Method for evaluating influence of roughness on average reflectivity of extreme ultraviolet curved-surface multilayer film reflector

Abstract

The invention relates to a method for evaluating the influence of roughness on the average reflectivity of an extreme ultraviolet curved-surface multilayer film reflector, which comprises the following steps of: manufacturing a film coating clamp with the same outline as an extreme ultraviolet curved-surface multilayer film reflector to be evaluated, and uniformly distributing holes for coating a small-size plane element sample on the film coating clamp; acquiring the surface roughness of the small-size planar multilayer film reflector samples at different positions; calculating the reflectivity of each small-size plane multilayer film reflector sample; and calculating the average reflectivity of the extreme ultraviolet curved-surface multilayer film reflector to be evaluated. The method is suitable for a short-wavelength thin film element of which the reflectivity is sensitive to roughness; the method can achieve the evaluation of the influence of the roughness on the average reflectivity of the extreme ultraviolet curved-surface multilayer film reflector under the condition that there is no device for testing the reflectivity of the extreme ultraviolet curved-surface multilayer film reflector. And meanwhile, the average reflectivity of the large-size extreme ultraviolet curved-surface multilayer film element can be calculated through the small-size planar multilayer film element, so that the process optimization cost of the large-size extreme ultraviolet curved-surface multilayer film element is greatly reduced.

Description

Technical Field

[0001] The invention relates to the application field of extreme ultraviolet optical technology, and in particular to a method for evaluating the effect of roughness on the average reflectivity of an extreme ultraviolet curved multilayer film reflector. Background Art

[0002] EUV lithography technology refers to integrated circuit lithography technology that uses 13.5nm EUV light as the exposure light source. Since most materials have absorption in the EUV band, a reflective optical system must be used to realize the design of the EUV lithography system. In order to pursue high efficiency, the reflectivity of the EUV multilayer film reflector must be maximized. The EUV multilayer film reflector is a one-dimensional Bragg crystal made of alternating high and low refractive indices. When the thickness of the multilayer film period meets the Bragg condition, the reflected light from each interface produces constructive interference, thereby achieving high reflection. A variety of curved multilayer film reflector elements of different sizes and shapes are required in the EUV lithography system. Compared with flat multilayer film reflector elements, the development of curved multilayer film reflector elements is more complicated. On the one hand, the incident angles of light at different positions on the curved element are often different. To meet the specific spectral performance requirements at different positions, it is often necessary to distribute the film thickness at different positions on the element according to a specific change law, that is, to form a specific gradient distribution. On the other hand, due to the different incident angles of the target sputtered particles at different positions on the curved surface component, the surface roughness of the film layer at different positions on the component is often different. For multilayer film reflector components in the extreme ultraviolet band, the surface roughness of the film layer will have a great influence on its reflectivity. In order to obtain a curved multilayer film reflector component with a high average reflectivity, there are a large number of reflectivity test requirements in the process of multilayer film process research and development. For the measurement of the reflectivity of extreme ultraviolet multilayer films, the commonly used method is to use a synchrotron radiation device to measure small sizes, and the test element is a planar element. In order to directly obtain the reflectivity of a curved surface element, a special measuring device must be developed, which has a long research and development cycle and is expensive. This has a great impact on the process research and development of extreme ultraviolet curved multilayer film reflectors. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the above-mentioned shortcomings and provide a method for evaluating the effect of roughness on the average reflectivity of an extreme ultraviolet curved surface multilayer film reflector. The present invention is suitable for short-wavelength thin-film components whose reflectivity is sensitive to roughness; on the one hand, it can realize the evaluation of the effect of roughness on the average reflectivity of an extreme ultraviolet curved surface multilayer film reflector in the absence of an extreme ultraviolet curved surface multilayer film reflector reflectivity testing device; on the other hand, it can infer the average reflectivity of a large-sized extreme ultraviolet curved surface multilayer film component through a small-sized planar multilayer film component, greatly reducing the process optimization cost of the large-sized extreme ultraviolet curved surface multilayer film component.

