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Interface roughness and density characterization of multilayer mirrors by using X-ray standing waves
Journal of Electron Spectroscopy and Related Phenomena 80 (1996) 449-452
I n t e r f a c e r o u g h n e s s a n d d e n s i t y c h a r a c t e r i z a t i o n of m u l t i l a y e r m i r r o r s b y using x - r a y standing waves
T. Kawamura, H. Takenal~ and T. Hayashi NTT Interdisciplinary Research Laboratories, 3-9-11, Midoricho, Musashino, Tokyo 180, Japan Although methods of fabricating multilayers for soft x-ray mirrors have recently been developed, problems such as roughness and density errors still need serious consideration. The traditional way to characterize the properties of multilayer mirrors has been by small angle x-ray scattering, TEM, and optical methods. However, even with these techniques, the dependence of reflectivity on interface roughness and the density of each layer has not been understood clearly, owing to the high sensitivity of reflectivity to several parameters.
1
INTRODUCTION
X-ray standing waves formed in multilayers, which are produced by a mechanism similar to that in crystals,Ill have been observed by measuring fluorescence yields[2] and X-ray scattering[3]. The measured standing wave fields were also used to analyze the local crystal structure of each layer by observing the diffraction from multilayers[3] and the selective extended X-ray absorption fine structure and to evaluate the density of films deposited on multilayers[4]. However, no standard procedure has been established for quantitative interpretation of the standing wave amplitude in multilayers, mainly because the amplitude of standing waves formed by multilayers depends on the many structural parameters of the multilayer. In crystals, the standing wave amplitude is mainly affected by X-ray beam convergence and imperfections in the crystal. The influence of these factors is easily estimated from the shape of the rocking curve of the Bragg diffraction. The standing wave amplitude is independent of the target atoms at the surfaces and at the interfaces. In contrast, in multilayers both the standing wave amplitude and the Bragg reflection profile are affected by various factors, such as the interface roughness and the density of each layer. 0368-2048/96/$15-00 (~ 1996 Elsevier Science B.V. All rights reserved PII S0368- 2048 (96) 03013-7
The effect of interface roughness on reflectivity is traditionally included by multiplying the theoretical reflectivity by the Debye-Waller factor, and this has been extended to include the reduction in amplitude at each interface[5]. The density variation during fabrication has also been evaluated by in situ visible eUipsometry[6]. However, it is still difficult to clarify the density variation and interface roughness independently with these methods, mainly because of the difficulty of measuring the absolute reflectivity accurately. We recently reported the possibility of determining the roughness and the density of multilayers independently by measuring the yield of X-ray fluorescence caused by x-ray standing waves[7]. In that report, we presented a quantitative method of managing the x-ray electric fields in multilayers and showed that there is interface diffusion in the Ni/C multilayer when using the x-ray standing wave technique. In this report, we describe a further analysis and present a precise interface model of Ni/C multilayer. 2
THEORITICAL
BASIS
As previously described[7], the standing wave amplitude in multilayers can be described using an expanded optical matrix based on Born's matrix. The effect of interface roughness is included as an
450 attenuation factor of the transmittance and reflectance coefficients[7]. The electrical amplitude of X-rays in multilayers was describes as :(z)
=
I E j l 2 0 + I-ysI2 + 2l,yslcos(~;
-
65z))
(1) where 1'/is the reflectivity and ~b5 is its phase factor (Er/Ei - 75 -- [75[ei~) • The z axis is set with its origin at the boundary of the j-th and j + 1-th layers and is perpendicular to the surface. The dependence of the third term in eq. (1) on the z coordinate indicates that X-ray beams in a multilayer form a standing wave at the Bragg reflection. Because the yield of secondary radiation from multilayers, such as fluorescence, is proportional to the X-ray intensity in the multilayers, information about the reflectivity and phase of each layer can be obtained by observing the secondary radiation. For periodic structures, such as the multilayers of an X-ray mirror, the fluorescence yield I I from multilayers can be analytically obtained from eq. (1) by multiplying by the atomic density distribution p(z) and integrating with respect to z. Assuming a rectangular density distribution, one can obtain I I as
=
1.8t 1.6 ~1.4 2.0
roughness = 0.0 A
P/l~ = 0.70 0.80 0.90 1.00 1.10
l(b)).
.... ........ .... ......
