JPH07191208A - Zone plate and its production - Google Patents

Abstract

PURPOSE:To provide a zone plate with which the max. diffraction efficiency is obtd. by taking absorption and interference conditions (phase difference=2pi) into consideration and using a process for production suitable for the same. CONSTITUTION:This zone plate 1 is constituted by forming plural concentrie circular zones expressed by rn=(2nlambdaf)<1/2> (where n; natural number, lambda; wavelength, f; focal length) in zone radius rn of the n-th zone by two kinds of materials varying in refractive index. At this time, the respective zones are composed of two kinds of the materials varying in the refractive index and the mixing ratios of two kinds of these materials are so continuously changed as to attain {n-(r<2>/lambdaf)}: (r<2>/lambdaf-n+1) according to the radius (r).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a zone plate used as an image forming optical system in an X-ray microscope or the like.

[0002]

2. Description of the Related Art Generally, the use of a zone plate as an image forming optical system is limited to a special purpose.
It is used for imaging the line region. The refractive index of all materials for electromagnetic waves in the soft X-ray region (wavelength 1 to several tens of nm) is about 1
Therefore, the refractive optical system cannot be used. Further, the reflectance of the substance is low in the soft X-ray region, and it is difficult to use a reflection type optical system. Therefore, an oblique incidence optical system utilizing total reflection is used, but even in that case, it is difficult to realize an optical system with large aberration and good performance. In addition, a direct-incidence type reflective optical system using a multilayer film may be used,
If the wavelength is shorter than 5 nm, the layer thickness becomes very thin and it becomes difficult to manufacture. Therefore, it is difficult to realize a direct-incidence type catoptric system capable of obtaining a sufficient reflectance.

Therefore, in the soft X-ray region, a zone plate optical system utilizing the diffraction phenomenon is often used, and an example thereof is shown in FIG. In this case, the zone plate 1
Is a total of n layers (n is a natural number) of the electromagnetic wave transmission zone (the white portion in the drawing) and the light shielding zone (the black portion in the drawing).
It is formed by alternately forming concentric circles and is configured as an amplitude type. In order to define the radius r _{n of} each zone, the following approximate equation is generally used. r _n = √ (nλf) (1) where λ is the wavelength and f is the focal length of the zone plate.

The theoretical maximum diffraction efficiency of this amplitude type zone plate is 1 / π ² = 10%, and in actuality, only a few% can be obtained due to absorption by the substance and manufacturing error. Therefore, instead of the light-shielding zone, a phase difference type zone plate is proposed in which a zone for changing the phase of the electromagnetic wave by π (half wavelength) is used to improve the diffraction efficiency up to 4 / π ² = 40%. However, even in this zone plate, the maximum diffraction efficiency is not obtained due to the effect of absorption by the substance. At present, when the zone plate is used as an objective lens of a microscope, a high resolution of 0.03 μm is realized. However, since it is very difficult to produce such a high resolution zone play and such a high resolution zone plate, sufficient diffraction efficiency has not been obtained. This is because the resolution of the zone plate is determined by the line width of the outermost zone plate, that is, the minimum line width.

This will be described below. As is well known, the resolution δ of the optical system is the wavelength λ and the numerical aperture N of the optical system.
It is determined by A and is expressed by the following equation. δ = 0.61λ / NA (2) The numerical aperture of the zone plate is determined by NA = λ / 2w (3) where w is the width of the outermost zone. Therefore, from the expressions (2) and (3), the resolving power δ of the zone plate optical system is given by δ = 1.22w (4). Therefore, the resolution is determined by the line width of the outermost zone and does not depend on the wavelength. Since the zone width of the zone plate gradually decreases from the center toward the outside, the width of the outermost zone corresponds to the minimum line width in the zone plate.

