JP2012151262A - Generation method and generation program of backscattering intensity in charged particle beam exposure, and manufacturing method of semiconductor device utilizing that method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate the backscattering intensity with higher accuracy by reducing the generation man-hour of parameters.SOLUTION: In a method of generating the backscattering intensity of charged particles, parameters of a k-th layer is determined according to the mixture ratio obtained by the weighted mean of pattern area density from a first layer to a (k-1)th layer and the depth. Intensities of downward transmission electrons, reflection electrons and upward transmission electrons are determined, and the sum of the reflection electrons on the uppermost layer directly under a resist layer and the upward transmission electrons is output as the backscattering intensity to the resist layer.

Description

  The present invention relates to a backscattering intensity generation method and generation program in charged particle beam exposure, and a semiconductor device manufacturing method using the method.

  In recent years, as the degree of integration of semiconductor devices has improved, the required pattern size has been reduced, and an exposure method using a charged particle beam, for example, an electron beam, has been used. The problem with such a charged particle beam exposure method (hereinafter simply referred to as the electron beam exposure method for simplicity) is that the resist dimensions vary due to the proximity effect. Electrons that have passed through the resist are scattered by the material constituting the substrate and returned to the resist, and the resist is re-exposed. The electrons returning to the resist are called backscattered electrons, and the dimension of the resist pattern after development varies according to the amount (intensity, energy) of backscattered electrons. This is the proximity effect. Since the amount of backscattered electrons is proportional to the density of the pattern of the nearby substance, the variation width of the resist dimension due to the proximity effect varies depending on the pattern layout.

  As a method for correcting this proximity effect, the influence of electrons returning from the substrate in each region is estimated based on the energy distribution (EID: Exposure Intensity Distribution) function given to the resist by electrons incident from one point, and accordingly, It has been proposed to optimize the exposure amount in the region or change the pattern size.

  Furthermore, there are a plurality of layers each having a pattern of a plurality of substances under the resist layer to which the electron beam is incident. A part of the energy of the electron beam incident on the resist layer is caused by forward scattering. While being accumulated in the resist layer, it is scattered by a plurality of lower layers and returns to the resist layer, and a part of the energy is accumulated in the resist layer. Electrons scattered in this lower layer and returning to the resist layer are backscattered electrons.

  By accurately estimating the backscattered electron intensity scattered by multiple layers below this resist, it is possible to accurately estimate the fluctuation range of the resist dimensions due to the proximity effect. The pattern width after exposure and development is made equal to the design value or equivalent by correcting the pattern.

  A method for accurately estimating the intensity of backscattered electrons scattered by a plurality of layers under the resist is described in, for example, the following patent documents.

JP 2005-101501 A JP 2007-27613 A JP 2004-31836 A

  Patent Document 1 proposes a SEEF (Simplified Electron Energy Flux) model as a model for estimating the backscattering intensity of electrons in electron beam exposure of a multilayer wiring structure. In this model, (1) the intensity of electrons that are transmitted downward, (2) the intensity of electrons that are reflected, and (3) the intensity of electrons that are transmitted upward, in each layer of the multilayer wiring structure. The sum of the reflected electron intensity and the upward transmitted electron intensity in the layer immediately below the layer is obtained as the backscattering intensity. Each layer contains a plurality of material patterns. For example, when the wiring layer is made of a silicon oxide film and a metal material, the parameters of the electron transmittance and the electron scattering length are set to the above three intensities. These two substances must be obtained in advance by an exposure experiment. In other words, as many as 12 parameters are necessary for one layer in the above example.

  For this reason, the number of parameters increases in proportion to the number of layers in the multilayer wiring structure, and in the case of a multilayer wiring structure exceeding 10 layers, the number of parameters exceeds 100. It is not realistic to extract in the above process because it requires excessive man-hours.

  Further, in the SEEF model, since the parameters in each layer are fixed values, in the case of a substrate having a large coarse density of the distribution of three-dimensional heavy metal (for example, tungsten W), the coarse density is not reflected in the parameters. There is also a problem that an error in the calculation result of the scattering intensity tends to be large.

  Accordingly, an object of the present invention is to provide a method capable of generating backscattering intensity by a simpler method or more accurately, and a manufacturing method for a semiconductor device using the method.

The first aspect of the method for generating the backscattering intensity in the charged particle beam exposure is that the layers from the first layer to the Nth layer each include a pattern of one substance or a plurality of substances on the first layer of the multilayer wiring structure. In the method for generating the backscattering intensity of the charged particles on the resist layer when the resist layer formed on is irradiated with a charged particle beam,
With respect to the kth (k ≦ N) kth layer from the resist layer, the reflection coefficient R corresponding to the number of particles reflected by the kth layer through the (k−1) th (k−1) th layer is reflected. _k and the reflection scattering length β _R and the downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that the charged particles that have reached the k-th layer pass through the k-th layer downward, According to the mixing ratio of the substance from the first layer to the (k-1) th layer and for each substance contained in the kth layer,
Further, the upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} corresponding to the number of particles that have passed through the k + 1th layer upward and transmitted through the kth layer are determined from the Nth layer. according to the mixing ratio of the substance up to the k + 1 layer and for each substance contained in the kth layer,
The generation method is as follows:
With respect to the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the A first step of dividing the area according to the reflection coefficient R _k , the downward transmission coefficient T _k , the upward transmission coefficient T ′ _k and the scattering length β with respect to the mixing ratio, and the distance between the surrounding area and the area of interest. Have
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
For the first layer, the downward transmitted charged particle intensity E ₁ in the first layer and the reflected charged particle intensity E ′ ₁ in the first layer are obtained by the area of the first step, respectively, A second step in which the lower transmitted charged particle intensity E and the reflected charged particle intensity E ′ in each layer are sequentially calculated from the area of the first step in order from the second layer to the Nth layer;
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure Then, in order from the N-1th layer to the first layer, a third step of obtaining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step,
And a fourth step of outputting the sum of the reflected charged particle intensity E ′ ₁ obtained in the first layer below the resist layer and the upward transmitted charged particle intensity E ″ ₁ as the backscattering intensity. .

  According to the first aspect, the backscattering intensity can be obtained with high accuracy.

It is a figure which shows the model of backscattering in this Embodiment. It is a figure explaining the calculation which calculates | requires the electron energy flow (electron intensity) of backscattering. It is a figure explaining the calculation which calculates | requires the electron energy flow (electron intensity) of backscattering. It is a figure explaining the parameter extraction of this Embodiment. It is a flowchart figure which shows the parameter extraction procedure in this Embodiment. It is a flowchart figure which produces | generates a resist independent parameter table. It is a flowchart figure which calculates the coefficient (specific gravity w) of mixing ratio calculation. It is a flowchart figure of registration dependent parameter table preparation. It is a figure which shows the mode of electron scattering. It is a figure explaining the production | generation of the parameter independent of a resist. It is another figure explaining the production | generation of a resist independent parameter. It is a figure which shows nine parameters of the resist independent parameter table 30 calculated | required with the calculation method. It is a figure which shows nine parameters of the resist independent parameter table 30 calculated | required with the calculation method. FIG. 14 is a diagram illustrating the relationship between the mixing ratio α ⁻ _k−1 and the specific gravity w. FIG. 15 is a specific flowchart of FIG. 14. It is a figure explaining registration dependence parameter table creation. It is a figure explaining registration dependence parameter table creation. It is a flowchart figure which shows the procedure of the backscattering intensity calculation in this Embodiment. It is a detailed flowchart figure of the procedure which determines the parameter of transmission, reflection, and scattering length of a k-th layer. It is a figure explaining the determination method of the parameter of transmission of the kth layer, reflection, and scattering length. It is a figure which shows the determination method of the parameter of a downward transmission coefficient and scattering length. It is a figure which shows the determination method of the parameter of a reflection count and scattering length. It is a figure which shows the determination method of the parameter of an upward transmission coefficient and scattering length. It is another flowchart figure of backscattering intensity calculation shown in FIG.

  The present invention is applied to charged particle beam exposure. Hereinafter, an example of electron beam exposure will be described. Therefore, an electron is illustrated as a charged particle, and an electron beam is illustrated as a charged particle beam.

[Exposure development process of semiconductor device manufacturing method]
First, an outline of the exposure and development process of the method for manufacturing a semiconductor device in the present embodiment will be described. The design pattern data generated by the integrated circuit design tool includes a substance or material to be processed and its pattern data, and is converted into exposure data having an exposure pattern and an exposure amount. That is, the exposure data includes the exposure amount of each shot in electron beam exposure and the pattern data of each shot. This electron beam exposure may be a point beam exposure method, a variable shaping exposure method, a partial batch exposure method, a projection type exposure method, or the like. However, when a projection type exposure method is used, the exposure amount is constant regardless of the pattern.

  When a pattern according to a design value is exposed with an exposure amount according to a design value, as described above, the development pattern varies due to the proximity effect. Accordingly, the proximity effect corrected exposure data is generated by the proximity effect correction step of correcting either or both of the shape and exposure amount of the exposure pattern in consideration of the proximity effect. This proximity effect correction step includes a step of generating the backscattering intensity with high accuracy. Then, according to the corrected exposure data, the exposure apparatus performs electron beam exposure on the semiconductor wafer or mask, develops the exposed resist, and patterns the layer below the resist layer. The patterning target film includes, for example, a wiring layer such as Al and Cu, and a via hole layer such as W and Cu.