1.20-
1.2 0
~1.0
._~
L //!I// I ~// I/fiil
~ 0.8 0.6 0.4 0.2 0
I
'~).60
I
0.65
I
I
0.70
0.75
0.80
Angle(degrees) 2.0
1.8 p = 1.0 PO roughness = 0 . 0 / ~ - -
5.0 ..... 10.0 ~ ....... 15.0/~ - - -
1.6
.2o.o A -
~1.4
1.2 0
~1.01 ~ , o.8 Q)
N
::
creases with increasing density (Fig.
IEjr {1 + 1 512+ 5=1
sin(6j/2)
21"r5[ ~-~
1 cos(~j - 65/2)~. (2)
--~ 0.6
0.4 0.2 0.0
Note that unlike in a reflective measurement, only the relative intensity of the fluorescence yield is necessary for evaluating the interface roughness and density of multilayers. Figures l(a) and l(b) show the calculated Ni Ka fluorescence profiles of Ni/C multilayers for various roughnesses and Ni layer densities. For the calculations, the interface height distribution was assumed to be an exponential function[8]. The overall shape of the fluorescence yield profiles can be explained by the change in the phase of the reflectivity at each layer, which is about ~r across the Bragg reflection[3]. The fluorescence yield profiles became flatter with increasing roughness (Fig. l(a)), and the dip width in the fluorescence yield in-
0.60
I
0.65
I
I
0.70 0.75 Angle(degrees)
0.80
Fig. 1 Ni Ka fluorescence yields of Ni/C multilayers for varous roughnesses and Ni layer densities. The flattening of the profiles is qualitatively explained by the dependence of the absolute reflectivity on roughness. When the roughness increases, the second and third terms in eq. (1) decrease, which leads to flattening of the fluorescence yield profiles. The width of the dip is thought to reflect a change in the refractive indices of the multilayers, analogous to the change in optical multilayer structures[9]. The refractive
451 indices are related to the multilayer density, which explains the widening of the dip in the fluorescence yield profiles. These features suggest that it is possible to independently determine both the roughness and the density of multilayers.
2nd and 3rd peak intensity, the multilayer structure changed by the diffusion between the nickel and carbon layers. 1.o
01 ' 1 II
Ill
°N --
3
Experimental
0.00~
O
The multilayer that we studied had 35 layer pairs, each consisting of a Ni layer and a C layer, deposited on a 3-inch wafer by RF magnetron sputtering[10]. The periodic length was estimated to be about 56.8/~ from the evaporation rates of carbon and nickel. Transmission electron micrographs showed sharp interfaces, amorphous carbon layers, and microcrystalline nickel layers. A first-order reflectivity of 87% was obtained using a double- crystal diffractometer with a Cu Kc~ source (A=1.54 ~). Both x-ray reflectivity and standing wave measurement were carried out with a conventional double-crystal spectrometer. For measuring the reflectivity at grazing incidence, a set of 50#mwide slits were used after the first crystal. The fluorescence and other scattering spectra were measured with a pure Ge solid-state detector and analyzed with a multi-channel analyzer. The beam divergence was estimated to be about 0.0020 ° from the rocking curve of the Si(111) crystals at a (+, +) arrangement. A double-crystal diffractometer with a Si(ll 1) monochromator was used in the X-ray standing wave experiments. The fluorescence and other scattering spectra were measured with a pure Ge solid-state detector and analyzed with a multichannel analyzer. The influence of elastic scattering on the Ni Kc~ fluorescence yield was estimated to be small from the fluorescence and secondary scattering spectra.
4
R e s u l t s and D i s c u s s i o n
Figure 2 shows the x-ray reflectivity of the Ni/C multilayer with a Mo K s source (A=0.709 /?k). The inset shows an enlargement of the 2nd and 3rd Bragg peaks. The periodic length was estimated about 54.6 ~ from the Bragg peaks. Considering both the change in periodic length and in
Measured-
0.6
~0.5
0.8
1.0
1".2
ffl e"
I
e'-
0.0 0.0
L 0.5
Measured -Designe d ......