0.03μ, which is the highest in the current state of the art
The outermost zone width of the zone plate having a resolving power of m is about 0.025 μm from the equation (4). It is very difficult to process such a fine line width, and electron beam lithography is used. However, in the case of such a fine line width, even if it can be realized, the aspect ratio is at most about 8, and the thickness of the zone plate is 0.2 μm at the maximum. For example, when Ti, which has large absorption in the wavelength region of 2.4 nm, is used for the light shielding zone, the light shielding amount is not sufficient when the thickness of the zone plate is 0.2 μm, and the diffraction efficiency is only about 6%. In order to obtain the theoretical maximum diffraction efficiency of 10%, the thickness of 0.4 μm is required.

[0007]

When a zone plate is used in a microscope, a high resolution can be obtained as described above, but the diffraction efficiency is low and a zone plate manufactured by electron beam lithography is insufficient. Since the thickness cannot be obtained, a bright optical system cannot be constructed. Further, in the case of a conventional retardation type zone plate using a zone having a phase difference of π (half wavelength) instead of the light shielding zone, whether or not the light shielding effect due to absorption occurs depends on the thickness of the zone plate. However, the thickness was not optimized in consideration of absorption.

The present invention has been made in view of the above-mentioned problems. The diffraction efficiency of the zone plate is greatly improved by continuously changing the phase in each zone, and the absorption and interference conditions (phase difference) are increased. ), The zone plate which can obtain high diffraction efficiency by a manufacturing method suitable for it is aimed at.

[0009]

For this purpose, the zone plate of the present invention has the zone radius r _n of the _nth zone as r _n = (2nλf)
^1/2 (however, n: natural number, λ: wavelength, f: focal length)
And a zone plate formed by forming a plurality of concentric zones, each zone having a different refractive index.
It is composed of two kinds of substances, and the mixing ratio of the two kinds of substances is continuously changed according to the radius r, and the mixing ratio is {n-
(R ² / λf)} preferably to continuously changes in accordance with ^{:( r 2 / λf-n +} 1). Further, according to the method for manufacturing a zone plate of the present invention, as described in claim 3, a cylindrical member made of one of the two kinds of substances having different refractive indexes or other substances is rotated to form the cylindrical member. The two types of substances having different refractive indices are {n- (r ² / λ
f)}: (r ² / λf−n + 1) (where n is a natural number, r is a radius, λ is a wavelength, f is a focal length), and a film is formed at a mixing ratio to form a zone. The zone plate is manufactured by cutting the columnar member in which the formation of the zone is completed in the direction perpendicular to the axis.

[0010]

Although a blazed grating is well known as a reflection type phase diffraction grating, the present invention applies this principle to a transmission type diffraction grating. Hereinafter, the diffraction efficiency of the zone plate (blaze zone plate) according to the present invention will be calculated. The function f (x) having a period of 2π can be expanded into a Fourier series as in the following equation.

[Equation 1]

Therefore, in the case of the amplitude type, 0 and 1 are set for each π.
In the periodic function that repeats and, 0 and 1 correspond to transmission and shading, respectively.

[Equation 2]Is represented by (N is an integer). Where x → πr² / Λf
Considering the variable transformation of, the radius of each zone is r_n= √ (n
It becomes a zone plate of λf). Where the 0th-order diffraction effect
The rate is (1/2)² = 25%, the diffraction efficiency of the first-order light is 1 / π
² And the well-known result.

On the other hand, consider the case of the phase difference type. 1 for every π
And a periodic function that repeats −1 (= exp (−jπ)) is given by the following equation.

[Equation 3] Therefore, 0th order light = 0%, 1st order light = 4 / π ² = 40.
5%, which is also a well-known result.

Here, 2 in each zone as shown in FIG.
Consider a blazed grating that changes by π (wavelength). The zone width of this blazed grating corresponds to the above-mentioned two of the amplitude type and the phase difference type, and the radius r _n of the zone boundary is r _n = √ (2nλf).
Considering that there is no absorption, the following equation

[Equation 4] Is obtained. Therefore, the diffraction efficiency E1 of the first-order diffracted light is
Is E ₁ = a ₁ cosx + b ₁ sinx = cosx−jsinx = exp (−jx) (9), and it can be seen that 100% diffraction is obtained in the + 1st order.