  As described above, in the proximity effect correction step, the step of obtaining the electron backscattering intensity is executed. Then, a desired semiconductor device is manufactured by using the exposure, development, and patterning processes based on the exposure data corrected for the proximity effect.

[Backscatter model]
FIG. 1 is a diagram showing a backscattering model in the present embodiment. FIG. 1A is a cross-sectional view of a semiconductor device. A contact hole layer 12 having a W contact hole with a pattern density in a SiO ₂ film is formed on a silicon substrate 10 and patterned thereon. A non-Al metal layer 13 is formed, and a resist layer 14 is formed thereon. That is, a multilayer structure of the metal layer 13, the contact hole layer 12, and the silicon substrate 10 exists under the resist layer 14 to be exposed and developed. The resist layer 14 is exposed and developed, and the Al metal layer 13 is patterned using the resist layer 14 as a mask. When the resist layer 14 is filled with a silicon oxide film, a wiring layer in which Al and silicon oxide film patterns are mixed is formed. The multilayer wiring structure is formed on the silicon substrate 10 by repeating the formation of the patterning material layer, the exposure and development of the resist thereon, and the patterning process of the patterning material layer using the developed resist. The

  Therefore, in the semiconductor manufacturing process for forming a multilayer wiring structure, as shown in FIG. 1B, an N-layer multilayer wiring structure is formed on the silicon substrate 10, and a resist layer 14 is formed on the first layer. In this state, there is a step in which the resist layer 14 is exposed to an electron beam.

  With the backscattering model shown in FIG. 1B, the distribution (map) of the intensity (energy flow) of backscattered electrons irradiated on the resist layer 14 is obtained by the following calculation. This calculation method is equivalent to, for example, that described in JP-A-2005-101501.

In the backscattering model according to the present embodiment, as shown in FIG. 1B, a multilayer wiring structure 20 composed of an N layer formed on the silicon substrate 10 is formed under the resist layer 14, and the multilayer wiring is formed. In each layer of the structure 10, for example the kth layer, it is assumed that the electron beam is transmitted or reflected as follows. That is, the electron (charged particle) intensity in the k-th layer 20k is equal to (1) the downward transmission electron (charged particle) intensity E _k-1 in the _k- 1th layer transmitted through the k−1th layer, and the downward transmission coefficient T _k. multiplies the downward transmission electron (charged particles) intensity E _k, the reflection coefficient R _k downward transmission electron (charged particles) intensity E _k-1 in (2) (k-1) -th layer in the k-th layer obtained by multiplying the The k-th layer _obtained by multiplying the reflected electron (charged particle) intensity E ′ _k in the k-th layer and (3) the electron (charged particle) intensity returning from the (k + 1) -th layer by the upward transmission coefficient T ′ _k. upward transmission electron (charged particles) intensity E in _"and a _k, electrons (charged particles) intensity returning from the (k + 1) th layer, the upward transmission electron (charged particles) in the k + 1 layer strength _E" and _{k + 1,} k + 1-th layer With reflected electron (charged particle) intensity E ′ _k It is.

  The above electron intensity is also referred to as electron energy flow.

Therefore, in the calculation of the backscattering intensity, the downward transmission electron intensity in the first layer obtained by multiplying the electron intensity E ₀ incident on the resist layer 14 by the downward transmission coefficient T ₁ for the first layer of the multilayer wiring structure 20. The reflected electron intensity E ′ ₁ in the first layer obtained by multiplying E ₁ by the reflection coefficient R ₁ is obtained. The electron intensity E ₀ incident on the resist layer 14 corresponds to the exposure intensity in the electron beam exposure process.

  Further, the downward transmitted electron intensity E and the reflected electron intensity E ′ are obtained in the same manner from the second layer to the Nth layer.

Thereafter, the reflected electron intensity E ′ _{N + 1 on} the silicon substrate 10 is obtained by multiplying the downward transmitted electron intensity E _N of the Nth layer by the reflection coefficient R on the silicon substrate. Then, the N th layer, after obtaining the upward transmission electron intensity E _"N in the N layer multiplied by _N 'upward transmission coefficient T to _{N + 1'} The backscattered electron intensity E, the first layer from the N-1 layer On the other hand, the upward transmitted electron intensity E ″ in each layer is obtained in order. Finally, the sum of the reflected electron intensity E ′ ₁ and the upward transmitted electron intensity E ″ ₁ obtained in the first layer below the resist layer 14 is obtained as the backscattering intensity to the resist layer.

  Each layer of the multilayer wiring structure 20 is, for example, a layer in which Al and silicon oxide patterns are mixed, a layer in which Cu and silicon oxide patterns are mixed, and a layer in which W and silicon oxide patterns are mixed. And the behavior of electron transmission and reflection scattering differs depending on the material irradiated with electrons. For example, silicon oxide is easy to permeate, aluminum Al and copper Cu are somewhat difficult to permeate, and heavy metal tungsten W is difficult to permeate. Therefore, the downward transmission coefficient T, the reflection coefficient R, and the upward transmission coefficient T ′ are different for each material. Furthermore, since the area density of different materials in each layer differs depending on a plurality of areas (small regions) divided in a lattice shape, the behavior of electron transmission and reflection scattering also differs depending on the area density of the materials in that area.

  In addition, incident electrons are scattered around. This scattering generally follows a Gaussian distribution, and the spread of the Gaussian distribution depends on the electron scattering length. Moreover, the electron scattering length varies depending on the material. Therefore, the electron intensity of downward transmission, reflection, and upward transmission in each layer is obtained using the area density method.

  In the area density method, each layer is divided into meshes to form a plurality of areas (small regions), and the surrounding area (x ′) in the region defined by the electron scattering length with respect to the area of interest (x, y) , y ′) to accumulate the number of electrons scattered from the target area (x, y). This number of electrons is the electron intensity (electron energy flow). In this case, the distribution that spreads due to electron scattering, such as a Gaussian distribution, decreases as the scattering distance increases, and the rate of the reduction depends on the electron scattering length.

2 and 3 are diagrams for explaining the calculation for obtaining the electron energy flow (electron intensity) of backscattering. First, S10 in FIG. 2 includes downward transmitted electron intensity (electron energy flow) E _k , reflected electron intensity (electron energy flow) E ′ _k , and upward transmitted electron intensity (electron energy flow) E in the kth layer. The respective arithmetic expressions (1), (2), and (3) for determining _k by area are shown. In this example, the kth layer is a layer made of W and silicon oxide SiO2.

For example, the downward transmission electron intensity (electron energy flow) E _k (x, y) of the k-th layer in Equation (1) is multiplied by the downward transmission coefficient Tk to the downward transmission electron intensity E _k−1 of the _k− 1th layer. Is required. In this calculation, the downward transmitted electron intensity E _k−1 (x ′, y ′) of the _k− 1th layer incident on the surrounding area (x ′, y ′) is converted into a Gaussian distribution g ( x-x ', y-y ', β TW, k) and the transmission coefficient _{T W} at W, around the W area (x ', y' multiplied by the area density alpha _{W, k} in) And downward transmission electron intensity E ′ _k−1 (x ′, y ′), Gaussian distribution g (x ′ ′, y ′ ′; β _{SiO2, k} ) in SiO 2, and transmission coefficient T in SiO 2. _The sum of _SiO2 and the product of the area density of SiO2 (1-α _{W, k} ) is divided into areas for all surrounding areas (x ′, y ′).

The reflected electron intensity (electron energy flow) E ′ _k of the k-th layer in equation (2) and the upward transmitted electron intensity (electron energy flow) E ″ _k of the k-th layer in equation (3) are also obtained in the same area. .

S11 in FIG. 2 includes parameters such as area density α _{W, k} , downward transmission coefficient, reflection coefficient, upward transmission coefficient, scattering length of each of equations (1), (2), and (3) in S10, and a Gaussian distribution. g (x, y; β) and its formula (4) are shown. It can be understood that if the scattering length β is long, the number of electrons in the area (x, y) is small and the Gaussian distribution is low, and if the scattering length β is short, the opposite is true.

Next, in S12 in FIG. 3, an arithmetic expression for obtaining a backscattering intensity (backscattering electron energy flow) E (x, y) that is an electron intensity (electron energy flow) reflected from each layer and returning to the resist. (5) is shown. As shown in FIG. 1, the electron intensity E (x, y) returning to the resist layer in the attention area (x, y) is the reflected electron intensity E ′ ₁ (x, y) of the first layer and the upward transmitted electron intensity E. ” ₁ (x, y), which is the sum of the backscattering intensities from the first layer to the (N + 1) th layer, as shown in FIG. Just as you did.

  Note that the operator “*” in the calculation formula (5) shown in S12 of FIG. 3 means convolution integration.

[Parameter extraction process]
In this embodiment, extraction of parameters necessary for calculating the backscattering intensity is obtained with as few experiments as possible. For this purpose, parameters (transmission coefficient, reflection coefficient, scattering length, etc.) necessary for backscattering intensity calculation are separated into components that depend on the resist and components that do not depend on (resist independent).