JL
~'.o
1.5
Angle (degree) Fig. 2 Measured and calculated X-ray reflectivity. Inset shows the schematic multilayer structure for calculation. To explain the experimental x-ray reflectivity, we calculated the x-ray reflectivity based on a nickel-carbon/carbon structure model with various thicknesses of a complex layer. From the peak intensities of the 2nd and 3rd Bragg reflections, the thickness ratio of the complex layer to the total layer was estimated to be 0.45 to 0.55, which is caused by the diffusion of nickel atoms into the carbon layer[7]. W e also found that the refractive index of nickel layer was about 80% of that of bulk nickel, which corresponds to 80% of the density of bulk nickel. The curves with marks in figure 3 shows the firstorder Bragg reflection and Ni Kcz fluorescence yield. The Ni K s fluorescence yield is normalized by the background intensity far from the Bragg reflection area. To determine the roughness and density parameters from x-ray standing wave signals, we calculated the fluorescence yield for various roughnesses and densities. The carbon density was fixed at the density of bulk carbon due to its small effect on the fluorescence yield profiles, and a two-layer model was assumed with a nickel density of 8.876 g/cm 3 and a carbon density of 2.26 g/cm 3. Comparing measured and calculated profiles, we obtained good correspondence by setting the interface roughness r, 10 A and the layer density to the bulk denisty of nickel[7]. This result is
452 inconsistent with the x-ray reflectivity measurement, which suggests a more complex structure for Ni/C multilayer. To solve this inconsistency, we introduce a new interface model consisting of four layers: nickel/nickel-carbon complex/carbon/nickelcarbon complex layers for Ni/C multilayers. The inset in figure 3 shows the intensity ratio of 2nd and 3rd Bragg reflection for various thicknesses of the carbon and nickel-carbon layers. The region in which the intensity ratio of 3rd to 2nd is bigger than 1.0 is limited to a thickness ratio of about 0.5 of the carbon layer and 11.5 A of complex layer. This suggests that most of the nickel layers change to nickel-carbon complex but there still remains a core nickel layer which reflects x-rays. In figure 3, we show calculated fluorescence profiles based on the four-layer model with various interface roughnesses between the carbon and complex layers. The following parameters were used for calculations: 3.2 A for the nickel layer, 28.4 A for carbon layers, and 11.5 A for complex layers. Good correspondence was obtained with 0.0 to 2.5 A interface roughness, suggesting a sharp interface between the carbon and complex layers. This result is consistent with the T E M observation and x-ray reflectivity measurement. 5
Conclusions
Our new method can independently determine the interface roughness and densities of multilayers according to simulation results for Ni Kc~ fluorescence yield profiles with various interface roughnesses and densities, which are related to the reflectivity and the phase of the reflectivity. A 54.6 A-thick 35-period Ni/C multilayer was analyzed using both x-ray reflectivity measurement and this new method. From the x-ray reflectvity measurement, the thickness ratio and density of the nickel layer are about 0.5 and 80% of bulk nickel. However, x-ray standing wave measurement shows that the density of the nickel layer is equal to the bulk and the interface roughness is about 10 A +3 A. This can be explained by the existence of a nickel-carbon complex layer between the nickel and carbon layers. The simulation results based on a four-layer model show good
agreement between measured and calculated profiles for both x-ray standing wave and x-ray reflectivity measurement. This is consistent with the T E M observation, supporting the four-layer intrface model. o 3.0[ "~ [
~20 j.~ " [ ~, 2.5
®
_~ t.0
N 2.0
[
o.4
/",.
d=lO.OA -11.0 A " "
/ \ 11.5A -/ \ 12.OA-/" -,~, / ,, . . - - .,.,. o.s
o.6
o.7
Thickness ratio
E
-- 0.5
r=5.0 ..... r=7.5 --. measured -o-
h,raoo
0.0
.... 0.3
S 0.35
,~-.~ 0.4
. . 0.45
0.5
Angle (degrees)
Fig. 3 Measured and calculated X-ray reflectivity. Inset shows the schematic multilayer structure for calculation. References 1. B. W. Batterman: Phys. Rev. 133(1964) A759. 2. T. W. Barbee and W. K. Warburton: Mater. Left. 3(1984) 17. 3. J. B. Kortright: J. Appl. Phys. 61(1987) 1130. 4. S. I. Zheludeva, et al.: Rev. Sci. Inst. 63(1992) 1519. 5. E. Spiller: Rev. Phys. Appl. 23(1988) 1687. 6. M. Yamamoto and A. Arai: Thin Solid Films 233(1993) 268. 7. T. Kawamura and H. Takenaka: J. Appl. Phys. 75(1994) 3806. 8. D. G. Stern: J. Appl. Phys. 65(1989) 491. 9. M. Born and E. Wolf: Principle of Optica (Pergamon, New York, 1965) 3rd ed. 51. 10. H. Takenaka, Y. Ishii, H. Kinoshita and K. Kurihara: Prec. SPIE 1345(1990) 213.
