JP2508018B2 - Fresnel Zone Plate - Google Patents

Description

The present invention relates to a Fresnel zone plate used as an imaging element in the field of X-ray linography.

(B) Conventional technology Since it is difficult to collect X-rays using refraction, Fresnel zone plates using diffraction are used as X-ray imaging elements.

Fresnel zone plates are currently manufactured by three methods: mechanical engraving by a ruling engine, electron beam straight line drawing, and holographic exposure.

The Fresnel zone plate is required to have a narrow ring width toward the outside, and the outermost shell ring width is λx / 2 to λx / 4 (λx:
It converges around the (used wavelength). Therefore, the diameter of the Fresnel zone plate for X-rays with a short operating wavelength (several to several hundreds of liters) is determined by the minimum ring width that can be manufactured.

However, the minimum ring width that can be produced by any of the above methods is about 0.2 μm, so only a Fresnel zone plate with a small diameter of around 0.1 mm could be produced. Due to the small aperture, the X-ray dose that can be used is limited, the exposure time becomes long, and the throughput deteriorates.

(C) Objective The present invention aims to realize a large diameter Fresnel zone plate with the ring width that can be manufactured at present.

(D) Configuration First, we will describe the case where an accurate ring marking can be made at the wavelength λx used for X-rays by mechanical marking or electron beam direct writing.

In FIG. 1, the radius of the n-th ring and the width of the opening of the Fresnel zone plate 2 are represented by rn, dn, and X-ray source 1, respectively.
The distance between the Fresnel zone plate 2 and the Fresnel zone plate 2 is a, and the distance between the plate 2 and the focal point (the position of the X-ray aberration-free image forming point) 3 is b.

Generally, if this is the Fresnel zone plate for the m-th order diffraction, the X-ray source 1-the upper end (diffraction point) of the nth ring 4-the X-ray passing through the condensing point 3 and the X-ray source 1- (n-1) th The optical path difference of the X-ray passing through the upper end 6 of the ring-the condensing point 3 is mλx.

However, γ ₀ = o.

In the expression (1), n is satisfied from 1 to n. Therefore, when these n expressions are arranged and the sums thereof are obtained, the following is obtained.

Than this Becomes

This represents the n-th ring radius of the Fresnel zone plate on which the m-th order diffracted light is focused, and (m) represents the diffraction order. The optical path difference between the X-ray source 1-diffraction point 4-converging point 3 and the X-ray source 1-the lower end of the nth ring 5-X-ray passing the converging point 3 should be mλx / 2. If the width d _n ^(m) of the opening of the n-th ring of the m-th order Fresnel zone plate is selected, Becomes

The multi-stage Fresnel zone plate has a number of zones n (radius up to the minimum ring width that can be manufactured with a certain diffraction order m).
r _n ^(m) ) is taken, and the further increase in diameter is to be achieved by increasing the diffraction orders.

Therefore, if the ring width can be accurately marked, given the minimum ring width d min that can be manufactured, the fabrication of the multi-stage Fresnel zone plate is as follows.

First, calculate the radius r _n ⁽¹⁾ and the ring width d _n ⁽¹⁾ in the 1st-order diffractive Fresnel zone plate (m = 1) to increase n, and b _n1 ⁽¹⁾ ＞ d min ＞ b _{n1 + 1} Find the number of zones n ₁ that gives ⁽¹⁾ . In the 1st order diffraction, the radius r _{n1 at} this time
^{Since (1)} is the fabrication limit, next, the diffraction order m is set to 2, and similarly n ₂ is obtained so that d _n2 ⁽²⁾ > d _min > d _{n2 + 1} ⁽²⁾ . Through the same procedure as above, r _n1 ⁽¹⁾ , r
_{Find n2} ⁽²⁾ , r _n3 ⁽³⁾ .... From this, the radius from 0 to r _n1 ⁽¹⁾ is the first diffraction order, and the radius is from r _n1 ⁽¹⁾ to r _n1 ⁽¹⁾
Up to _n2 ⁽²⁾ , the second-order diffraction has a radius from r _n2 ⁽²⁾ to r _n3
⁽³⁾ up to the 3 order diffraction ...... Fresnel zone (3) and (4) as given by formulas radius r _n ^(m) and ring width
Engraving with d _n ^(m) makes it possible to increase the diameter of the Fresnel zone plate using high-order diffraction.

Next, a case of manufacturing a multi-stage Fresnel zone plate by holographic exposure will be described. When accurate marking lines are possible, there is no aberration in principle, but since the exposure wavelength λ _H and the use wavelength λ _X are different in holographic exposure, the aberration that occurs must also be considered. Factors that determine the maximum radius of the Fresnel zone plate in the m-th order diffraction include the aberration at the focal point and the conservation of the diffraction order m in addition to the minimum ring width that can be manufactured. First, given the maximum manufacturable radius γ ₀ in the pre-diffraction order (m-1) as shown in Fig. 2, X-ray source 1-diffraction point 4-focus point 3 and X-ray source 1 The radius γ ₁ of the next (first in the m-th order diffraction) ring such that the optical path difference between the lower end 6 of the n-th ring and the focal point 3 is mλx is obtained.