FIG. 4 is a diagram for explaining parameter extraction according to the present embodiment. Parameters required for backscattering intensity calculation are divided into resist-dependent parameters and resist-independent parameters. Resist-independent parameters, the transmission coefficient for each material and each layer in the multilayer wiring structure 20 of the N layer and the layer N + 1 of the substrate from the first layer with respect to the incident electron E _0, the reflection coefficient, the scattering length. These parameters can be extracted by executing a Monte Carlo simulation of electron scattering, and can be extracted without performing an exposure experiment with an actual sample.

  Furthermore, as will be described later, the transmission coefficient, reflection coefficient, and scattering coefficient of each layer are made different depending on the mixing ratio of substances in the upper layer or the lower layers, so that a higher accuracy coefficient is used. be able to. The substance mixing ratio is a value obtained by weighting the area density α of the substance in each layer by the specific gravity w of each layer. The specific gravity w of each layer is also extracted by Monte Carlo simulation of electron scattering. In other words, it is a kind of resist-independent parameter.

On the other hand, the resist-dependent parameter is a conversion ratio C _{M, k} in which the electron intensity E returned to the resist layer 14 is converted into stored energy ΔE that is accumulated in the resist layer 14 and consumed as exposure energy. Based on the experimental result (exposure and developed pattern width), it is obtained by the least square method. The conversion ratio C _{M, k} depends on the depth in the substrate where electrons are back-scattered, and is extracted corresponding to each material M (Al, Cu, W, SiO 2, etc.) of each layer k.

  FIG. 5 is a flowchart showing a parameter extraction procedure in the present embodiment. The parameter extraction procedure includes a step (S20) in which a Monte Carlo simulation of electron scattering is performed on the substrate condition 22 that specifies the substrate structure of the semiconductor product to create a resist-independent parameter table 30 (S20). The parameters (transmission coefficient, reflection coefficient, scattering length, etc.) of the resist-independent parameter table 20 are obtained for each depth z from the resist layer of the target material in the target layer, and a plurality of layers above and below the target material. It is extracted at every mixing ratio of the mixed materials. A specific method will be described in detail later.

Further, the parameter extraction procedure includes a step (S22) of calculating a coefficient (specific gravity w _k ) of each layer for calculating the mixing ratio. In the step of calculating the density w _k, with reference to the resist-independent parameter table 30, the mixing ratio coefficient table 31 consisting of a specific gravity w _k is determined by calculation. As shown in FIG. 5, the specific gravity w _k is obtained for each of the transmission coefficients T and T ′ and the reflection coefficient R. The specific gravity w _k for the downward transmission coefficient T and the reflection coefficient R is the specific gravity of the layer above it for each of the layers 1 to _k . For example, for the third layer, the specific weights w ₁ and w ₂ of the first and second layers above it are extracted. For the k-th layer, which specific gravity _w 1 _{to w k-1} of the first 1 to k-1 layer of the upper are extracted from. Conversely, the mixing ratio of the parameter extraction of the upward transmission coefficient T 'in the case of obtaining the upward transmission electron intensity, because it is the mixing ratio of a plurality of layers below the target layer material, the specific gravity w _N ~ multiple layers of lower w _{k + 1} is extracted. A specific method will be described in detail later.

The parameter extraction procedure includes a step of creating a resist-dependent parameter table (S24). The resist-dependent parameter table 32 includes conversion ratios C _{M, k for} converting the electron intensity E returned to the resist layer for each layer and each material into the electron intensity ΔE accumulated in the resist as the exposure energy of the resist. It is. That is, the conversion ratio C is extracted for each material M for each layer k. The resist-dependent parameter table 32 is obtained by the least square method based on the pattern width of the developed pattern obtained by performing an exposure experiment on a sample having a typical structure of the product. At that time, the resist-independent parameter table 30 and the mixing ratio coefficient (specific gravity w) parameter table 31 are referred to. A specific method will be described in detail later.

[Registry-independent parameter table]
FIG. 6 is a flowchart for generating a resist-independent parameter table. A method for generating the resist-independent parameter table shown in FIGS. 12 and 13 will be described with reference to FIGS.

  FIG. 9 is a diagram showing the state of electron scattering. The electron energy flow E0 incident on an arbitrary position of the resist layer 14 is scattered forward by the resist layer 14, a part of the incident energy is accumulated as exposure energy, and the electron energy flow transmitted through the resist layer 14 The light is transmitted or reflected while being scattered in the multilayer wiring structure 20 and the silicon substrate 10, and returns to the resist layer 14. Scattering in the multilayer wiring structure 20 and the silicon substrate 10 does not depend on the resist material.

  Such electron scattering behavior can be calculated by Monte Carlo simulation in which each electron is scattered using random numbers. That is, parameters (downward and upward transmission coefficients, reflection coefficients, scattering lengths, etc.) of each layer can be obtained by calculation without experiments.

  Furthermore, transmission and reflection in a layer at a certain depth vary depending on the difference in layer structure until electrons reach the layer. Therefore, in the present embodiment, when the parameters of the target material in the target layer are obtained, the layer structure until electrons reach the target material is substituted with the mixed material.

  In the conventional method, the parameters are obtained on the assumption that all multilayer structures have a uniform mixing ratio regardless of the mixing ratio α of the mixed material above or below the target material area. Therefore, depending on the multilayer structure, the accuracy of the parameters is low and includes errors.

  FIG. 10 is a diagram illustrating the generation of resist-independent parameters. As shown in FIG. 10A, incident electrons E pass through a plurality of layers made of materials having various area densities and reach a mixed material M (for example, Cu). However, since the layer structure of the actual product is diverse, as shown in FIG. 10B, the layer structure 34 on the target material M is replaced with the mixed material 36 and depends on the mixing ratio α of the mixed material. Generate the parameters to be According to the model of FIG. 10B, the incident electrons E pass through the mixed material 36 having the Cu mixing ratio α and reach the target material Cu having the thickness Δz at the depth z.

  In the first step S200 in the flowchart of FIG. 6, the substrate structure is set based on the substrate conditions (substrate and multilayer wiring structure) of the product. Specifically, the target material Cu shown in the model of FIG. 10B, the depth z of the target material, and the mixing ratio α of the mixed material above the target material are set.

  Using these as input conditions, Monte Carlo simulation of electron scattering is performed, and the distribution of the electron energy flow incident on the target material and the electron energy flow transmitted or reflected by the target material is obtained (S202). Here, the electron energy flow is the total amount of energy passing through the area (small unit area) of the target material, and is the electron intensity. In addition, Monte Carlo simulation of electron scattering can be performed by using commercially available simulation software.

  Then, the input and output electron energy flows to the target material are approximated by a Gaussian distribution from the obtained electron energy flow distribution (S204). Finally, the transmission coefficient T and the reflection coefficient R are calculated from the intensity ratio of the input and output Gaussian distributions, and the scattering length is calculated from the spread of each Gaussian distribution (S206).

  The above steps S200 to S206 are performed for all the depths z, all the target materials M, and all the mixing ratios, and the respective parameters are extracted.

FIG. 11 is another diagram illustrating the generation of resist-independent parameters. FIG. 11 illustrates steps S204 and S206 in the flowchart of FIG. FIG. 11A shows the generation of the transmittance T of the downward transmission electrons and the scattering length β. When the incident electron E ₀ passes through the mixed material 36 having the mixing ratio α and the electron energy flow reaching the target material M is approximated by a Gaussian distribution, the input electron energy flow E _in to the target material M becomes the scattering length β _in . E _in × G (β _in ) multiplied by the dependent Gaussian distribution G (β _in ). In other words, it is considered that the incident electron is diluted with a Gaussian distribution and spreads into an electron energy flow. Furthermore, when the electron energy flow that permeates downward through the target material M is approximated by a Gaussian distribution, the output electron energy flow Eout from the target material M is multiplied by a Gaussian distribution G (β _out ) that depends on the scattering length β _out . , E _out × G (β _out ).

From the ratio of the intensity of these Gaussian distributions, the downward transmittance T _M (z, α) is
T _M (z, α) = E _out / E _in
It becomes.

On the other hand, scattering length beta _TM is believed to spread the area beta ² _in a scattering length beta _in the time of input is spread spread area beta ² _out of scattering length beta ² _out of output, the scattering length for the purpose material M beta _{Since the} spread area β ² _TM by _TM is β ² _out −β ² _in ,
β ² _in = β ² _out + β ² _TM
β _TM (z, α) = √ (β ² _out −β ² _in )
It becomes.

Also in the case of the reflected electrons in FIG. 11B and the upward transmitted electrons in FIG. 11C, the respective parameters, reflection coefficient R _M (z, α) and scattering length β _RM (z, α) are calculated by the same calculation as described above. ), An upward transmission coefficient T ′ _M (z, α) and a scattering length β _T′M (z, α).

12 and 13 are diagrams showing nine parameters of the resist-independent parameter table 30 obtained by the above calculation method. This parameter assumes that the multilayer wiring structure has a structure in which a plurality of layers made of Cu and SiO 2 are stacked. FIG. 12 shows downward transmission coefficients T _Cu and T _Si , reflection coefficients R _Cu and R _Si , and upward transmission coefficients T ′ _Cu and T ′ _Si for the target materials Cu and SiO 2 (Si in the figure). Each coefficient is determined for each of the mixing ratio α (0% to 100%) of the depth direction z and Cu. Further, in FIG. 13, object material Cu and SiO2 scattering length of the downward transmission for (in the figure Si) β _TCu, β _TSi, reflection scattering length _{beta RCu,} beta _RSi, scattering length of the upward transmission beta _T'Cu, β _T′Si is shown. The respective scattering lengths are determined for each of the mixing ratio α (0% to 100%) of the depth direction z and Cu.