I n t e r f a c e r o u g h n e s s a n d d e n s i t y c h a r a c t e r i z a t i o n of m u l t i l a y e r m i r r o r s b y using x - r a y standing waves
T. Kawamura, H. Takenal~ and T. Hayashi NTT Interdisciplinary Research Laboratories, 3-9-11, Midoricho, Musashino, Tokyo 180, Japan Although methods of fabricating multilayers for soft x-ray mirrors have recently been developed, problems such as roughness and density errors still need serious consideration. The traditional way to characterize the properties of multilayer mirrors has been by small angle x-ray scattering, TEM, and optical methods. However, even with these techniques, the dependence of reflectivity on interface roughness and the density of each layer has not been understood clearly, owing to the high sensitivity of reflectivity to several parameters.
1
INTRODUCTION
X-ray standing waves formed in multilayers, which are produced by a mechanism similar to that in crystals,Ill have been observed by measuring fluorescence yields[2] and X-ray scattering[3]. The measured standing wave fields were also used to analyze the local crystal structure of each layer by observing the diffraction from multilayers[3] and the selective extended X-ray absorption fine structure and to evaluate the density of films deposited on multilayers[4]. However, no standard procedure has been established for quantitative interpretation of the standing wave amplitude in multilayers, mainly because the amplitude of standing waves formed by multilayers depends on the many structural parameters of the multilayer. In crystals, the standing wave amplitude is mainly affected by X-ray beam convergence and imperfections in the crystal. The influence of these factors is easily estimated from the shape of the rocking curve of the Bragg diffraction. The standing wave amplitude is independent of the target atoms at the surfaces and at the interfaces. In contrast, in multilayers both the standing wave amplitude and the Bragg reflection profile are affected by various factors, such as the interface roughness and the density of each layer. 0368-2048/96/$15-00 (~ 1996 Elsevier Science B.V. All rights reserved PII S0368- 2048 (96) 03013-7
The effect of interface roughness on reflectivity is traditionally included by multiplying the theoretical reflectivity by the Debye-Waller factor, and this has been extended to include the reduction in amplitude at each interface[5]. The density variation during fabrication has also been evaluated by in situ visible eUipsometry[6]. However, it is still difficult to clarify the density variation and interface roughness independently with these methods, mainly because of the difficulty of measuring the absolute reflectivity accurately. We recently reported the possibility of determining the roughness and the density of multilayers independently by measuring the yield of X-ray fluorescence caused by x-ray standing waves[7]. In that report, we presented a quantitative method of managing the x-ray electric fields in multilayers and showed that there is interface diffusion in the Ni/C multilayer when using the x-ray standing wave technique. In this report, we describe a further analysis and present a precise interface model of Ni/C multilayer. 2
THEORITICAL
BASIS
As previously described[7], the standing wave amplitude in multilayers can be described using an expanded optical matrix based on Born's matrix. The effect of interface roughness is included as an
450 attenuation factor of the transmittance and reflectance coefficients[7]. The electrical amplitude of X-rays in multilayers was describes as :(z)
=
I E j l 2 0 + I-ysI2 + 2l,yslcos(~;
-
65z))
(1) where 1'/is the reflectivity and ~b5 is its phase factor (Er/Ei - 75 -- [75[ei~) • The z axis is set with its origin at the boundary of the j-th and j + 1-th layers and is perpendicular to the surface. The dependence of the third term in eq. (1) on the z coordinate indicates that X-ray beams in a multilayer form a standing wave at the Bragg reflection. Because the yield of secondary radiation from multilayers, such as fluorescence, is proportional to the X-ray intensity in the multilayers, information about the reflectivity and phase of each layer can be obtained by observing the secondary radiation. For periodic structures, such as the multilayers of an X-ray mirror, the fluorescence yield I I from multilayers can be analytically obtained from eq. (1) by multiplying by the atomic density distribution p(z) and integrating with respect to z. Assuming a rectangular density distribution, one can obtain I I as
=
1.8t 1.6 ~1.4 2.0
roughness = 0.0 A
P/l~ = 0.70 0.80 0.90 1.00 1.10
l(b)).
.... ........ .... ......
