JPH09129635A - Semiconductor shape prediction simulation and system thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a semiconductor shape prediction simulation method, which can predict the shape of a semiconductor, which is close to the shape of the real semiconductor, and reduces the labor of users, and the system of the method. SOLUTION: Three-dimensional meshes 8 are set on an analytic plane, which is the object of a simulation. The meshes 8 are made to expand and nodes 7 are made to displace on the basis of the principle of a virtual work. The shape of a semiconductor is predicted by the positions of the nodes 7. A constraint in the principle of the virtual work makes it a condition that some out of the nodes 7 are displaced only on the analytic plane, some of the nodes 7 are displaced outside of the analytic plane and a stress from the outside of the analytic plane acts on some of the nodes 7. By imposing this constraint, the nodes 7 can be brought close to an actualer restraint and in the prediction for the shape of the semiconductor, the shape of the semiconductor, which is remarkably close to the shape of the real semiconductor, can be predicted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a semiconductor shape prediction simulation method and system for predicting the shape of a semiconductor, and in particular, it can predict the shape of a semiconductor close to the actual shape of the semiconductor, and the effort of the user in setting the simulation parameters. The present invention relates to a semiconductor shape prediction simulation method and system for reducing the noise.

[0002]

2. Description of the Related Art A silicon thermal oxide film is used to electrically isolate active elements on an LSI. However, LOCOS that is widely used in the current LSI manufacturing
In a process such as a (Local Oxidation of Silicon) process, as shown in FIG. 18, the interface 4 between the uneven silicon 1 and the oxide film 2 is oxidized, so that part of the silicon 1 is changed to the oxide film 2. High stress mainly occurs near the bird's beak below the nitride film 3 due to the volume expansion at this time. Further, such stress causes crystal defects in the silicon 1 substrate, and deteriorates electrical characteristics such as data storage time of DRAM.

Various semiconductor shape prediction simulation methods have been conducted since the early 1980s in order to evaluate the stress generated in such an oxidation process and to predict the shape of the finally formed oxide film 2. It has been announced by the institution. Such a semiconductor shape prediction simulation method treats the oxide film 2 as a viscous fluid (Reference 1: D.Chin, SYOh, SMHu, and RWDutton, IEEE
Trans. Electron Devices, ED-30, (1983), p.744) and those that treat the oxide film 2 as a viscoelastic body (Reference 2: Naoto Saito et al., The Japan Society of Mechanical Engineers (ed. Issue (1
991), p.2057). When the oxide film is treated as a viscoelastic body, it is desirable in terms of accuracy to handle the stress-strain relationship of the oxide film separately for the volume deformation component as shown in FIG. 19 and the shear deformation component as shown in FIG.

However, in order to decompose the deformation into the volume deformation component and the shear deformation component, the stress component in the direction perpendicular to the analysis plane corresponding to the cross section of the layer structure including the oxide film to be simulated is also included. It is necessary to perform stress analysis. At this time, it is necessary to impose some constraint in the direction perpendicular to the analysis plane.

[0005]

However, conventionally, there are a constraint condition of plane strain that the displacement in this direction is zero and a constraint condition of plane stress that is not restrained at all. There are two types of semiconductor shape prediction simulation methods. The constraint of plane stress ignores the actual constraint that exists, and the constraint of plane strain is stricter than it actually is, resulting in overestimation of stress. Therefore, when comparing the oxide film shape predicted by simulation under these constraint conditions with the actually formed oxide film shape, there is a problem that the shape is different.

FIG. 21 is a diagram showing a conventional simulation system. In FIG. 21, 10 is a computer which is the main body of the simulation system for predicting the shape of the actual semiconductor, 13 is a hard copy output machine for printing the oxide film shape predicted by the simulation, and 17 is displayed on the display of the computer 10. 3 is a screen of a specific example of a simulation result. In the simulation system shown in FIG. 21, among the parameters necessary for performing the simulation, the activation volume of the interfacial reaction rate constant and the oxidation species diffusion coefficient (Reference 3: P. Sutardja, WGO
ldham, IEEE Trans.Electron Devices, ED-36, (1989), p.2
415), there is a parameter determined by shape comparison between the oxide film shape predicted by simulation and the actual oxide film shape.

Conventionally, in order to obtain such parameters, first, a photograph of the actual oxide film shape is taken. Further, the computer 10 predicts the oxide film shape as shown on the screen 17, and the hard copy output machine 13 prints the predicted oxide film shape. The shape of the oxide film on the photograph and the shape of the oxide film on the printed matter are compared. The parameters are modified by shape comparison. Under the corrected parameters, the computer 10 creates the oxide film shape again. In this way, the prediction of oxide film shape by simulation, shape comparison, and parameter modification are repeated. After the repetition, if the shape of the oxide film by the simulation and the shape of the oxide film by the photograph become the same, the repetition is finished. The parameter at the time when it ends is the correct parameter.

By the way, the user mainly performs the above-mentioned comparison work. In order to facilitate shape comparison, the scales of the oxide film shape on the photograph and the oxide film shape on the printed matter must be the same. For this purpose, the user performs a work to make the scales of both the same by making a reduced or enlarged copy of the hard copy of the oxide film shape by simulation or a reduced or enlarged copy of the photograph. Conventionally, there is a problem that such complicated work is required.

