Abstract

A new theory of multilayers with enhanced normal reflectance has been developed based on the superposition of a few layers of various different radiation-absorbing materials. Every layer in the multilayer had a sub-quarterwave optical thickness. The theory was developed for materials with small refractive-index differences, although it is also valid in some cases for materials with large refractive-index differences. Reflectance enhancements were obtained in a very broad band and over a wide range of incidence angles. The theory is particularly suited to designing multilayers with enhanced reflectance in the extreme ultraviolet for wavelengths above 50 nm. In this spectral region the reflectance of single layers of all materials is relatively low, and standard multilayers are not possible because of the high absorption of materials.

© 2001 Optical Society of America

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References

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  1. P. Boher, L. Hennet, Ph. Houdy, “Three materials soft X-ray mirrors—theory and application,” in Advanced X-ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
    [CrossRef]
  2. J. I. Larruquert, R. A. M. Keski-Kuha, “Multilayer coatings with high reflectance in the EUV spectral region from 50 to 121.6 nm,” Appl. Opt. 38, 1231–1236 (1999).
    [CrossRef]
  3. J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet for thin films of ion-beam-deposited SiC, Mo, Mg2Si, and InSb, and evaporated Cr,” Appl. Opt. 39, 2772–2781 (2000).
    [CrossRef]
  4. G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
    [CrossRef]
  5. J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet of thin films of ion-beam-deposited carbon,” Opt. Commun. 183, 437–443 (2000).
    [CrossRef]
  6. E. D. Palik, Handbook of Optical Constants of Solids II (Academic, San Diego, Calif., 1998).
  7. J. I. Larruquert, R. A. M. Keski-Kuha (unpublished data; see Table I).
  8. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego Calif., 1998).
  9. J. A. Méndez, J. I. Larruquert, J. A. Aznárez, “Preservation of FUV aluminum reflectance by overcoating with C60 films,” Appl. Opt. 39, 149–156 (2000).
    [CrossRef]

2000 (3)

1999 (1)

Aznárez, J. A.

Blumenstock, G. M.

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Boher, P.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft X-ray mirrors—theory and application,” in Advanced X-ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Ginter, M. L.

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Hennet, L.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft X-ray mirrors—theory and application,” in Advanced X-ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Houdy, Ph.

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft X-ray mirrors—theory and application,” in Advanced X-ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

Keski-Kuha, R. A. M.

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet for thin films of ion-beam-deposited SiC, Mo, Mg2Si, and InSb, and evaporated Cr,” Appl. Opt. 39, 2772–2781 (2000).
[CrossRef]

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet of thin films of ion-beam-deposited carbon,” Opt. Commun. 183, 437–443 (2000).
[CrossRef]

J. I. Larruquert, R. A. M. Keski-Kuha, “Multilayer coatings with high reflectance in the EUV spectral region from 50 to 121.6 nm,” Appl. Opt. 38, 1231–1236 (1999).
[CrossRef]

J. I. Larruquert, R. A. M. Keski-Kuha (unpublished data; see Table I).

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

Larruquert, J. I.

Méndez, J. A.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids II (Academic, San Diego, Calif., 1998).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego Calif., 1998).

Appl. Opt. (3)

Opt. Commun. (1)

J. I. Larruquert, R. A. M. Keski-Kuha, “Reflectance measurements and optical constants in the extreme ultraviolet of thin films of ion-beam-deposited carbon,” Opt. Commun. 183, 437–443 (2000).
[CrossRef]

Other (5)

E. D. Palik, Handbook of Optical Constants of Solids II (Academic, San Diego, Calif., 1998).

J. I. Larruquert, R. A. M. Keski-Kuha (unpublished data; see Table I).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego Calif., 1998).

P. Boher, L. Hennet, Ph. Houdy, “Three materials soft X-ray mirrors—theory and application,” in Advanced X-ray/EUV Radiation Sources and Applications, J. P. Knauer, G. K. Shenoy, eds., Proc. SPIE1345, 198–212 (1990).
[CrossRef]

G. M. Blumenstock, R. A. M. Keski-Kuha, M. L. Ginter, “Extreme ultraviolet optical properties of ion-beam-deposited boron carbide thin films,” in X-Ray and Extreme Ultraviolet Optics, R. B. Hoover, A. B. Walker, eds., Proc. SPIE2515, 558–564 (1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the incident, reflected, and transmitted rays for (a) one thin film on an opaque substrate and (b) two thin films on an opaque substrate.

Fig. 2
Fig. 2

Calculated reflectance of an opaque layer of IBD SiC and of different multilayers optimized at 83.4 nm. From left to right, the materials begin from the outermost layer to the opaque substrate.

Fig. 3
Fig. 3

Intrinsic multilayer reflectance dependence on wavelength. Refractive indices of the materials are set constant in the calculation throughout the spectral range shown, equal to their values at 83.4 nm. Materials and film thickness data starting with the outermost layer were those for the optimized multilayer at 83.4 nm: 8.0 nm SiC/3.7 nm B4C/5.5 nmC/opaque Al2O3. SiC film reflectance of 0.363 at 83.4 nm is displayed for reference.

Fig. 4
Fig. 4

Calculated reflectance versus angle of incidence with respect to the normal for opaque IBD SiC and for the following multilayer that was optimized at 83.4 nm (starting with the outermost layer): 7.6 nm SiC/3.2 nm B4C/4.4 nm C/2.6 nm Al2O3/opaque MgF2. The radiation is assumed to be unpolarized.

