Source: http://aoot.osa.org/oe/abstract.cfm?uri=oe-25-26-32215
Timestamp: 2019-04-22 16:00:44+00:00

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The basic properties in the extreme ultraviolet (EUV) of one-dimensional photonic crystals (Bragg reflectors) with incorporated superlattices are investigated by a numerical study using the multiple scattering method. The superlattice is realized in the “standard” Mo/Si system by periodically replacing certain Mo layers by Si layers. At 13.5 nm–the wavelength of interest for EUV lithography–the superlattice sharpens the reflection peak at normal incidence with only weak reduction of the peak value. Between normal incidence and total reflection at large angles, additional reflection peaks appear at certain angles where the reflection is zero for the “standard” Mo/Si system. By combining different superlattices and depth grading, the range of additional reflection peaks is extended towards all-angle reflection. The effect of interface imperfections is considered for the case of the interdiffusion of Mo and Si. The extension to other frequency ranges is addressed via band structure calculations.
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Fig. 1 Contour plot of the reflectance R at normal incidence in the complex permittivity plane for values representative for the EUV. R values are calculated for a PhC with double layers consisting of an element with permittivity ε and silicon. A few 1D PhCs (element/Si) are indicated. The total number of double layers is 40. The period of the PhC is 6.9 nm. The thickness of the silicon layer is 60% of the period. The “standard” PhC with Mo/Si layers has the highest reflectance (0.74).
Fig. 3 Reflectance at normal incidence of superlattice-2 (a), −3 (b), −4 (c), −5 (d) and of the PhC without superlattice (e). The number of double layers is 80, 60, 53, 50 and 40, respectively. This way the number of Mo/Si interfaces is constant (40).
Fig. 4 Contour plot of the reflectance vs. wavelength and angle of incidence. From top to bottom: superlattice-3, −4 and −5. Positive (negative) angle: s (p) polarization. Dashed curves: positions of Bragg reflections according to Eq. (1). Solid curve: critical angle of total reflection according to Eq. (2). Details see text.
Fig. 5 Reflectance as a function of angle of incidence for superlattice-4 (middle) and 5 (bottom) at 13.5 nm. For comparison the reflectance for the “standard” PhC is shown (top). Positive (negative) angle: s (p) polarization. The dotted-blue and yellow curves for superlattice-5 are for an interdiffusion layer with σ = 0.07 and 0.35 nm, respectively. Details in the text.
Fig. 6 Reflectance as a function of angle of incidence for combined superlattices-4 and 5 without (top) and with depth grading (bottom) at 13.5 nm. Positive (negative) angle: s (p) polarization. Details of the grading see text.
Fig. 7 Band structure (reduced frequency a/λ vs. wavevector kz) of the basic structure (dashed) and superlattice-4 (solid) for kx = 0. The lowest gap of the basic structure is at kz = π/a, the lowest mini-gap of superlattice-4 at kz = π/4a. The mini-gaps are indicated by red arrows.
Table 1 Peak values and full widths at half maximum (FWHM) of the reflectance peaks at normal incidence (2nd and 3rd column). Angles of strong reflectance R near 13.5 nm (4th column): bold angles indicate additional reflection peaks due to the superlattices (details in Figs. 4 and 5).
Table 2 Comparison of peak reflectance and peak width of superlattice PhCs and standard PhCs for normal incidence at 13.5 nm. Details see text.
(1) sin( α )= n 2 ( λ peak )− k sl λ peak 2 Λ sl .
(2) sin α crit =n(λ).
Peak values and full widths at half maximum (FWHM) of the reflectance peaks at normal incidence (2nd and 3rd column). Angles of strong reflectance R near 13.5 nm (4th column): bold angles indicate additional reflection peaks due to the superlattices (details in Figs. 4 and 5).
Comparison of peak reflectance and peak width of superlattice PhCs and standard PhCs for normal incidence at 13.5 nm. Details see text.

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