Next, when this ring is made at the exposure wavelength λ _H , γ ₀ , γ
₁ is the (n-1) th and nth radii γ at λ _H , respectively
_n-1, gamma corresponds to _n, the convergence point of two spherical waves at the exposure wavelength 7 and diffraction points 4 convergence point 8 converging point 7 ring lower end 6
-Determine the condensing positions ξ and η of the spherical wave so that the optical path difference at the converging point 8 becomes λ _H.

It is sufficient to determine n, ξ, and η so as to satisfy the expression (6), but this is not uniquely determined, so here, for the time being, consider only the case of ξ = η as the first approximation. become that way. However, (m) represents the diffraction order. Next, the maximum radius where the given diffraction order m is stored is found. As shown in FIG. 3, m of λ _X of X-ray by (n-1) th and nth rings (radius γ _n-1 , γ _n ) made with λ _H
If the imaging positions (focus points) of the 2nd and (m + 1) th order diffracted lights are 9 and 10 (distances from the Fresnel zone plate 2 are b _m and b _{m + 1} , respectively), Becomes Now, assuming that the diffraction order m of the convergent light closest to the focus point 3 with no aberration is defined by b _{m + 1} <b <b _m (9), from equations (8) and (9) Becomes Assuming that the diffraction order of X-rays focused near b is m _N by the outermost shell ring (radius γ _N ) created with exposure wavelength λ _H and exposure distance ξ ^(m) And in order for this to be equal to the diffraction order m initially given, Therefore, if it is approximated as γ _N ² , γ _{N + 1} ² << a ² , b ² , Becomes

The radius of the nth ring when exposed with two spherical waves (ξ = η) is And the number of rings when γ _max is determined is N
And N is defined as γ _N <γ _max <γ _{N + 1} , Becomes From equations (13) and (12), the maximum radius γ _{N in} which the diffraction order m given at the beginning is stored can be found. The width d _N of the opening of the Nth zone is Given in.

Also, as shown in FIG. 3, the aberration C _N on the image plane is Defined by

The maximum radius of the Fresnel zone plate in the mth diffraction is
First, from the conservation of the diffraction order, it is controlled by the equations (11), (12), and (13). Furthermore, given the minimum ring width d _min that can be manufactured and the allowable aberration C at the image formation point, d _min < It is restricted so that d _N , C> C _N.

(E) Example Using 5.4Å as the wavelength λx used, a = 150 mm b = 680 mm
And

First, Fig. 4 shows the calculation result of the maximum radius when accurate carving is possible. However, the minimum line width d _min that can be manufactured is 0.
It was set to 2 μm.

Next, the result of the holographic exposure is shown in FIG.
The exposure wavelength λ _H is 4416Å of He-Cd laser, and d _min =
The distance was 0.14 μm and C = 0.18 mm.

In the above holographic exposure method, the simplest case was considered for simplicity, but it is not necessary to limit to the case of a spherical wave of ξ = η, and the aberration etc. can be reduced so that
This ξ, η or the exposure wavefront may be optimized.

(F) Effects Since the present invention allows the Fresnel zone plate to have a large diameter in the X-ray region, it is expected that the use efficiency of X-rays is increased, the exposure time is shortened, and the throughput is improved. .

[Brief description of drawings]

FIG. 1 is a diagram for explaining a general m-th order diffractive Fresnel zone plate, FIG. 2 is a diagram for explaining an m-th order diffractive Fresnel zone plate by holographic exposure, and FIG. 3 is a Fresnel zone made by holographic exposure. Fig. 4 is a diagram for explaining image formation by a plate, Fig. 4 is an example of calculation of the maximum radius that can be manufactured when accurate marking is possible, and Fig. 5 is an example of calculation of the maximum radius when the holographic exposure method is used. is there. 1 ... X-ray source, 2 ... Fresnel zone plate 3 ... Focus point 4 ... Top of nth ring (diffraction point) 5 ... Bottom of nth ring 6 ... (n-1) th Upper end of the ring of 7 ... Convergence point of two spherical waves at exposure wavelength 9 ... Image forming position of m-th order diffracted light by nth zone and (n-1) th zone 10 ... nth zone And the imaging position of the (m + 1) th order diffracted light by the (n-1) th zone

Claims (1)

(57) [Claims] 1. A Fresnel zone plate comprising a multi-stage Fresnel zone for collecting light in higher diffraction orders from the center to the outside.