Tables (4)

Tables Icon

Table 1 Optical Constants of Different Materials at 83.4 nm

Tables Icon

Table 2 Reflectance of Sub-Quarterwave Multilayers at 83.4 nma

Tables Icon

Table 3 Optical Constants of Different Materials at 53.6 nm

Tables Icon

Table 4 Reflectance of Sub-Quarterwave Multilayers at 53.6 nm

Equations (56)

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r=rinc,1+r1,2 exp(4πixN1 cos θ1/λ)1+rinc,1r1,2 exp(4πixN1 cos θ1/λ),
r1,2=N-(N+ΔN)N+(N+ΔN)=-ΔN2N+O(ΔN2).
r=rinc,1-(1-rinc,12)ΔN2Nexp4πiNxλ,
R=Rinc,1-4|Ninc+N|4RezNΔN exp4πiNxλ,
z=NincN(Ninc*2-N*2).
dRdx=16πλ|Ninc+N|4exp-4πkxλ×Im[zΔN exp(iϕ)]|x=xext=0,
ϕ=4πnxλ.
tan ϕext=Im(zΔN)Re(zΔN)=-ΔnA+ΔkBΔnB-ΔkA
A=(ninc2+kinc2+n2+k2)(ninck-kincn)
B=(ninc2+kinc2-n2-k2)(nincn+kinck).
d2Rdx2=-44πλ2n|Ninc+N|4exp-4πkxmaxλ×|zΔN|2Im(zΔN)sin φmax<0.
Im(zΔN)>0
ΔnA+ΔkB>0.
Av=(1+n2+k2)kBv=(1-n2-k2)n.
Rmax=Rinc,1+4n|Ninc||Ninc-N||N||Ninc+N|3|ΔN|exp-4πkxmaxλ.
dRdx=16πλ|Ninc+N|4|zΔN|sin(ϕmax-ϕ)×exp-4πkxλ.
r=rinc,1-1-rinc,122NΔN1 exp4πiNx1λ+ΔN2 exp4πiN(x1+x2)λ.
R=Rinc,1-4|Ninc+N|4RezNΔN1 exp4πiNx1λ+ΔN2 exp4πiN(x1+x2)λ.
Δn1A+Δk1B>0,
Δn1Δk2<Δn2Δk1.
tan ϕmax1=-Δn1A+Δk1BΔn1B-Δk1A,
tan ϕmax2=Δn2Δk1-Δk2Δn1Δn1Δn2+Δk1Δk2
Rmax=Rinc,1+4n|Ninc|Ninc-N||N|Ninc+N|3×|ΔN1|exp-4πkxmax1λ+|ΔN2|exp-4πk(xmax1+xmax2)λ.
Δn1A+Δk1B>0(layer1),
Δn1Δk2<Δn2Δk1(layer2),
Δn2Δk3<Δn3Δk2(layer3),
Δnm-1Δkm<ΔnmΔkm-1(layerm).
tan ϕmax1=-Δn1A+Δk1BΔn1B-Δk1A(layer1),
tan ϕmax2=Δn2Δk1-Δk2Δn1Δn1Δn2+Δk1Δk2(layer2),
tan ϕmax3=Δn3Δk2-Δk3Δn2Δn2Δn3+Δk2Δk3(layer3),
tan ϕmax,m=ΔnmΔkm-1-ΔkmΔnm-1Δnm-1Δnm+Δkm-1Δkm(layerm),
Rmax=Rinc,1+4n|Ninc||Ninc-N||N||Ninc+N|3×|ΔN1|exp-4πkxmax1λ+|ΔN2|exp-4πk(xmax1+xmax2)λ++|ΔNm|exp-4πki=1mxmax,iλ.
ϕi=4πnixiλ,i=1tom,
R=Rinc,1-4|Ninc+N|4RezNΔN1 exp4πiNx1λ+ΔN2 exp4πiN(x1+x2)λ.
Rx1(xmax1, xmax2)=0,
Rx2(xmax1, xmax2)=0,
2Rx22(xmax1, xmax2)<0,
2Rx122Rx22-2Rx1x22(xmax1, xmax2>0.
Im{zΔN2 exp[i(ϕmax1+ϕmax2)]}=0,
Im[zΔN1 exp(iϕmax1)]=0,
n|z|2|ΔN2|2Im(zΔN1)Im(u)sin ϕmax1 sin ϕmax2>0,
n2|z|4|ΔN1|2|Δn2|2Im2(zΔn1)Im(u)sin ϕmax1 sin2 ϕmax2>0,
ϕmax1=4πnxmax1λ,
ϕmax2=4πnxmax2λ.
tan ϕmax1=-Im(zΔN1)Re(zΔN1),
tan ϕmax2=-Im(ΔN2/ΔN1)Re(ΔN2/ΔN1),
Im(zΔN1)>0,
Im(ΔN2/ΔN1)<0.
Δn1A+Δk1B>0,
Δn1Δk2<Δn2Δk1,
Rmax=Rinc,1+4n|Ninc||Ninc-N||N||Ninc+N|3×|ΔN1|exp-4πkxmax1λ+|ΔN2|exp-4πk(xmax1+xmax2)λ.
Rx2(x1, x2)=-4πλ4|Ninc+N|4×exp-4πk(x1+x2)λΔN2ΔN12ImΔN2ΔN1×sin(ϕmax1+ϕmax2)sin(ϕ1-ϕmax1+ϕ2-ϕmax2)
Rx1(x1, x2)=-4πλ4|Ninc+N|4×exp-4πkx1λ|zΔN1|×sin(ϕ1-ϕmax1)+Rx2.
Im(zΔN2)>0.

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