Patent Number: 051630788
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In accordance with the embodiments shown in the drawings, the present invention will be described in detail below. FIRST EMBODIMENT In this embodiment, where the multilayer film reflecting mirrors each comprised of Ni and Sc (the number of layers: 201, an X-ray wavelength: 39.8 .ANG.) are fabricated within the tolerance defined by Equation (8), the deteriorative state of the reflectance against the optimum design value of the film thickness is simulated by changing in turn the film thickness of each layer of Ni and Sc, the incident angle .phi. of X rays, and a deviation SD from the optimum design value of the film thickness. The simulation is performed by the following procedure. That is, it is assumed that, with respect to 100 multilayer film reflecting mirrors, the tolerance of the film thickness is generated at random within the deviation SD in the probability according to the normal distribution given by Equation (7), and the reflectances of individual reflecting mirrors and their generation frequency (which is hereinafter called merely the frequency) are thus obtained. By Equation (1), the reflectance is calculated for each layer in regard to the film thickness deviated from the optimum design value. Also, the complex indices of refraction of Ni and Sc in the case of the X-ray wavelength of 39.8 .ANG. are derived from the tables of atomic scattering factors by B. Henke [B. Henke, Atomic Data & Nuclear Data Tables 27, pp. 1-144 (1982)] and the literature [Sadao Aoki, Phys. Appl., Vol. 56, No. 3, pp. 16-18 (1981)], resulting in the following numerical data: EQU n(Ni)=0.9882-0.0041183i EQU n(Sc)=0.9975-0.0005738i EMBODIMENT 1-1 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of normal incidence, namely, .phi.=0.degree.. The film thickness of each Ni layer is 8.2 .ANG., that of each Sc layer 11.8 .ANG., and the deviation SD 0.8 .ANG.. FIG. 8 shows the relationship between the reflectance and the frequency in Embodiment 1-1. The design value of the reflectance is 24%, and according to FIG. 8, the mirrors exhibiting the reflectances of a half (12%) of the design value or more are 36 ones, which indicates that Equation (8) is effective. EMBODIMENT 1-2 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=30.degree.. The film thickness of each Ni layer is 8.8 .ANG., that of each Sc layer 14.4 .ANG., and the deviation SD 1.2 .ANG.. FIG. 9 shows the relationship between the reflectance and the frequency in Embodiment 1-2. The design value of the reflectance is 28%, and according to FIG. 9, the mirrors exhibiting the reflectances of a half (14%) of the design value or more are 30 ones. EMBODIMENT 1-3 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=60.degree.. The film thickness of each Ni layer is 13.4 .ANG., that of each Sc layer 27.1 .ANG., and the deviation SD 3.0 .ANG.. FIG. 10 shows the relationship between the reflectance and the frequency in Embodiment 1-3. The design value of the reflectance is 36%, and according to FIG. 10, the mirrors exhibiting the reflectances of a half (18%) of the design value or more are 42 ones. EMBODIMENT 1-4 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=75.degree.. The film thickness of each Ni layer is 26.3 .ANG., that of each Sc layer 55.8 .ANG., and the deviation SD 9.0 .ANG.. FIG. 11 shows the relationship between the reflectance and the frequency in Embodiment 1-4. The design value of the reflectance is 39%, and according to FIG. 11, the mirrors exhibiting the reflectance of a half (20%) of the design value or more are 52 ones. As mentioned above, according to the first embodiment, each deviation SD satisfies Equation (8) and hence the multilayer film reflecting mirror having a desired quality of reflection can be fabricated in the probability of 30% or more. SECOND EMBODIMENT In this embodiment, the states of the reflectances of the multilayer film reflecting mirrors each comprised of Ni and Sc (the number of layers: 101, the X-ray wavelength: 39.8 .ANG.) are simulated like the first embodiment. Also, the optical constants are the same as in the first embodiment. EMBODIMENT 2-1 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=0.degree.. The film thickness of each Ni layer is 8.6 .ANG., that of each Sc layer 11.4 .ANG., and the deviation SD 1.2 .ANG.. FIG. 12 shows the relationship between the reflectance and the frequency in Embodiment 2-1. The design value of the reflectance is 11%, and according to FIG. 12, the mirrors exhibiting the reflectances of a half (6%) of the design value or more are 30 ones, which indicates that Equation (8) is effective. EMBODIMENT 2-2 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=30.degree.. The film thickness of each Ni layer is 9.7 .ANG., that of each Sc layer 13.4 .ANG., and the deviation SD 1.5 .ANG.. FIG. 13 shows the relationship between the reflectance and the frequency in Embodiment 2-2. The design value of the reflectance is 14%, and according to FIG. 13, the mirrors exhibiting the reflectances of a half (7%) of the design value or more are 41 ones. EMBODIMENT 2-3 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=60.degree.. The film thickness of each Ni layer is 14.8 .ANG., that of each Sc layer 26.3 .ANG., and the deviation SD 3.0 .ANG.. FIG. 14 shows the relationship between the reflectance and the frequency in Embodiment 2-3. The design value of the reflectance is 34%, and according to FIG. 14, the mirrors exhibiting the reflectances of a half (17%) of the design value or more are 57 ones. EMBODIMENT 2-4 In this embodiment, the multilayer film reflecting mirrors are designed on the condition of .phi.=75.degree.. The film thickness of each Ni layer is 26.3 .ANG., that of each Sc layer 55.8 .ANG., and the deviation SD 7.5 .ANG.. FIG. 15 shows the relationship between the reflectance and the frequency in Embodiment 2-4. The design value of the reflectance is 39%, and according to FIG. 15, the mirrors exhibiting the reflectances of a half (20%) of the design value or more are 64 ones. THIRD EMBODIMENT In this embodiment, the states of the reflectances of the multilayer film reflecting mirrors each comprised of Re (rhenium) and Al (aluminum) (the number of layers: 41, the X-ray wavelength: 210 .ANG.) are simulated by the same procedure as in the above embodiments. The incident angle is set at .phi.=15.degree., the film thickness of each Re layer is 28.3 .ANG., and that of each Al layer is 80 .ANG.. Also, the optical constants of Re and Al are cited from the literature [Takeshi Namioka et al., "Developments of Light Sources and Optical systems for Soft X-ray Lithography", Report of Research by Scientific Research-Aid Fund for the 1985 Fiscal Year (Test Research (2)), pp. 1-36, 1986], resulting in the following numerical data: EQU n(Re)=0.65-0.12i EQU n(Al)=0.99-0.00458i FIG. 16 shows the relationship between the reflectance and the frequency in the third embodiment in which the deviation SD is 6.0 .ANG.. The design value of the reflectance is 64%, and according to FIG. 16, the mirrors exhibiting the reflectances of a half (32%) of the design value or more are 87 ones, which indicates that Equation (8) is effective.