  The above product model is an example in which the multilayer wiring structure is made of Cu and SiO2. As another product model, when the multilayer wiring structure includes, for example, Al and SiO2 layers and W and SiO2 layers, the respective parameters are obtained for each mixing ratio α of relatively hard W and relatively soft Al and SiO2. It is done. The wiring layer generally has a pattern of a conductive material such as metal and an insulating material such as SiO2. Therefore, the mixing ratio α is determined corresponding to the area density of the conductive material such as metal. That is, in such an example, the mixing ratio α is one type for the multilayer wiring structure.

  Here, the mixing ratio α is a value obtained by mixing the area density α of each layer.

The downward transmission coefficient T _{Cu in} FIG. 12 will be described. As the depth direction z increases, the lateral scattering of electrons increases, so the downward transmission decreases. Further, as the mixing ratio α of hard Cu as compared with SiO 2 is larger (for example, 100%), the scattering in the lateral direction of electrons increases until the target material is reached, and thus the downward transmittance decreases. This tendency is opposite in the case of the reflection coefficient R _Cu . Furthermore, for the upward transmission coefficient T _'Cu, it has the same tendency and a downward transmission coefficient.

_Describing the downward transmission scattering length _{βTCu in} the target material Cu in FIG. 13, the scattering length has a peak at a certain depth z, and the scattering length becomes zero when the depth becomes deeper. Moreover, as the Cu mixing ratio α is larger (for example, 100%), the scattering length peak becomes a shallower z, and as it is smaller (for example, 0%), the scattering length peak becomes a deeper z. Again, the higher the mixing ratio α of Cu, the smaller the scattering in the target material because the electrons scattered in the lateral direction are limited and the electrons that can pass through the target material are limited. On the contrary, the lower the Cu mixing ratio α, the longer the vertical direction, and the greater the scattering of the target material.

[Mixing ratio coefficient table]
In the present embodiment, the transmission coefficients T and T ′, the reflection coefficient R, and the scattering length β of the parameter table independent of the resist are obtained by Monte Carlo simulation of electron scattering. In the simulation, the mixing ratio α of the multilayer wiring structure to reach the target material was used.

  However, in a multilayer wiring structure of an actual product, the area density α of a certain material, for example, Cu is different in each layer. For example, when the area density of hard Cu is higher in the shallower layer than in SiO2 and lower in the deeper layer, the downward transmittance is relatively small, but in the opposite case, the downward transmittance tends to be relatively high. It was done. That is, the parameters differ depending on the area density of Cu in each layer of the multilayer wiring structure through which electrons reaching the target material have passed.

Therefore, in this embodiment, when extracting the parameter corresponding to the target product from the parameter table 30 in the calculation of the backscattering intensity, the area density α of each layer of the multilayer wiring structure through which electrons pass is weighted by the specific gravity w of each layer. The parameters are extracted based on the mixing ratio α ⁻ obtained in the above manner. For this purpose, it is necessary to obtain the specific gravity w of each layer in advance as the mixing ratio coefficient table 31.

FIG. 7 is a flow chart for calculating a mixing ratio calculation coefficient (specific gravity w). FIG. 14 is a diagram showing the relationship between the mixing ratio α ⁻ _k−1 and the specific gravity w. FIG. 15 is a specific flowchart.

As shown in FIG. 14, the mixing ratio alpha ^- _k-1 is the area ratio alpha ₁ to? _K-1 of the first layer to the k-1 layer, a specific gravity _w 1 _{to w k-1} of each layer It is obtained by weighting calculation. It is as the arithmetic expression in FIG. Then, the specific gravity of _{w 1 ~w k-1} can be obtained in advance by calculation described below.

First, Monte Carlo simulation of electron scattering is performed on the layer structure of the pattern area density α _{1 to} α _k−1 from the first layer to the (k−1) th layer in the same manner as the creation of the resist-independent parameter table 30. The parameter value of the target material M of the kth layer is calculated (S220). In this case, the combinations of pattern area density α of each layer are all combinations (2 ^k-1 ways) for two types (0, 1 in the figure) of 0% or 100%, or rational selection appropriately selected by the experimental design method It is a combination of various numbers.

FIG. 15 shows 11 combinations of board numbers # 1 to # 11. The substrate numbers # 1 to # 11 are substrate structures in which the Cu ratio (area density α) of the first to eighth layers is 0 (0%) or 1 (100%). These eleven by Monte Carlo simulation of electron scattering above for the substrate structure of the ninth layer material Cu or SiO2 (in the figure Si) is calculated on the down transmission coefficient _{T M, 9} of (S220). On the other hand, based on the 11 downward transmission coefficients T _{M, 9} and the depth z of the ninth layer, the downward transmission coefficients T _Cu , T _Si in the resist-independent parameter table 30 in FIG. Then, each mixing ratio α ^- ₈ is extracted (S222).

Then, by regression analysis by the least squares method, the mixing ratio alpha ^- calculating the ₈ first layer to the eighth layer of a specific gravity _w 1 to w ₈ for calculating (S224). As a result, an expression for calculating the mixing ratio α ^- ₈ shown in S224 in FIG. 15 is obtained. The specific weights w _{1 to} w ₈ are the mixing ratio coefficient table 31.

In the above description, a mixing ratio coefficient table having specific gravity w ₁ to w ₈ for the downward transmission coefficients T _Cu and T _Si was obtained. In the same manner, a mixing ratio coefficient table of specific gravity w ₁ to w ₈ for reflection coefficients R _Cu and R _{Si and} a mixing ratio coefficient table of specific gravity w ₉ to w _N for upward transmission coefficients T ′ _Cu and T ′ _Si are obtained. Each can be requested. Both can be obtained approximately by Monte Carlo simulation of electron scattering and the least square method by regression analysis.

  Thereby, the mixing ratio reflecting the influence from each layer can be obtained separately for each of the downward transmission coefficient, the reflection coefficient, and the upward transmission coefficient.

As described above, the mixing ratio coefficient table 31 including the specific weights w _{1 to} w ₈ can be generated by calculation by executing a Monte Carlo simulation of electron scattering.

[Registration dependent parameter table]
Next, a method for generating a resist dependence parameter table will be described. As described with reference to FIG. 4, a part of the electron energy flow E returning to the resist layer 14 is accumulated in the resist as exposure energy of the resist. Accordingly, the stored energy flow ΔE is obtained by multiplying the returned electron energy flow E by the conversion ratios _{CM and K.} As shown in FIG. 5, the resist dependence parameter table 32 has the conversion ratios C _{M, K} for each material M and for each layer k.

In the present embodiment, the conversion ratios _{CM, K} are obtained from the results of exposure experiments. That is, the exposure energy flow ΔE accumulated in the resist layer can be obtained from the pattern width after development measured in the exposure experiment on the experimental multilayer wiring structure sample. Therefore, the conversion ratios C _{M, K} corresponding to the coefficients of the calculation formula of the exposure energy flow ΔE can be obtained by the least square method based on the experimental results.

  FIG. 8 is a flowchart for creating a resist dependence parameter table. First, as an exposure experiment, a resist layer is formed on a substrate sample having a multilayer wiring structure in which the pattern area density of each layer is different, and an evaluation pattern composed of line and space patterns with different line widths, pitches, and numbers is formed. Electron beam exposure is performed, and the line width of the developed pattern is measured (S240).

For each material M in each layer k, optimization is performed by applying the least square method based on the experimental value of the stored energy flow estimated from the measured line width, using the conversion coefficient C _MK for the stored energy flow as a parameter. (S242).

  The above-described registration-dependent parameter table creation will be further described below with a specific example.

  16 and 17 are diagrams for explaining creation of a resist dependence parameter table. First, FIG. 16 shows the total energy Ez of electrons reflected from the depth z to z + Δz (Δz = 250 nm) calculated by the Monte Carlo simulation of electron scattering, the total energy DEz of energy accumulated in the resist, and its The conversion coefficient Cz = DEz / Ez. In this example, the resist material name is PMMA, and the acceleration voltage of the electron beam is 50 kV. Further, the conversion coefficient Cz has a depth dependency, but does not show a substance dependency. Further, in FIG. 16, the depth dependency of the conversion coefficient Cz = DEz / Ez is important, and the magnitudes of the energy Ez and DEz are not so meaningful.

  According to FIG. 16, the total energy DEz accumulated in the resist varies depending on the depth z, and the accumulated energy due to the electrons reflected from the certain depth z is the largest. Similarly, the backscattered electron energy flow Ez returning to the resist from each depth z also differs depending on the depth z, and the energy flow Ez of electrons reflected from a certain depth z is the largest. The conversion coefficient Cz = DEz / Ez differs depending on the depth z, and the conversion coefficient Cz = DEz / Ez increases as the depth z increases.

