may not be ideal from process point of view. In the simulation, EUVL APSM with different phase step heights [all yield net 180-degreee phase difference in the adjacent regions (ignore the multiples of 360 degrees)] was evaluated. It is found that image imbalance effect in EUVL using APSM is relatively small and is negligible for the smallest step. As the step heights increase, the image imbalance effect also increases. In the case of step height of 23.58nm, which corresponding m=3, image imbalance induced space difference in the zero and 180 degree phase regions is about 1.5nm for the 25nm periodic lines. As the pitch increases, the imaging imbalance effect diminishes.