However, in reality, the two substances used have absorption, and the absorption becomes large in the soft X-ray region, so it is necessary to consider the complex refractive index of the substance used. Now, absorption and phase changes t (x) and φ (x) as shown in FIG.
Considering a transmissive blazed grating having the following, the substances 1 and 2 are mixed in a ratio of (x / 2π): {1- (x / 2π)} in order to make the phase change in the zone as described above. I decided to. That is, the mixing ratio is changed to 0 → 1 or 1 → 0 according to the change of x → 2π. Needless to say, it is not always necessary to change it from 0 to 1, but it is also possible to change it from 0 to 0.9, 0.1 to 0.8, or the like. Further, instead of mixing the two substances to make them inhomogeneous (corresponding to GRIN), they may be simply constituted by a thickness ratio.

Here, the refractive index of the substance 1 is n ₁ −jk ₁ ,
Assuming that the refractive index of the substance 2 is n ₂ −jk ₂ and the thickness of the zone plate is d, f (x), t (x), φ (x)
F (x) = t (x) exp {−jφ (x)} (10) t (x) = exp {(k ₂ −k ₁ ) xd / λ} exp (−2πk ₂ d / λ) ) (11) φ (x) = (n ₁ −n ₂ ) xd / λ + 2πn ₂ d / λ (12) (where n ₁ , k ₁ , n ₂ and k ₂ are the actual refractive indices of the respective substances). Part and imaginary part).

Here, if C = exp (-2πk ₂ d / λ) exp (-j2πn ₂ d / λ) (13), then

[Equation 5]

[0017]

[Equation 6] Is obtained.

The first-order diffracted _{light, = a 1 cosx + b 1} sinx {(a 1/2) + (b 1/2) j} exp (jx) + {(a 1/2) - (b 1/2) j } Exp (-jx) (16), the diffraction efficiency of the + 1st order diffracted light is obtained by the following equation. _{E 1 = | (a 1/} 2) - (b 1/2) j | 2 (17) Therefore, the thickness d of the zone plate, it is preferable to determine, as the value E ₁ is maximum. Then, this value is slightly smaller than the thickness obtained from the interference condition 2π (for one wavelength) when there is no absorption, and is preferably set to about 0.6 to 0.9 times the thickness. Note that, in the above equation, the zone plate is represented by the conversion of x → 2πr ² / λf, which is the same as the normal zone plate.

The actual mixing ratio of the two substances is the zone radius r
_In the case of a zone plate having zone boundaries of _n = √ (2nλf) (n; natural number, λ; wavelength, f; focal length), FIG.
It becomes the ratio shown in. That is, substance 1: substance 2 = 2nπ- (2πr ² / λf): {2πr ² / λf-2 (n-1) π} = {n- (r ² / λf)} :( r ² / λf-n + 1 ) (18) However, the mixing ratio may be a curve-like change as shown in FIG. 6 or a linear (proportional) change thereof. The zone plates are r _n and r _n-1.
It has a zone consisting of between and, and the mixing ratio there is as follows. That is, between r ₁ = √ (2λf) and r ₀ = 0, φ (r) = (2π / λf) (r
−r ₀ ) ² r ₂ = √ (4λf) and r ₁ = √ (2λf), φ (r) = (2π /
Between (λf) (r−r ₁ ) ² r ₃ = √ (6λf) and r ₂ = √ (4λf), φ (r) = (2π /
The relationship is λf) (r−r ₂ ) ² .

Since the thickness d of the zone plate optimally designed so as to satisfy the above expression (17) is generally larger than the value possible by the conventional technique, it is necessary to devise the manufacturing method. is there. Further, a special method is required to form the two kinds of substances in a zone at a predetermined ratio according to, for example, the formula (18). For example, first, a thin wire (several tens to several hundreds of μm) is rotated as shown in FIG. 9A, and two kinds of substances are formed in a predetermined ratio so that each zone has the above mixing ratio. In addition, about this, Pro
c. A basic manufacturing method is proposed on page 103 of SPIE, 316 (1981). The radius of film formation is based on the formula described in claim 1, for example. After forming several tens to several thousands of layers, the surroundings are covered with a substance having substantially the same mechanical characteristics (for example, abrasion degree and hardness) or a substance such as epoxy as shown in FIG. As shown in FIG. 3C, the cutting is performed in a vertical direction with a cutting means such as a microtome so as to be slightly thicker than a desired thickness d. Then, the cut pieces are carefully processed by polishing, ion etching or the like to smooth the cut surface. As described above, the absorption of the substance used in determining the thickness of the zone plate is taken into consideration, so that the maximum diffraction efficiency is obtained. Further, the zone plate formed by cutting the zone formed on the wire can be mass-produced.