1.20-
1.2 0
~1.0
._~
L //!I// I ~// I/fiil
~ 0.8 0.6 0.4 0.2 0
I
'~).60
I
0.65
I
I
0.70
0.75
0.80
Angle(degrees) 2.0
1.8 p = 1.0 PO roughness = 0 . 0 / ~ - -
5.0 ..... 10.0 ~ ....... 15.0/~ - - -
1.6
.2o.o A -
~1.4
1.2 0
~1.01 ~ , o.8 Q)
N
::
creases with increasing density (Fig.
IEjr {1 + 1 512+ 5=1
sin(6j/2)
21"r5[ ~-~
1 cos(~j - 65/2)~. (2)
--~ 0.6
0.4 0.2 0.0
Note that unlike in a reflective measurement, only the relative intensity of the fluorescence yield is necessary for evaluating the interface roughness and density of multilayers. Figures l(a) and l(b) show the calculated Ni Ka fluorescence profiles of Ni/C multilayers for various roughnesses and Ni layer densities. For the calculations, the interface height distribution was assumed to be an exponential function[8]. The overall shape of the fluorescence yield profiles can be explained by the change in the phase of the reflectivity at each layer, which is about ~r across the Bragg reflection[3]. The fluorescence yield profiles became flatter with increasing roughness (Fig. l(a)), and the dip width in the fluorescence yield in-
0.60
I
0.65
I
I
0.70 0.75 Angle(degrees)
0.80
Fig. 1 Ni Ka fluorescence yields of Ni/C multilayers for varous roughnesses and Ni layer densities. The flattening of the profiles is qualitatively explained by the dependence of the absolute reflectivity on roughness. When the roughness increases, the second and third terms in eq. (1) decrease, which leads to flattening of the fluorescence yield profiles. The width of the dip is thought to reflect a change in the refractive indices of the multilayers, analogous to the change in optical multilayer structures[9]. The refractive
451 indices are related to the multilayer density, which explains the widening of the dip in the fluorescence yield profiles. These features suggest that it is possible to independently determine both the roughness and the density of multilayers.
2nd and 3rd peak intensity, the multilayer structure changed by the diffusion between the nickel and carbon layers. 1.o
01 ' 1 II
Ill
°N --
3
Experimental
0.00~
O
The multilayer that we studied had 35 layer pairs, each consisting of a Ni layer and a C layer, deposited on a 3-inch wafer by RF magnetron sputtering[10]. The periodic length was estimated to be about 56.8/~ from the evaporation rates of carbon and nickel. Transmission electron micrographs showed sharp interfaces, amorphous carbon layers, and microcrystalline nickel layers. A first-order reflectivity of 87% was obtained using a double- crystal diffractometer with a Cu Kc~ source (A=1.54 ~). Both x-ray reflectivity and standing wave measurement were carried out with a conventional double-crystal spectrometer. For measuring the reflectivity at grazing incidence, a set of 50#mwide slits were used after the first crystal. The fluorescence and other scattering spectra were measured with a pure Ge solid-state detector and analyzed with a multi-channel analyzer. The beam divergence was estimated to be about 0.0020 ° from the rocking curve of the Si(111) crystals at a (+, +) arrangement. A double-crystal diffractometer with a Si(ll 1) monochromator was used in the X-ray standing wave experiments. The fluorescence and other scattering spectra were measured with a pure Ge solid-state detector and analyzed with a multichannel analyzer. The influence of elastic scattering on the Ni Kc~ fluorescence yield was estimated to be small from the fluorescence and secondary scattering spectra.
4
R e s u l t s and D i s c u s s i o n
Figure 2 shows the x-ray reflectivity of the Ni/C multilayer with a Mo K s source (A=0.709 /?k). The inset shows an enlargement of the 2nd and 3rd Bragg peaks. The periodic length was estimated about 54.6 ~ from the Bragg peaks. Considering both the change in periodic length and in
Measured-
0.6
~0.5
0.8
1.0
1".2
ffl e"
I
e'-
0.0 0.0
L 0.5
Measured -Designe d ......