[0004] The technical solution of the present invention is as follows:

[0005] A method for evaluating the effect of roughness on the average reflectivity of an extreme ultraviolet curved multilayer film reflector is characterized by comprising the following steps:

[0006] Step 1. Make a coating fixture with the same profile as the EUV curved multilayer reflector to be evaluated, and the coating fixture has M holes evenly distributed on it for coating small-sized planar element samples;

[0007] Step 2. Use atomic force microscopy to obtain the surface roughness σ of small-sized planar multilayer mirror samples at different positions i i , i=1,2,3……M;

[0008] Step 3. Calculate the reflectivity R of each small-size planar multilayer reflector sample i ;

[0009] Step 4. Calculate the average reflectivity of the EUV curved multilayer mirror to be evaluated

[0010] The fourth step is to calculate the average reflectivity of the EUV curved multilayer film reflector to be evaluated. The formula is as follows:

[0011]

[0012] Where S is the total surface area of ​​the EUV curved multilayer reflector, S i is the annular area corresponding to position i.

[0013] According to the above-mentioned evaluation method of the effect of roughness on the average reflectivity of the EUV curved multilayer film reflector, the characteristic is that S and S i Follow the steps below to obtain:

[0014] 1) The profile equation of the EUV curved multilayer reflector to be evaluated is obtained as follows:

[0015]

[0016] Wherein, Roc is the radius of curvature of the vertex of the EUV curved multilayer film reflector, and N is the conic coefficient of the EUV curved multilayer film reflector;

[0017] 2) Calculate the total surface area S0 of the top of the EUV curved multilayer reflector cut at different positions i i and the annular area S i , the formula is as follows:

[0018]

[0019] S i =S0 i+1 -S0 i(4)

[0020] Among them, D xy is the projection area of ​​the top of the curved multilayer film reflector cut off at position i on the xy plane, z x and z y are the derivatives of the profile equation with respect to x and y, respectively. For position i = M, i = M + 1 is the edge of the EUV curved multilayer reflector, S0 M+1 That is, the total surface area S of the extreme ultraviolet curved multilayer film reflector.

[0021] The step 3 calculates the reflectivity R of each small-sized planar multilayer reflector sample. i , including the following steps:

[0022] 1) Let i = 1, assume that the light source is at the focal point close to the element, and calculate the incident angle α of the incident light beam at position i on the sample surface i , the formula is as follows:

[0023]

[0024] Among them, r i is the radius of the bottom circle at position i, h i is the vertical height from position i to the top of the EUV curved multilayer reflector, and the calculation formula is as follows:

[0025]

[0026] k i is the slope at position i, calculated as follows:

[0027]

[0028] 2) The total number of film layers of the EUV curved multilayer film reflector to be evaluated is Q layers, the air is j=0 layer, and the substrate is j=Q+1 layer;

[0029] 3) Calculate the incident angle θ of the incident light beam on the jth layer of the small-size planar multilayer reflector at position i ij :

[0030] (a) Let j = 1;

[0031]

[0032] Where n0 is the refractive index of air, is the complex refractive index of the jth layer of the small-size planar multilayer reflector at position i;

[0033] (c) Let j = j + 1 and repeat step (b) until j = Q + 1;

[0034] 4) Let j = Q, calculate the j-th layer of the small-size planar multilayer reflector at position i and consider the interface roughness σ ij The reflection coefficient rc' ij ; Assuming the substrate is infinitely thick, then rc' i(Q+1) =0;

[0035]

[0036]

[0037]

[0038]

[0039] 5) Let j = j-1, repeat steps 4) to 5) until j = 0, and obtain the surface roughness σ of the air layer of the small-sized planar multilayer film reflector at position i i0 The reflection coefficient rc' i0 ;

[0040] 6) Calculate the reflectivity R of the small-sized planar multilayer reflector sample at position i i , the formula is as follows:

[0041] R i = abs(rc' i0 ) 2 (13)

[0042] 7) Let i = i + 1, and repeat steps 1) to 7) until i = M;

[0043] Among them, d ij is the thickness of the jth layer of the small-size planar multilayer reflector at position i, b ij is the amplitude factor, for the air layer b i0 =1, F ij is the Fresnel coefficient of the vertical polarization component, rc ij is the reflection coefficient of the jth layer of the small-size planar multilayer film reflector at position i without considering the influence of interface roughness, and λ is the wavelength of the incident light beam.