[0021]

Embodiments of the present invention will now be described in detail with reference to the drawings. FIG. 1 is a characteristic diagram showing the diffraction efficiency of the zone plate of the first embodiment of the present invention. This zone plate 1
, Each zone is arranged as shown in FIG.
It is configured as a zone plate for 0.4 nm.

Generally, considering the diffraction efficiency in consideration of absorption, both of the two kinds of substances used have little absorption, and
It is a condition of material selection that the materials are selected so that the difference between the real parts of the refractive indices of the two materials is as large as possible, and that they are matched with the zone plate as thin as possible.

In the zone plate having the structure shown in FIG.
As an example of a combination with less absorption that satisfies the above conditions,
The combination of the substance Sc and the substance Co is selected,
The thickness of the phrased zone plate (BZP) is 0.29
When the thickness is μm, a diffraction efficiency of 12% is obtained. In this case, the thickness at which maximum efficiency is obtained assuming no absorption, that is, the phase difference of the electromagnetic waves generated by the zones is 2π (1
Interference condition φ = 2π (n ₁ −n ₂ ) d ₁ /
Thickness obtained from λ = 2π d ₁ = λ / (n ₁ −n ₂ ).
The thickness is about 0.63 times 0.46 μm. For comparison, the diffraction efficiency of the conventional phase zone plate (PZP) is also shown, but the maximum diffraction efficiency is P in this example.
ZP is better. However, since BZP has a wider peak width, it has less wavelength dependence and can be used in a wider range of wavelengths. In addition, as an example of a combination of substances having low absorption, any one of groups (Sc, Ti, Ba)
One substance and any one of the groups (Co, Ni, Cu)
Excellent combination with three substances.

FIG. 2 is a characteristic diagram showing the diffraction efficiency of the zone plate of the second embodiment of the present invention. In this zone plate 1, each zone is arranged as shown in FIG. 10 and is configured as a zone plate for a wavelength of 3.2 ± 0.32 nm. In this zone plate, a combination of the substance Sc and the substance Cr and a combination of the substance Sc and the substance V are selected as an example of a combination having a small absorption which satisfies the above condition, and the thickness of the phrased zone plate (BZP) is selected. Diffraction efficiencies of 26% and 22% are obtained at 0.48 μm and 0.67 μm, respectively, and these diffraction efficiencies are superior to PZP. In this case, the substances Sc, C
The thickness of the combination of r is about 0.77 times the thickness of 0.62 μm determined by the above interference condition.

FIG. 3 is a characteristic diagram showing the diffraction efficiency of the zone plate of the third embodiment of the present invention. The zone plate 1 has zones arranged as shown in FIG. 10 and is configured as a zone plate for a wavelength of 2.4 ± 0.24 nm. In this zone plate, a combination of the substance V and the substance Fe is selected as an example of a combination with less absorption that satisfies the above condition, and when the thickness of the phrased zone plate (BZP) is 0.43 μm,
A maximum diffraction efficiency of 30% is obtained. In this case, the thickness of the combination of the substances V and Fe is about 0.81 times the thickness of 0.53 μm determined by the above interference condition. For comparison, the diffraction efficiency of PZP is also shown, but since this is 22%, this example is superior. In addition, as an example of a combination of substances having low absorption, a combination of any one substance of the group (V, Mg) and any one substance of the group (Fe, Co, Ni) is excellent.