  Thus, it was confirmed that the conversion coefficient differs depending on the depth z. According to Bethe's stopping power, the energy accumulated in the unit length of the resist depends on the energy of the electrons. In view of such dependency of the conversion coefficient Cz, in this embodiment, the stored electron energy flow ΔE (x, y) in which the conversion coefficient Cz is assigned to each material of each layer, and exposure experiment data (incident electron energy flow). And the development pattern line width), the conversion coefficient Cz is obtained.

FIG. 17 is a diagram for explaining step S242 of creating a resist dependence parameter table. First, the conversion coefficient C _MK is assigned to each material of each layer (S242-1). This is the same as the resist-independent parameters (transmission coefficients T, T ′, reflection coefficient R, and their scattering length β) obtained for each depth z for each material.

Then, this conversion coefficient C _MK is introduced into the calculation formula (5) (see FIG. 3) of the backscattered electron energy flow E (x, y) (S242-2). Since the stored energy flow ΔE (x, y) = C _MK × E (x, y), the stored energy flow ΔE (x, y) is expressed as in equations (6) and (7) in FIG. be able to. That is, equations (6) and (7) are obtained by assigning the conversion coefficient C _MK to the term of the backscattered electron energy flow returning from each layer of equation (5). In equation (6) (7), the reflection coefficient _R k (x, y) is multiplied by a conversion factor _{C MK,} the reflection coefficient obtained by adding a resist dependence _R ^ k (x, y) is set to. The reason for this is that if conversion coefficients are assigned to the transmission coefficients T _k (x, y) and T ′ _k (x, y), these transmission coefficients are terms of backscattered electron energy flow from different layers in equation (5). This is because it is not easy to obtain the conversion coefficient by the method of least squares.

Finally, exposure and development experiments are performed on samples of various substrate configurations, and conversion coefficients are extracted by the least square method or the like based on the exposure experiment data that is the experimental results (pattern width measurement values) (S242-). 3). In the equations (6) and (7), the electron transmission coefficients T _{M, K} , T ′ _{M, K} , their scattering lengths β _{TM, K} , β _{T′M, K} , reflection counts R _{M, K} , their scattering lengths β _{RM and K} are parameters calculated by Monte Carlo simulation of electron scattering as described above, and conversion coefficients _{CM and K} are parameters extracted by exposure experiments.

  As described above, according to the present embodiment, parameters for calculating the backscattered electron intensity can be obtained by resist-independent parameters (transmission coefficients T, T ′, reflection coefficient R, By dividing into the scattering length β and the mixing ratio coefficient w) and the resist dependent parameter (conversion coefficient C) obtained by the exposure experiment, the number of parameters to be extracted from the experiment can be reduced. Conventionally, the transmission coefficients T and T ′, the reflection coefficient R, and the scattering length β are all extracted based on the exposure experiment. Therefore, excessive man-hours are required for parameter extraction. Since some parameters are obtained by Monte Carlo simulation and only the conversion coefficient is extracted based on the exposure experiment, the number of parameter extraction steps can be reduced.

Further, according to the present embodiment, the parameters of the transmission coefficients T, T ′, the reflection coefficient R, and the scattering length β are extracted for each upper layer or lower layer mixing ratio α ⁻ through which electrons reaching the target material have passed. Create a parameter table. Therefore, in response to a multilayer wiring structure of products backscatter intensity calculation, the mixing ratio of the respective layers of the area ratio alpha and specific gravity w alpha ^- look, the mixture ratio alpha ^- optimal parameters corresponding to the parameter table Since the backscattering intensity is calculated after extraction, a highly accurate calculation result can be obtained.

[Calculation process of backscattering intensity for proximity effect correction]
FIG. 18 is a flowchart showing the procedure of backscattering intensity calculation in the present embodiment. The procedure of this flowchart shows the procedure performed by the computer executing the backscattering intensity calculation program.

A resist-independent parameter table 30, a mixing ratio coefficient table 31, and a resist-dependent parameter table 32 have already been created for the target semiconductor device. Therefore, an area density map 42 of the kth layer is created from the pattern data 40 of the kth layer of the multilayer wiring structure of the semiconductor device to be exposed (S30). The pattern data 40 is pattern data for each material of the k-th layer, and the area density map is an area density α for each material of a plurality of areas (minimum regions) obtained by dividing the k-th layer in a lattice shape. For example, if the k-th layer is made of Cu and SiO2, based on the area density alpha _Cu of Cu, the area density of the SiO2 will be 1-alpha _Cu. The k-th layer area density map 42 is created from the first layer to the N-th layer below the resist layer.

  When pattern data 40 for the kth layer is input to a computer that executes a backscattering intensity calculation program, an area density map 42 for the kth layer is generated (S30). This is repeated from the first layer to the Nth layer.

  Next, parameters such as transmission coefficients T and T ', reflection coefficient R, and their scattering length β of the k-th layer are determined from the area density map 42 (S32). The parameters are determined by determining the area density map 42 of the first layer to the Nth layer, the mixing ratio coefficient table 31 having the specific gravity w, the transmission coefficients T and T ′, the reflection coefficient R, and the resist having the scattering length β. This is performed with reference to the independent parameter table 30.

  FIG. 19 is a detailed flowchart of a procedure for determining the transmission, reflection, and scattering length parameters of the k-th layer. FIG. 20 is a diagram for explaining a method for determining transmission, reflection, and scattering length parameters of the k-th layer. The parameter determination procedure of FIG. 19 will be described with reference to FIG.

First, with respect to each area of the kth layer, the pattern area density (for example, α _Cu ) of the first layer to the (k−1) th layer thereon is referred to, and the specific gravity in the column of the kth layer in the mixing ratio coefficient table w ₁ ~w _k-1 was added by multiplying the layers of the pattern area density (alpha _Cu) mixing ratio alpha ^- Request _k-1 (S320). As shown in FIG. 20, with respect to the target material M in the area of the k-th layer, the area ratio α _{1 to} α _k−1 of the first layer to the (k− ₁₎ -th layer is set to the mixing ratio coefficient table 31 the specific gravity of _w 1 _{to w k-1} of the first layer to the k-1 layer of the inner by adding by multiplying respectively, the mixing ratio alpha ^- Request _k-1.

Then, resist refers to the non-dependent parameter table 30, object material material mixing ratio from the corresponding table of M alpha ^- T _Cu in the example of _k-1 and the corresponding parameters to the depth z of the k-th layer (FIG. 20 ) Is extracted (S322). Other parameters R and β can be similarly extracted from the table.

FIG. 21 is a diagram illustrating a method for determining the parameters of the downward transmission coefficient and the scattering length. Mixture ratio for the mixed material of the multilayer structure on the purposeful material area alpha ^- _k-1 look (S320), with reference to the resist-independent parameter table 30, the downward transmission coefficient T _Cu and its scattering length beta _{T , Cu} are extracted (S322).

FIG. 22 is a diagram showing a method for determining parameters of reflection count and scattering length. In the same manner as described above, the mixing ratio α ^- _k-1 is obtained for the mixed material having a multilayer structure on the area where the target material is present (S320), and the reflection coefficient R _Cu and its reflection coefficient R _Cu are determined by referring to the resist-independent parameter table 30. The scattering length β _{R and Cu} are extracted (S322).

Next, the layers for each area of the k-th layer, with reference to the pattern area density of the (k + 1) th layer to the N layer below it, the specific gravity of w _{k + 1} to w _N column of the k-th layer mixing ratio table Is multiplied by the pattern area density to obtain a mixing ratio α ^- _{k + 1} (S324). Then, referring to the resist-independent parameter table 30, the parameters of the upward transmission coefficient corresponding to the mixing ratio α ⁻ _{k + 1} and the depth z of the k-th layer are extracted from the table corresponding to the material of the target material M (S326). .

FIG. 23 is a diagram illustrating a method for determining the parameters of the upward transmission coefficient and the scattering length. Mixture ratio for the mixed material of the multilayer structure under a purpose material area α ^- _{k + 1} a calculated (S324), with reference to the resist-independent parameter table 30, an upward transmission coefficient T _'Cu and its scattering length beta _{T' , Cu} are extracted (S326).

  The parameter determination step S32 of transmission, reflection, and scattering length is extracted for every area and material for all the first to Nth layers. This parameter determination step S32 is extracted in advance as a preparation step for backscattering intensity calculation. However, it may be extracted each time it is necessary for the backscattering intensity calculation described later.

Returning to FIG. 18, next, an incident electron energy flow map (E ₀ ) 44 is generated from the exposure pattern data (uncorrected pattern data) 44 to be corrected by the backscattering intensity (S34). That is, the computer inputs the uncorrected pattern data 44 to be corrected, obtains the sum of the product of the area density and the exposure dose of the area (small area) divided into a grid, and enters the incident electron energy flow E for each area. _{Find 0} . That is, the incident electron energy flow map (E ₀ ) 44 means an initial value of the electron energy flow, and the process S35 is an initialization process.

  The size of this area (small region) is determined by the acceleration voltage of electrons and the spread of backscattering, and about 1 μm is appropriate when it is incident on the Si substrate at an acceleration voltage of about 50 kV. In addition, the calculation can be speeded up by increasing the size of the area in the lower layer.

Therefore, the calculation of the electron energy flow maps 46, 48, 50 from the first layer to the Nth layer is finally performed. First, the calculation of the downward transmitted electron energy flow map E _k 46 in the k-th layer (S36) and the calculation of the reflected electron energy flow map E ′ _k 48 (S38) are repeated in the order of the first layer to the N-th layer. . This calculation formula is as shown in formulas (6) and (7) of FIG. That is, the calculations of Expressions (6) and (7) are performed using the initial value electron energy flow map (E ₀ ) and the parameters extracted in advance in step S32.

