Linewidth measurement simulations for semiconductor circuits by scatterometry using FDTD and time shortening calculation method

Abstract

This paper shows the basic numerical calculation methods for measuring linewidths between 45-80nm using normal and oblique incident lightwaves to control the resist and silicon linewidths for the next-generation semiconductor circuits. The shape measurement method by nondestruction and noncontact, using the light wave scattering method is called Scatterometry. While using the scatterometry with the actual manufacturing process, it is necessary to compare the characteristics in proportion to the trench shape with the measured values in the real-time. In this paper, we use the finite-difference time-domain (FDTD) method as the numerical analysis method. FDTD method takes a lot of time to analyze with the Maxwell equation in the time domain until the electromagnetic fields are stabilized. Then, the examinations on the methods for shortening the FDTD calculation times are carried out by using the periodicity and the sub-grids. By using the periodicity and the incident plane waves, we only calculate the electromagnetic fields in the half pitched region of the grooves. Next, FDTD divides the analytic region into main- and sub-grids. We only allocate the silicon substrates and air parts to the main-cells. The sub-grids are created by dividing in the main-grids in the resist parts, because the resist parts have to be exmained with the minute groove changes. The oblique incidence analysis is important for ellipsometry and many other applications. It is ascertained for silicon that the amplitude reflectance calculated by using FDTD agreed well with Fresnel's law for TE and TM modes to the largest angle. Then, the oblique incidence amplitude reflectance for the resist grooves on silicon is calculated. Finally, we confirm the FDTD analysis is effective to obtain the reflected light characteristics close to the real photolithographic models.