Effect of roughness, deterministic and random errors in film thickness on the reflecting properties of aperiodic mirrors for the EUV range

By the example of three aperiodic multilayer Mo/Si mirrors (AMM) for the wavelength ranges 17–21 nm, 24–29 nm, and 28–33 nm we have studied numerically the effect of the linearly determinisctic and random fluctuations of the film thickness and the interlayer roughness on the spectral dependences of the reflection coefficient. The simulation results are used to solve the inverse problem of reconstructing the interlayer roughness and the thickness of individual films from the measured dependences of the extreme UV radiation reflection coefficients. It is shown that the 'asymmetry' of the boundaries affects the magnitude and slope of the reflection coefficient plateau. Random fluctuations of the film thickness with the variance of 1%–2% weakly influence the reflection characteristics of AMMs and allow reliable reconstruction of the thickness of individual films. The fluctuations with the variance 8%–10% allow the estimation of individual thicknesses, but the reflection curve in this case strongly differs from the desirable one. Larger fluctuations do not allow the reconstruction of the AMM structure. The basic criteria for high-quality AMM synthesis are formulated.