Required optical characteristics of materials for phase-shifting masks

The reflectivity and transmission of a multiple-layer substrate are simulated to predict the optimum choice of materials for the fabrication of phase-shifting masks for optical lithography. Two types of materials are described: a transparent shifter layer with a refractive index closely matching that of quartz, and a partially transparent layer (5-15% transmission) inducing a 180° phase shift of light compared with air. A possible refractive index n and extinction coefficient k are defined, for both layers of the partially transparent material. The fabrication tolerances are calculated in terms of refractive index, extinction coefficient, and thickness accuracy. One of the major technological challenges for both material types is to control the thickness to ±2%, which is required to satisfy the phase-shifting mask specifications for deep UV lithography (±0.5% transmission control and ±4° phase control). These criteria were calculated by the simulation of the phase and transmission errors, thereby inducing a ±10% linewidth variation of the resist patterns on the wafers.