[0044] According to the above-mentioned evaluation method of the effect of roughness on the average reflectivity of the EUV curved multilayer film mirror, the method is characterized in that the interface roughness can be obtained by fitting the X-ray reflectivity test.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1) The present invention is applicable to short-wavelength thin-film elements whose reflectivity is sensitive to roughness.

[0047] 2) The method of the present invention can realize the evaluation of the influence of roughness on the average reflectivity of the extreme ultraviolet curved surface multilayer film reflector in the absence of an extreme ultraviolet curved surface multilayer film reflector reflectivity testing device.

[0048] 3) The average reflectivity of large-sized EUV curved multilayer film elements can be inferred through small-sized planar multilayer film elements, which greatly reduces the process optimization cost of large-sized EUV curved multilayer film elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a schematic diagram of the appearance of the extreme ultraviolet curved multilayer film reflector of the present invention.

[0050] Figure 2 Schematic diagram of a clamp used in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be further described below in conjunction with the embodiments and drawings.

[0052] refer to Figure 1 In this embodiment, the extreme ultraviolet curved multilayer film reflector is set to be an ellipsoidal shape, with a vertex curvature radius Roc=378.5320, a cone coefficient N=-0.6002, an ellipsoidal crown base radius L=100 mm, and a height H of 13.3027 mm.

[0053] Make a fixture with the same profile as the EUV curved multilayer reflector, such as Figure 2 , radius r i The interval is 15mm, with a total of 13 positions. The reflectivity evaluation method of this embodiment only needs to use the relevant data at 7 positions on one side. The structure of the prepared multilayer film system is sub / (Si / Mo) 50 Si / air, sub is a silicon substrate, and the central wavelength λ is 13.5nm. The complex refractive index of Mo material at 13.5nm is The complex refractive index of Si material and substrate at 13.5nm is The refractive index of air is n0 = 1-0i. The designed film thickness and the surface roughness data of the small-sized planar multilayer film reflector characterized by atomic force microscopy are shown in Table 1.

[0054] Calculate the vertical height h according to formula (6): i , calculate the slope k at different positions i according to formula (7) i Assuming that the wavelength λ of the incident light beam is 13.5 nm and the light source is at the focus of the ellipsoid close to the element, the incident angle α of the light beam at position i of the multilayer film reflector is calculated according to formula (5): i According to formulas (3) and (4), the annular area S at position i of the EUV curved multilayer reflector is calculated as iThe total surface area S can be calculated by the formula or by the annular area S i The calculation results are shown in Table 1.

[0055] The interface roughness of this embodiment uses the surface roughness data. The actual interface roughness is slightly lower than the surface roughness and can be obtained by X-ray reflectivity test fitting. The reflectivity R of the small-sized planar multilayer film reflector sample is calculated according to formulas (8) to (13): i , the calculation results are shown in Table 1.

[0056] Table 1. Example data

[0057]

[0058] Finally, the average reflectivity of the EUV curved multilayer film reflector described in the embodiment is evaluated according to formula (1): The more samples there are, the more accurate the evaluation results will be.

[0059] It can be seen that the present invention can overcome the shortcomings of the prior art, realize the evaluation of the influence of roughness on the average reflectivity of the EUV curved multilayer film reflector, and greatly reduce the process optimization cost of large-size EUV curved multilayer film elements.