JL
~'.o
1.5
Angle (degree) Fig. 2 Measured and calculated X-ray reflectivity. Inset shows the schematic multilayer structure for calculation. To explain the experimental x-ray reflectivity, we calculated the x-ray reflectivity based on a nickel-carbon/carbon structure model with various thicknesses of a complex layer. From the peak intensities of the 2nd and 3rd Bragg reflections, the thickness ratio of the complex layer to the total layer was estimated to be 0.45 to 0.55, which is caused by the diffusion of nickel atoms into the carbon layer[7]. W e also found that the refractive index of nickel layer was about 80% of that of bulk nickel, which corresponds to 80% of the density of bulk nickel. The curves with marks in figure 3 shows the firstorder Bragg reflection and Ni Kcz fluorescence yield. The Ni K s fluorescence yield is normalized by the background intensity far from the Bragg reflection area. To determine the roughness and density parameters from x-ray standing wave signals, we calculated the fluorescence yield for various roughnesses and densities. The carbon density was fixed at the density of bulk carbon due to its small effect on the fluorescence yield profiles, and a two-layer model was assumed with a nickel density of 8.876 g/cm 3 and a carbon density of 2.26 g/cm 3. Comparing measured and calculated profiles, we obtained good correspondence by setting the interface roughness r, 10 A and the layer density to the bulk denisty of nickel[7]. This result is
452 inconsistent with the x-ray reflectivity measurement, which suggests a more complex structure for Ni/C multilayer. To solve this inconsistency, we introduce a new interface model consisting of four layers: nickel/nickel-carbon complex/carbon/nickelcarbon complex layers for Ni/C multilayers. The inset in figure 3 shows the intensity ratio of 2nd and 3rd Bragg reflection for various thicknesses of the carbon and nickel-carbon layers. The region in which the intensity ratio of 3rd to 2nd is bigger than 1.0 is limited to a thickness ratio of about 0.5 of the carbon layer and 11.5 A of complex layer. This suggests that most of the nickel layers change to nickel-carbon complex but there still remains a core nickel layer which reflects x-rays. In figure 3, we show calculated fluorescence profiles based on the four-layer model with various interface roughnesses between the carbon and complex layers. The following parameters were used for calculations: 3.2 A for the nickel layer, 28.4 A for carbon layers, and 11.5 A for complex layers. Good correspondence was obtained with 0.0 to 2.5 A interface roughness, suggesting a sharp interface between the carbon and complex layers. This result is consistent with the T E M observation and x-ray reflectivity measurement. 5
Conclusions
Our new method can independently determine the interface roughness and densities of multilayers according to simulation results for Ni Kc~ fluorescence yield profiles with various interface roughnesses and densities, which are related to the reflectivity and the phase of the reflectivity. A 54.6 A-thick 35-period Ni/C multilayer was analyzed using both x-ray reflectivity measurement and this new method. From the x-ray reflectvity measurement, the thickness ratio and density of the nickel layer are about 0.5 and 80% of bulk nickel. However, x-ray standing wave measurement shows that the density of the nickel layer is equal to the bulk and the interface roughness is about 10 A +3 A. This can be explained by the existence of a nickel-carbon complex layer between the nickel and carbon layers. The simulation results based on a four-layer model show good
agreement between measured and calculated profiles for both x-ray standing wave and x-ray reflectivity measurement. This is consistent with the T E M observation, supporting the four-layer intrface model. o 3.0[ "~ [
~20 j.~ " [ ~, 2.5
®
_~ t.0
N 2.0
[
o.4
/",.
d=lO.OA -11.0 A " "
/ \ 11.5A -/ \ 12.OA-/" -,~, / ,, . . - - .,.,. o.s
o.6
o.7
Thickness ratio
E
-- 0.5
r=5.0 ..... r=7.5 --. measured -o-
h,raoo
0.0
.... 0.3
S 0.35
,~-.~ 0.4
. . 0.45
0.5
Angle (degrees)
Fig. 3 Measured and calculated X-ray reflectivity. Inset shows the schematic multilayer structure for calculation. References 1. B. W. Batterman: Phys. Rev. 133(1964) A759. 2. T. W. Barbee and W. K. Warburton: Mater. Left. 3(1984) 17. 3. J. B. Kortright: J. Appl. Phys. 61(1987) 1130. 4. S. I. Zheludeva, et al.: Rev. Sci. Inst. 63(1992) 1519. 5. E. Spiller: Rev. Phys. Appl. 23(1988) 1687. 6. M. Yamamoto and A. Arai: Thin Solid Films 233(1993) 268. 7. T. Kawamura and H. Takenaka: J. Appl. Phys. 75(1994) 3806. 8. D. G. Stern: J. Appl. Phys. 65(1989) 491. 9. M. Born and E. Wolf: Principle of Optica (Pergamon, New York, 1965) 3rd ed. 51. 10. H. Takenaka, Y. Ishii, H. Kinoshita and K. Kurihara: Prec. SPIE 1345(1990) 213.