FIG. 4 is a characteristic diagram showing the diffraction efficiency of the zone plate of the fourth embodiment of the present invention. In this zone plate 1, each zone is arranged as shown in FIG.
It is configured as a zone plate for ± 0.1 nm. In this zone plate, a combination of the substance Mg and the substance Mo is selected as an example of a combination having less absorption that satisfies the above condition, and when the thickness of the phrased zone plate (BZP) is 0.85 μm, the maximum is obtained. A diffraction efficiency of 22% is obtained, which is better than PZP. In this case, the thickness of the combination of the substances Mg and Mo is 1.12 μ which is determined by the above interference condition.
It is about 0.76 times m. In addition, as an example of a combination of substances having low absorption, groups (B, C, Mg, Al,
Any one substance of Si) and group (Mo, Nb,
The combination of Cr) with any one substance is excellent.

FIG. 5 is a characteristic diagram showing the diffraction efficiency of the zone plate of the fifth embodiment of the present invention. The zone plate 1 has zones arranged as shown in FIG. 10, and is configured as a zone plate for wavelengths of 0.6 ± 0.06 nm. In this zone plate, a combination of the substance B and the substance Ru is selected as an example of a combination with less absorption that satisfies the above condition, and when the thickness of the phrased zone plate (BZP) is 1.5 μm, the maximum is obtained. A diffraction efficiency of 37% is obtained. In this case, substance B,
The thickness of the Ru combination is about 0.86 times the thickness of 1.75 μm determined by the above interference condition. In addition, as an example of a combination of substances having low absorption, a group (B, M
g, C, Sc) any one substance and group (C
o, Ni, Cu, Tc, Ru, Rh, Pd)
Excellent combination with three substances.

As described above, the zone plate needs to have a thickness of about 0.3 to 1.5 μm, and since the composition ratio of the substance is changed according to the radius, the ultrathin multilayer film different from the conventional method is used. Zone plate is manufactured using the technology. For example, first, a thin copper wire having a thickness of several tens to several hundreds of μm is prepared. This wire shall have a surface or smooth material. Next, the surface is smoothed by electropolishing (alternatively, a substance such as B4 C that forms a smooth surface when formed into a film may be formed on the wire). The surface roughness is preferably several Å to several tens Å rms or less. The wire is placed on a jig that can be rotated about its axis.

Next, two kinds of materials are formed on the wire by magnetron sputtering. At that time, the film is formed while controlling the composition ratio (mixing ratio) of the film so as to follow the equation (18), for example. At that time, the change in the composition ratio of the film is set by adjusting the distance between the wire and each substance with respect to the target (instead, the opening / closing time of the shutter should be finely controlled according to the composition ratio). Alternatively, only one of the two substances may be changed or both of them may be changed. When several hundreds to several thousands of layers are formed, the surroundings are covered with a substance having mechanical characteristics similar to at least one of the two types of substances. Once it is covered sufficiently thick (for example, at least twice the diameter of the manufactured zone plate), the thin wire-shaped zone plate is further surrounded by a resin such as epoxy to make it easy to handle (for example, a 20 × 20 mm prism). Shape).

In this state, a cutting device such as a microtome cuts the film perpendicularly to the axis to a thickness of, for example, several microns so that the thickness d becomes slightly larger than the desired thickness d. Next, the sheet-shaped zone plate is carefully polished by polishing, ion etching or the like so as not to damage the surface or the internal structure, and thinned to a desired thickness d. At this time, a plurality of zone plate wires can be collectively operated, and in this case, a plurality of zone plates can be manufactured at one time, which enables mass production.

When this method is used, the thickness of the zone plate can be arbitrarily set up to a thickness of about several tens of μm, so that the thickness for optimizing the diffraction efficiency can be considered with high priority and high efficiency can be obtained. It becomes possible to manufacture zone plates.
Furthermore, a multilayer film can be formed to a minimum of about 1 nm, and therefore a zone plate with a resolution of 1.22 nm can be manufactured.