As shown in FIG. 1B, a downward transmission electron energy flow map E ₁ and a reflected electron energy flow map E ′ _{1 of} the first layer are calculated from the initial electron energy flow map (E ₀ ), The downward transmission electron energy flow map E ₂ and the reflection electron energy flow map E ′ _{2 of} the second layer are calculated from the downward transmission electron energy flow map E ₁ of the first layer, and this is repeated until the (N + 1) th layer.

In the calculation of reflection electron energy stream map E _'k, as described in equation (7) in FIG. 17, transform coefficient C _M of the resist dependent parameter table _{32, K} is referred to, the conversion factor C _M to the reflection coefficient R _{, K} multiplied. Therefore, the influence of the conversion coefficient corresponding to the energy accumulation rate in the resist is converted into the reflected electron energy flow map.

When the calculation of the downward transmitted electron energy flow map E _k from the first layer to the (N + 1) th layer (S36) and the calculation of the reflected electron energy flow map E ′ _k (S38) are completed, the first to the first layer from the Nth layer The calculation of the upward transmitted electron energy flow map E ″ _k 50 (S40) is repeated until the layers are completed. When this calculation is completed, the reflected electron energy flow map E ′ _{1 of} the first layer and the upward transmitted electron energy flow map E The sum of ₁ is output as a backscattered electron energy flow map back to the resist layer. In addition, since the influence of the conversion coefficient is included, this sum is a backscattered electron energy flow map accumulated in the resist corresponding to ΔE (x, y) in the equations (6) and (7) shown in FIG. It is.

  Although not shown, after calculating the backscattering intensity, the proximity effect is estimated based on the energy of each area of the backscattered electron energy flow map, and the exposure data pattern and the exposure amount are corrected. Then, the exposure process for the actual product is performed based on the corrected exposure data.

FIG. 24 is another flowchart of the backscattering intensity calculation shown in FIG. In FIG. 24, it is assumed that the area density map creation step S30 of the first to Nth layers and the electron energy flow map initialization step S34 shown in FIG. 18 have been completed. First, in the k-th layer, the mixing ratio α ⁻ is calculated from the multilayer structure seen from the incident position on the target material at the depth z, and the downward transmission coefficient is calculated from the mixing ratio α ⁻ and the depth z. Tk, reflection coefficient Rk, their scattering length βk, and conversion coefficient Ck are determined (corresponding to step S32 in FIG. 18), and according to the determined parameters, the electron energy flow incident from the layer to the next lower layer is determined. The distribution (map) Ek is calculated, and the distribution (map) E′k of the reflected energy flow in the layer is calculated (corresponding to steps S36 and S38 in FIG. 18). The calculation of the k-th layer is executed in order from the first layer to the (N + 1) -th layer.

Next, in the k-th layer, the mixing ratio α ⁻ is calculated from the multilayer structure seen from the back side incident position on the target material at the depth z, and the upward direction is calculated from the mixing ratio α ⁻ and the depth z. The transmission coefficient T′k and its scattering length βk are determined (corresponding to step S32 in FIG. 18), and the distribution (map) E ″ k of the electron energy flow incident from the layer to the next upper layer is determined by the determined parameters. Calculation (corresponding to step S40 in Fig. 18) The calculation of the k-th layer is executed in order from the N-th layer to the first layer.

  As described above, the backscattering intensity calculation procedure in FIG. 24 determines the parameters of each layer when calculating the electron energy flow map of that layer. The rest is the same as the calculation procedure of FIG.

As described above, according to the present embodiment, the parameters of the transmission coefficients T and T ′, the reflection coefficient R, and the scattering length β are set for each upper layer or lower layer mixing ratio α ⁻ through which electrons reaching the target material have passed. Extract and create a parameter table. Thus, the backscattering strength calculated, corresponding to the multilayer wiring structure of products backscatter intensity calculation, the mixing ratio of the area ratio alpha and specific gravity w alpha ^- extract determined, the optimum parameters corresponding thereto from the parameter table Can be done. Therefore, a more accurate calculation result can be obtained.

  The above embodiment is summarized as follows.

(Appendix 1)
When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a method for generating a backscattering intensity of the charged particles to a layer,
With respect to the kth (k ≦ N) kth layer from the resist layer, the reflection coefficient R corresponding to the number of particles reflected by the kth layer through the (k−1) th (k−1) th layer is reflected. _k and the reflection scattering length β _R and the downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that the charged particles that have reached the k-th layer pass through the k-th layer downward, According to the mixing ratio of the substance from the first layer to the (k-1) th layer and for each substance contained in the kth layer,
Further, the upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} corresponding to the number of particles that have passed through the k + 1th layer upward and transmitted through the kth layer are determined from the Nth layer. according to the mixing ratio of the substance up to the k + 1 layer and for each substance contained in the kth layer,
The generation method is as follows:
With respect to the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the A first step of dividing the area according to the reflection coefficient R _k , the downward transmission coefficient T _k , the upward transmission coefficient T ′ _k and the scattering length β with respect to the mixing ratio, and the distance between the surrounding area and the area of interest. Have
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
Furthermore, after determining the downward transmitted charged particle intensity E ₁ in the first layer and the reflected charged particle intensity E ′ ₁ in the first layer for the first layer by the area of the first step, respectively. , A second step of sequentially determining the lower transmitted charged particle intensity E and the reflected charged particle intensity E ′ in each layer from the second layer to the Nth layer by the area of the first step,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure Then, in order from the N-1th layer to the first layer, a third step of obtaining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step,
And a fourth step of outputting the sum of the reflected charged particle intensity E ′ ₁ obtained in the first layer below the resist layer and the upward transmitted charged particle intensity E ″ ₁ as the backscattering intensity. A method for generating the backscattering intensity of charged particles.

(Appendix 2)
In Appendix 1,
In the first step of dividing the area, the mixing ratio α ^{− of the} substance from the first layer to the (k−1) th layer is determined by the respective substances of the first layer to the k−1th layer above the target area. The charged particle backscattering intensity obtained by multiplying the area ratio (α _{1 to} α _k-1 ) by the specific gravity (w _{1 to} w _k-1 ) of each of the first to k-1 layers Generation method.

(Appendix 3)
In Appendix 1 or 2,
In the first step of dividing the area, the mixing ratio α ⁻ of the substances from the Nth layer to the (k + 1) th layer is the area ratio (α of each of the substances from the Nth layer to the (k + 1) th layer below the target area. _N in to? _{k + 1),} the method of generating the backscattering intensity of the first through N of the (k + 1) th layer, respectively layers gravity _(w N _{to w k + 1)} multiplied by the sum to sought charged particles.

(Appendix 4)
In any one of Supplementary Notes 1, 2, and 3,
When obtaining the reflected charged particle intensity in the second step, the reflection coefficient R _k is multiplied by a conversion coefficient C _k which is a ratio of the charged particle intensity returning to the resist layer accumulated by exposure of the resist layer. Then, a method of generating the backscattering intensity of the charged particles to obtain the reflected charged particle intensity.

(Appendix 5)
In Appendix 1,
Further, a simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the reflection coefficient R _k and the reflection scattering length β _R at the k-th layer and the downward transmission coefficient are calculated. T _k and downward transmission scattering length β _T are generated for each substance contained in the k-th layer according to the mixing ratio of the substances from the first layer to the (k−1) -th layer, and in the k-th layer The upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} are generated for each of the substances included in the k-th layer according to the mixing ratio of the substances from the Nth layer to the (k + 1) th layer. A method for generating a backscattering intensity of a charged particle, which includes a first parameter generation step.

(Appendix 6)
In Appendix 5,
Further, the simulation of electron scattering is performed on a plurality of multilayer wiring structure samples each layer having a predetermined area density combination, and the downward transmission coefficient and reflection coefficient of the kth layer for each multilayer wiring structure sample. Or by referring to a table of the downward transmission coefficient, reflection coefficient, or upward transmission coefficient of the depth z of the k-th layer generated in the first parameter generation step. Extracting the upper or lower mixing ratio of the k-th layer of the wiring structure sample, and based on the extracted mixing ratio of the plurality of multilayer wiring structure samples and the area density of each layer of the plurality of multilayer wiring structure samples , A method for generating the backscattering intensity of charged particles, which has a second parameter generation step for obtaining the specific gravity w of each layer.

(Appendix 7)
In Appendix 6,
The second parameter generation step is a method for generating a backscattering intensity of a charged particle, in which the specific gravity w of each layer is obtained for each of the downward transmission coefficient, the reflection coefficient, and the upward transmission coefficient.

(Appendix 8)
In Appendix 6,
In the first step of dividing the area, the mixing ratio α ⁻ of the substance from the first layer to the (k−1) th layer is set to the substance of each of the first layer to the k−1th layer above the target area. the area ratio of the (alpha ₁ to? _k-1), multiplied by the second parameter generation step is from the first layer obtained in the k-1 layer each specific gravity _(w 1 _{to w k-1)} A method for generating the backscattering intensity of a charged particle obtained by addition.