Claims

1. A method for evaluating the effect of roughness on the average reflectivity of an extreme ultraviolet curved multilayer film reflector, characterized in that The following steps are involved: Step 1. Make a coating fixture with the same profile as the EUV curved multilayer reflector to be evaluated, and the coating fixture has M holes evenly distributed on it for coating small-sized planar element samples; Step 2. Use atomic force microscopy to obtain the surface roughness σ of small-sized planar multilayer mirror samples at different positions i i , i=1,2,3……M; Step 3. Calculate the reflectivity R of each small-size planar multilayer reflector sample i ; Step 4. Calculate the average reflectivity of the EUV curved multilayer mirror to be evaluated 2. The method for evaluating the effect of roughness on the average reflectivity of an extreme ultraviolet curved multilayer film reflector according to claim 1, characterized in that: The fourth step is to calculate the average reflectivity of the EUV curved multilayer film reflector to be evaluated. The formula is as follows: Where S is the total surface area of ​​the EUV curved multilayer reflector, S i is the annular area corresponding to position i.

3. The method for evaluating the effect of roughness on the average reflectivity of an EUV curved multilayer film reflector according to claim 2, characterized in that: S and S i Follow the steps below to obtain: 1) The profile equation of the EUV curved multilayer reflector to be evaluated is obtained as follows: Wherein, Roc is the radius of curvature of the vertex of the EUV curved multilayer film reflector, and N is the conic coefficient of the EUV curved multilayer film reflector; 2) Calculate the total surface area S0 of the top of the EUV curved multilayer reflector cut at different positions i i and the annular area S i , the formula is as follows: S i =S0 i+1 -S0 i (4) Among them, D xy is the projection area of ​​the top of the curved multilayer film reflector cut out at position i on the xy plane, z x and z y are the derivatives of the profile equation with respect to x and y, respectively. For position i = M, i = M + 1 is the edge of the EUV curved multilayer reflector, S0 M+1 That is, the total surface area S of the extreme ultraviolet curved multilayer film reflector.

4. The method for evaluating the effect of roughness on the average reflectivity of an EUV curved multilayer film reflector according to claim 1, characterized in that: The step 3 calculates the reflectivity R of each small-sized planar multilayer reflector sample. i , including the following steps: 1) Let i = 1, assume that the light source is at the focal point close to the element, and calculate the incident angle α of the incident light beam at position i on the sample surface i , the formula is as follows: Among them, r i is the radius of the bottom circle at position i, h i is the vertical height from position i to the top of the EUV curved multilayer reflector, and the calculation formula is as follows: k i is the slope at position i, calculated as follows: 2) The total number of film layers of the EUV curved multilayer film reflector to be evaluated is Q layers, the air is j=0 layer, and the substrate is j=Q+1 layer; 3) Calculate the incident angle θ of the incident light beam on the jth layer of the small-size planar multilayer reflector at position i ij : (a) Let j = 1; (b) Where n0 is the refractive index of air, is the complex refractive index of the jth layer of the small-size planar multilayer reflector at position i; (c) Let j = j + 1 and repeat step (b) until j = Q + 1; 4) Let j = Q, calculate the j-th layer of the small-size planar multilayer reflector at position i and consider the interface roughness σ ij The reflection coefficient rc' ij ; Assuming the substrate is infinitely thick, then rc' i(Q+1) =0; 5) Let j = j-1, repeat steps 4) to 5) until j = 0, and obtain the surface roughness σ of the air layer of the small-sized planar multilayer film reflector at position i i0 The reflection coefficient rc' i0 ; 6) Calculate the reflectivity R of the small-sized planar multilayer reflector sample at position i i , the formula is as follows: R i =abs(rc' i0 ) 2 (13) 7) Let i = i + 1, and repeat steps 1) to 7) until i = M; Among them, d ij is the thickness of the jth layer of the small-size planar multilayer reflector at position i, b ij is the amplitude factor, for the air layer b i0 =1, F ij is the Fresnel coefficient of the vertical polarization component, rc ij is the reflection coefficient of the jth layer of the small-size planar multilayer film reflector at position i without considering the influence of interface roughness, and λ is the wavelength of the incident light beam.

5. The method for evaluating the effect of roughness on the average reflectivity of an EUV curved multilayer film reflector according to claim 4, characterized in that: The interface roughness can be obtained by fitting the X-ray reflectivity test.

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