When used in an actual image forming optical system, the zone plate may be shaped as in the following embodiments. The radius r _{n of} each zone is (1)
It is given by the expression r _n = √ (nλf). For example, if λ = 3 nm and f = 1 mm, then n
= 1,000, r ₁₀₀₀ = 54.77, so the first substance is formed on a wire of φ = 109.54 μm up to r ₁₀₀₁ = 54.80 μm: r ₄₉₉₉ = 122.46 μm r ₅₀₀₀ = 122 The first and second materials are alternately formed up to 0.47 μm. Then, the periphery thereof is hardened with epoxy or the like and cut and polished to form a zone plate. As a result, a zone plate having a diameter of 244.94 μm is formed. The inside of φ109.54 μm does not contribute to the image formation, but this part is usually the position where the 0th-order light-shielding plate is placed, and there is no inconvenience.
It becomes an annular optical system of No. 5. The line width of the outermost shell is 0.01μ
m, the resolving power is 0.012 μm, and NA = 0.15.

[0033]

As described above, in the zone plate of the present invention, the zone radius r _n of the _nth zone is r _n =
(2nλf) ^1/2 (where n is a natural number, λ is a wavelength,
f: focal length), a zone plate formed by forming a plurality of concentric zones, each zone being composed of two kinds of substances having different refractive indices, and the mixing ratio of the two kinds of substances being For example, {n- (r ² / λf)} :( r
² / λf−n + 1), the cylindrical member made of one of the two kinds of substances having different refractive indexes or other substances is rotated, and Two types of materials with different refractive indices are converted into {n- (r ^{2
/ Λf)} :( r 2 /} λf-n + 1) is formed in a mixing ratio defined by forming a zone, a cylindrical member which forms is complete multiple zones with respect to the axis was cut vertically By manufacturing the zone plate, it is possible to manufacture the zone plate that can obtain the maximum diffraction efficiency in consideration of the absorption and the interference condition (phase difference = 2π).

[Brief description of drawings]

FIG. 1 is a characteristic diagram showing diffraction efficiency of a zone plate according to a first embodiment of the present invention.

FIG. 2 is a characteristic diagram showing the diffraction efficiency of the zone plate of the second embodiment of the present invention.

FIG. 3 is a characteristic diagram showing the diffraction efficiency of the zone plate of the third embodiment of the present invention.

FIG. 4 is a characteristic diagram showing the diffraction efficiency of the zone plate of the fourth embodiment of the present invention.

FIG. 5 is a characteristic diagram showing the diffraction efficiency of the zone plate of the fifth embodiment of the present invention.

FIG. 6 is a diagram illustrating a mixing ratio of two kinds of substances in the zone plate of the present invention.

FIG. 7 is a diagram illustrating a phase characteristic of the zone plate of the present invention.

FIG. 8 is a diagram illustrating absorption characteristics of the zone plate of the present invention together with phase changes.

9A to 9C are views for explaining a method for manufacturing a zone plate of the present invention.

FIG. 10 is a diagram for explaining the zone arrangement of the zone plate of the present invention.

[Explanation of symbols]

 1 Blazed zone plate (zone plate)

Claims (3)

[Claims] 1. A zone radius r _n of the _n -th zone is a plurality of concentric zones represented by r _n = (2nλf) ^1/2 (where n is a natural number, λ is a wavelength, and f is a focal length). A zone plate formed by forming each zone by two kinds of substances having different refractive indexes, and the mixing ratio of the two kinds of substances is continuously changed according to the radius r. Characteristic zone plate. 2. The mixing ratio is continuously changed according to {n- (r ² / λf)} :( r ² / λf-n + 1). Zone plate. 3. One of two kinds of substances having different refractive indexes
Rotates a cylindrical member composed of other substances,
The two types of substances having different refractive indexes are added to the columnar member as {n- (r²/ Λf)}: (r²/ Λf-n + 1)
However, n; natural number, r _n; Radius, λ; wavelength, f; focal length
Separation) to form a zone by forming a film with a mixing ratio defined by
The cylindrical member on which multiple zones have been formed is suspended from the shaft.
Characterized by manufacturing the zone plate by cutting in the vertical direction
And a method for manufacturing a zone plate.