(Appendix 9)
In Appendix 6,
In the first step of dividing the area, the mixing ratio α ⁻ of the substance from the Nth layer to the (k + 1) th layer is set to the area ratio (α of each substance of the Nth layer to the (k + 1) th layer below the target area. _{N to} α _{k + 1} ) multiplied by the specific gravity (w _{N to} w _{k + 1} ) of each of the ( _N ) th layer to the ( _{k + 1} ) th layer obtained in the second parameter generation step and added to obtain the backscattering intensity of the charged particle Generation method.

(Appendix 10)
In Appendix 4,
Further, a plurality of different evaluation patterns are exposed and developed on a multilayer wiring structure sample having a different area density of each layer, and the conversion coefficient C _k is _obtained based on a measured value of the line width of the evaluation pattern after the development. A method for generating a backscattering intensity of a charged particle, which includes a parameter generation step.

(Appendix 11)
When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a method for generating a backscattering intensity of the charged particles to a layer,
A simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the k−1th kth (k ≦ N) kth layer from the resist layer. The reflection coefficient R _k and the reflection scattering length β _R corresponding to the number of particles reflected by the k-th layer, and the charged particles reaching the k-th layer are the k-th layer. The downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that pass through the K + 1 layer, and the upward corresponding to the number of particles that the charged particles that have passed through the (k + 1) th layer upward pass through the kth layer A first parameter generation step for generating a transmission coefficient T ′ _k and an upward transmission scattering length β _{T ′} for each of the substances included in the k-th layer;
A multilayer wiring structure sample having a different area density of each layer is exposed and developed with a plurality of different evaluation patterns, and the charged particle intensity returning to the resist layer is measured based on the measured line width of the evaluation pattern after the development. A second parameter generation step for _obtaining a conversion coefficient C _k which is a ratio accumulated by exposure of the layer;
For the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the reflection coefficient R _k , downward transmission coefficient T _k , upward transmission coefficient T ′ _k and the scattering length β, and a first step of dividing the area according to the distance between the surrounding area and the area of interest,
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
A second step of sequentially determining the downward transmitted charged particle intensity E in each layer by the area of the first step in order from the first layer to the Nth layer;
In order from the first layer to the N-th layer, the reflection coefficient R _k is multiplied by the conversion coefficient C _k to obtain the reflected charged particle intensity E ′ in each layer by the area of the first step. 3 processes,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure And then, sequentially from the (N-1) th layer to the first layer, a fourth step for determining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step;
A fifth step of outputting the sum of the reflected charged particle intensity E ′ ₁ and the upward transmitted charged particle intensity E ″ ₁ obtained in the first layer below the resist layer as the backscattering intensity;
A method for generating the backscattering intensity of charged particles having:

(Appendix 12)
Performing the method for generating the backscattering intensity of the charged particles according to any one of appendices 1 to 11,
An exposure data correction step of correcting exposure data having an exposure pattern and an exposure intensity based on the backscattering intensity of the generated charged particles;
A method for manufacturing a semiconductor device, comprising: exposing a resist layer in accordance with the corrected exposure data.

(Appendix 13)
When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a charged particle backscattering intensity generation program for causing a computer to execute a step of generating a backscattering intensity of the charged particle to the layer,
With respect to the kth (k ≦ N) kth layer from the resist layer, the reflection coefficient R corresponding to the number of particles reflected by the kth layer through the (k−1) th (k−1) th layer is reflected. _k and the reflection scattering length β _R and the downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that the charged particles that have reached the k-th layer pass through the k-th layer downward, According to the mixing ratio of the substance from the first layer to the (k-1) th layer and for each substance contained in the kth layer,
Further, the upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} corresponding to the number of particles that have passed through the k + 1th layer upward and transmitted through the kth layer are determined from the Nth layer. according to the mixing ratio of the substance up to the k + 1 layer and for each substance contained in the kth layer,
The generating step includes
With respect to the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the A first step of dividing the area according to the reflection coefficient R _k , the downward transmission coefficient T _k , the upward transmission coefficient T ′ _k and the scattering length β with respect to the mixing ratio, and the distance between the surrounding area and the area of interest. Have
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
Furthermore, after determining the downward transmitted charged particle intensity E ₁ in the first layer and the reflected charged particle intensity E ′ ₁ in the first layer for the first layer by the area of the first step, respectively. , A second step of sequentially determining the lower transmitted charged particle intensity E and the reflected charged particle intensity E ′ in each layer from the second layer to the Nth layer by the area of the first step,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure Then, in order from the N-1th layer to the first layer, a third step of obtaining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step,
And a fourth step of outputting the sum of the reflected charged particle intensity E ′ ₁ obtained in the first layer below the resist layer and the upward transmitted charged particle intensity E ″ ₁ as the backscattering intensity. A program for generating the backscattering intensity of charged particles.

(Appendix 14)
When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a charged particle backscattering intensity generation program for causing a computer to execute a step of generating a backscattering intensity of the charged particle to the layer,
The generating step includes
A simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the k−1th kth (k ≦ N) kth layer from the resist layer. The reflection coefficient R _k and the reflection scattering length β _R corresponding to the number of particles reflected by the k-th layer, and the charged particles reaching the k-th layer are the k-th layer. The downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that pass through the K + 1 layer, and the upward corresponding to the number of particles that the charged particles that have passed through the (k + 1) th layer upward pass through the kth layer A first parameter generation step for generating a transmission coefficient T ′ _k and an upward transmission scattering length β _{T ′} for each of the substances included in the k-th layer;
A multilayer wiring structure sample having a different area density of each layer is exposed and developed with a plurality of different evaluation patterns, and the charged particle intensity returning to the resist layer is measured based on the measured line width of the evaluation pattern after the development. A second parameter generation step for _obtaining a conversion coefficient C _k which is a ratio accumulated by exposure of the layer;
For the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the reflection coefficient R _k , downward transmission coefficient T _k , upward transmission coefficient T ′ _k and the scattering length β, and a first step of dividing the area according to the distance between the surrounding area and the area of interest,
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
A second step of sequentially determining the downward transmitted charged particle intensity E in each layer by the area of the first step in order from the first layer to the Nth layer;
In order from the first layer to the N-th layer, the reflection coefficient R _k is multiplied by the conversion coefficient C _k to obtain the reflected charged particle intensity E ′ in each layer by the area of the first step. 3 processes,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure And then, sequentially from the (N-1) th layer to the first layer, a fourth step for determining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step;
A fifth step of outputting the sum of the reflected charged particle intensity E ′ ₁ and the upward transmitted charged particle intensity E ″ ₁ obtained in the first layer below the resist layer as the backscattering intensity;
A program for generating the backscattering intensity of charged particles having:

10: Silicon substrate 14: Resist layer 20: Multilayer wiring structure

Claims (11)

When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a method for generating a backscattering intensity of the charged particles to a layer,
With respect to the kth (k ≦ N) kth layer from the resist layer, the reflection coefficient R corresponding to the number of particles reflected by the kth layer through the (k−1) th (k−1) th layer is reflected. _k and the reflection scattering length β _R and the downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that the charged particles that have reached the k-th layer pass through the k-th layer downward, According to the mixing ratio of the substance from the first layer to the (k-1) th layer and for each substance contained in the kth layer,
Further, the upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} corresponding to the number of particles that have passed through the k + 1th layer upward and transmitted through the kth layer are determined from the Nth layer. according to the mixing ratio of the substance up to the k + 1 layer and for each substance contained in the kth layer,
The generation method is as follows:
With respect to the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the A first step of dividing the area according to the reflection coefficient R _k , the downward transmission coefficient T _k , the upward transmission coefficient T ′ _k and the scattering length β with respect to the mixing ratio, and the distance between the surrounding area and the area of interest. Have
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
Furthermore, after determining the downward transmitted charged particle intensity E ₁ in the first layer and the reflected charged particle intensity E ′ ₁ in the first layer for the first layer by the area of the first step, respectively. , A second step of sequentially determining the lower transmitted charged particle intensity E and the reflected charged particle intensity E ′ in each layer from the second layer to the Nth layer by the area of the first step,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure Then, in order from the N-1th layer to the first layer, a third step of obtaining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step,
And a fourth step of outputting the sum of the reflected charged particle intensity E ′ ₁ obtained in the first layer below the resist layer and the upward transmitted charged particle intensity E ″ ₁ as the backscattering intensity. A method for generating the backscattering intensity of charged particles. In claim 1,
In the first step of dividing the area, the mixing ratio α ^{− of the} substance from the first layer to the (k−1) th layer is determined by the respective substances of the first layer to the k−1th layer above the target area. The charged particle backscattering intensity obtained by multiplying the area ratio (α _{1 to} α _k-1 ) by the specific gravity (w _{1 to} w _k-1 ) of each of the first to k-1 layers Generation method. In claim 1 or 2,
In the first step of dividing the area, the mixing ratio α ⁻ of the substances from the Nth layer to the (k + 1) th layer is the area ratio (α of each of the substances from the Nth layer to the (k + 1) th layer below the target area. _N in to? _{k + 1),} the method of generating the backscattering intensity of the first through N of the (k + 1) th layer, respectively layers gravity _(w N _{to w k + 1)} multiplied by the sum to sought charged particles. In any one of claims 1, 2, and 3,
When obtaining the reflected charged particle intensity in the second step, the reflection coefficient R _k is multiplied by a conversion coefficient C _k which is a ratio of the charged particle intensity returning to the resist layer accumulated by exposure of the resist layer. Then, a method of generating the backscattering intensity of the charged particles to obtain the reflected charged particle intensity. In claim 1,
Further, a simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the reflection coefficient R _k and the reflection scattering length β _R at the k-th layer and the downward transmission coefficient are calculated. T _k and downward transmission scattering length β _T are generated for each substance contained in the k-th layer according to the mixing ratio of the substances from the first layer to the (k−1) -th layer, and in the k-th layer The upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} are generated for each of the substances included in the k-th layer according to the mixing ratio of the substances from the Nth layer to the (k + 1) th layer. A method for generating a backscattering intensity of a charged particle, which includes a first parameter generation step. In claim 5,
Further, the simulation of electron scattering is performed on a plurality of multilayer wiring structure samples each layer having a predetermined area density combination, and the downward transmission coefficient and reflection coefficient of the kth layer for each multilayer wiring structure sample. Or by referring to a table of the downward transmission coefficient, reflection coefficient, or upward transmission coefficient of the depth z of the k-th layer generated in the first parameter generation step. Extracting the upper or lower mixing ratio of the k-th layer of the wiring structure sample, and based on the extracted mixing ratio of the plurality of multilayer wiring structure samples and the area density of each layer of the plurality of multilayer wiring structure samples , A method for generating the backscattering intensity of charged particles, which has a second parameter generation step for obtaining the specific gravity w of each layer. In claim 4,
Further, a plurality of different evaluation patterns are exposed and developed on a multilayer wiring structure sample having a different area density of each layer, and the conversion coefficient C _k is _obtained based on a measured value of the line width of the evaluation pattern after the development. A method for generating a backscattering intensity of a charged particle, which includes a parameter generation step. When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a method for generating a backscattering intensity of the charged particles to a layer,
A simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the k−1th kth (k ≦ N) kth layer from the resist layer. The reflection coefficient R _k and the reflection scattering length β _R corresponding to the number of particles reflected by the k-th layer, and the charged particles reaching the k-th layer are the k-th layer. The downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that pass through the K + 1 layer, and the upward corresponding to the number of particles that the charged particles that have passed through the (k + 1) th layer upward pass through the kth layer A first parameter generation step for generating a transmission coefficient T ′ _k and an upward transmission scattering length β _{T ′} for each of the substances included in the k-th layer;
A multilayer wiring structure sample having a different area density of each layer is exposed and developed with a plurality of different evaluation patterns, and the charged particle intensity returning to the resist layer is measured based on the measured line width of the evaluation pattern after the development. A second parameter generation step for _obtaining a conversion coefficient C _k which is a ratio accumulated by exposure of the layer;
For the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the reflection coefficient R _k , downward transmission coefficient T _k , upward transmission coefficient T ′ _k and the scattering length β, and a first step of dividing the area according to the distance between the surrounding area and the area of interest,
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
A second step of sequentially determining the downward transmitted charged particle intensity E in each layer by the area of the first step in order from the first layer to the Nth layer;
In order from the first layer to the N-th layer, the reflection coefficient R _k is multiplied by the conversion coefficient C _k to obtain the reflected charged particle intensity E ′ in each layer by the area of the first step. 3 processes,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure And then, sequentially from the (N-1) th layer to the first layer, a fourth step for determining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step;
A fifth step of outputting the sum of the reflected charged particle intensity E ′ ₁ and the upward transmitted charged particle intensity E ″ ₁ obtained in the first layer below the resist layer as the backscattering intensity;
A method for generating the backscattering intensity of charged particles having: Implementing the method for generating the backscattered intensity of charged particles according to any one of claims 1 to 8,
An exposure data correction step of correcting exposure data having an exposure pattern and an exposure intensity based on the backscattering intensity of the generated charged particles;
A method for manufacturing a semiconductor device, comprising: exposing a resist layer in accordance with the corrected exposure data. When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a charged particle backscattering intensity generation program for causing a computer to execute a step of generating a backscattering intensity of the charged particle to the layer,
With respect to the kth (k ≦ N) kth layer from the resist layer, the reflection coefficient R corresponding to the number of particles reflected by the kth layer through the (k−1) th (k−1) th layer is reflected. _k and the reflection scattering length β _R and the downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that the charged particles that have reached the k-th layer pass through the k-th layer downward, According to the mixing ratio of the substance from the first layer to the (k-1) th layer and for each substance contained in the kth layer,
Further, the upward transmission coefficient T ′ _k and the upward transmission scattering length β _{T ′} corresponding to the number of particles that have passed through the k + 1th layer upward and transmitted through the kth layer are determined from the Nth layer. according to the mixing ratio of the substance up to the k + 1 layer and for each substance contained in the kth layer,
The generating step includes
With respect to the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the A first step of dividing the area according to the reflection coefficient R _k , the downward transmission coefficient T _k , the upward transmission coefficient T ′ _k and the scattering length β with respect to the mixing ratio, and the distance between the surrounding area and the area of interest. Have
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
Furthermore, after determining the downward transmitted charged particle intensity E ₁ in the first layer and the reflected charged particle intensity E ′ ₁ in the first layer for the first layer by the area of the first step, respectively. , A second step of sequentially determining the lower transmitted charged particle intensity E and the reflected charged particle intensity E ′ in each layer from the second layer to the Nth layer by the area of the first step,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure Then, in order from the N-1th layer to the first layer, a third step of obtaining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step,
And a fourth step of outputting the sum of the reflected charged particle intensity E ′ ₁ obtained in the first layer below the resist layer and the upward transmitted charged particle intensity E ″ ₁ as the backscattering intensity. A program for generating the backscattering intensity of charged particles. When the resist layer formed on the first layer of the multilayer wiring structure in which each layer from the first layer to the Nth layer includes a pattern of one substance or a plurality of substances is irradiated with a charged particle beam, the resist In a charged particle backscattering intensity generation program for causing a computer to execute a step of generating a backscattering intensity of the charged particle to the layer,
The generating step includes
A simulation of electron scattering is performed on the structure of the semiconductor device for which the backscattering intensity of the charged particles is to be calculated, and the k−1th kth (k ≦ N) kth layer from the resist layer. The reflection coefficient R _k and the reflection scattering length β _R corresponding to the number of particles reflected by the k-th layer, and the charged particles reaching the k-th layer are the k-th layer. The downward transmission coefficient T _k and the downward transmission scattering length β _T corresponding to the number of particles that pass through the K + 1 layer, and the upward corresponding to the number of particles that the charged particles that have passed through the (k + 1) th layer upward pass through the kth layer A first parameter generation step for generating a transmission coefficient T ′ _k and an upward transmission scattering length β _{T ′} for each of the substances included in the k-th layer;
A multilayer wiring structure sample having a different area density of each layer is exposed and developed with a plurality of different evaluation patterns, and the charged particle intensity returning to the resist layer is measured based on the measured line width of the evaluation pattern after the development. A second parameter generation step for _obtaining a conversion coefficient C _k which is a ratio accumulated by exposure of the layer;
For the target area of the k-th layer, the charged particle intensity from the surrounding area including the target area, the area density α _{k of the} substance in each of the surrounding areas in the k-th layer, and the reflection coefficient R _k , downward transmission coefficient T _k , upward transmission coefficient T ′ _k and the scattering length β, and a first step of dividing the area according to the distance between the surrounding area and the area of interest,
The charged particle intensity in the first step is calculated by (1) multiplying the downward transmitted charged particle intensity E _k−1 in the k−1 layer transmitted through the k−1 layer by the downward transmission coefficient T _k. The downward transmitted charged particle intensity E _{k in} the k-th layer determined in step (2), and (2) the downward transmitted charged particle intensity E _k−1 in the _k− 1th layer multiplied by the reflection coefficient R _k. Reflected charged particle intensity E ′ _k in the k-th layer and (3) upward transmitted charged particle intensity E in the k-th layer obtained by multiplying the charged particle intensity returning from the k + 1-th layer by the upward transmission coefficient T ′ _k "and a _k, charged particle intensity returning from the (k + 1) th layer, upwardly transmitted charged particle intensity E in the first k + 1 layer" and k _{+ 1,} it is the sum of the reflected charged particle intensity E _'k in the (k + 1) -th layer ,
A second step of sequentially determining the downward transmitted charged particle intensity E in each layer by the area of the first step in order from the first layer to the Nth layer;
In order from the first layer to the N-th layer, the reflection coefficient R _k is multiplied by the conversion coefficient C _k to obtain the reflected charged particle intensity E ′ in each layer by the area of the first step. 3 processes,
The calculated a multilayer wiring area of the upwardly transmitted charged particle intensity E "said _N first step amount in the N-th layer to the charged particle intensity said multiplied by the upward transmission coefficient T _'N reflected from the substrate under the structure And then, sequentially from the (N-1) th layer to the first layer, a fourth step for determining the upward transmitted charged particle intensity E ″ in each layer by the area of the first step;
A fifth step of outputting the sum of the reflected charged particle intensity E ′ ₁ and the upward transmitted charged particle intensity E ″ ₁ obtained in the first layer below the resist layer as the backscattering intensity;
A program for generating the backscattering intensity of charged particles having:

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