Further, it is desirable that the parameter such as the activation volume physically has a constant value regardless of the oxidation temperature. However, if a simulation is performed by setting a constant value for the activation volume parameter regardless of the oxidation temperature,
The result of the simulation is different from the actual shape. This is because the simulation model is incomplete. Therefore, parameters such as activation volume are determined by shape comparison. There is a problem that it is difficult for the user to set the parameters determined by this shape comparison by himself. Especially, when a general user who is not familiar with the simulation uses the simulation system.

The present invention has been made to solve these problems, and in predicting the shape of a semiconductor, it is possible to predict the shape of the semiconductor close to the actual shape, and
An object of the present invention is to obtain a semiconductor shape prediction simulation method and system for reducing the labor of the user in setting the simulation parameters.

[0011]

According to a first aspect of the present invention, there is provided a semiconductor shape prediction simulation method for predicting a cross-sectional shape of a layer structure including an oxide film by using a finite element method, A first step of setting an element including a plurality of nodes on an analysis plane corresponding to the cross section; and a second step of expanding the element to displace the plurality of nodes of the element based on the principle of virtual work. And a third step of predicting the shape of the cross section based on the position of the node on the analysis plane, the constraint condition imposed on the element in the principle of the virtual work is that of the node Of these, some of the nodes are displaced by a first constraint condition only on the analysis plane, and some of the nodes are displaced by an outward direction from the analysis plane to the outside of the analysis plane. And the constraint condition of Of serial nodes, for some nodes and a third constraint stress in the outer direction acts.

In the problem solving means according to claim 2 of the present invention, the node under the third constraint condition is the same as the node under the second constraint condition, and the node under the first constraint condition. Among the displacements under the second constraint condition, the components of the displacement in the direction perpendicular to the analysis plane are the same as all the nodes under the second constraint condition, except for the nodes. Of the stresses under the constraint condition of No. 3, the sum of all the nodes under the third constraint condition of the stress component in the direction perpendicular to the analysis plane is zero.

In the problem solving means according to claim 3 of the present invention, the outward direction is a direction perpendicular to the analysis plane.

[0014] The means for solving the problem according to claim 4 of the present invention is:
In the second step, the nodes are displaced based on a governing equation derived from the virtual work principle and using an implicit method.

The problem solving means according to claim 5 of the present invention is
A semiconductor shape prediction simulation system for predicting the shape of a semiconductor, comprising: a scanner for capturing the first semiconductor shape from a photograph of a first semiconductor shape, which is the shape of an actual semiconductor; A main body of the system for predicting the shape of a semiconductor, and displaying the first semiconductor shape that has been taken in and a second semiconductor shape that is obtained by predicting the shape of the actual semiconductor on the display in an overlapping manner; Equipped with.

In the means for solving the problems according to claim 6 of the present invention, the photograph has a printed scale, and the system selects two positions on the scale displayed on the display. , For the user of the system to select the first and second semiconductor shapes displayed on the display, or to select the destination of the selected first or second semiconductor shape. Further pointing device and input means for inputting the actual distance between the two points, the main body receives the one selected by the pointing device and the actual distance, and the first or the first Rotate the semiconductor shape of 2 to display on the display,
The selected first or second semiconductor shape is moved to the destination and displayed on the display, or based on the actual distance and the position of the two points, the first or second semiconductor shape. Is enlarged or reduced to make the scales of the first and second semiconductor shapes the same and displayed on the display.

The problem solving means according to claim 7 of the present invention is
A semiconductor shape prediction simulation system for predicting the shape of an oxide film, comprising: a low stress viscosity coefficient, an activation volume of an oxidation species diffusion coefficient, and an interfacial reaction rate that are preset at each oxidation temperature when the oxide film is formed. Parameters such as a constant activation volume, a viscous coefficient activation volume, or a stress time step are set in advance, and the parameters are displayed on the display so that the user of the system can select them. Based on this, the shape of the oxide film is predicted.

[0018]

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiment 1 FIG. First, a model of a general oxide film semiconductor shape prediction simulation method will be described with reference to FIGS. 13 to 15, 1 is silicon which is a substrate, 2 is an oxide film formed on silicon 1, 3 is a nitride film which is a mask on oxide film 2, and 4 is an interface between silicon 1 and oxide film 2. 5 is a transition region where the interface 4 has moved.

The two-dimensional oxidation process will be described below with reference to Reference 2. First, referring to FIG. 13, oxidizing species (H 2 O or O 2) in the gas phase are supplied to the oxide film 2,
It diffuses inside and reaches the interface 4 (oxidizing species diffusion process). Next, with reference to FIG. 14, the interface 4 moves to the silicon 1 side due to the oxidation at the interface 4, and the moved interface is set as the transition region 5 (interface moving process). Next, referring to FIG. 15, the transition region 5 is expanded, and the oxide film 2 that was originally present is pushed up by the expansion and stress is generated (volume expansion process). The above is a general simulation model, and the semiconductor shape prediction simulation method will be described in more detail below along with this model.

First, the oxidizing species diffusion process will be described.
Oxidizing species in the gas phase are supplied to the oxide film 2, diffuse in the oxide film 2 and reach the interface 4. The local concentration of oxidizing species at the interface 4 is obtained by solving the steady-state diffusion equation, ▽ (Deff ▽ C) = 0, and calculating the concentration distribution of oxidizing species. Where C
Is the concentration of oxidizing species, ∇ is the vector operator Nabla, and Deff is the oxidizing species diffusion coefficient which is the effective coefficient of oxidizing species.

[0021]

(Equation 1)

Here, Deff0 is the diffusion coefficient of the oxidizing species when stress does not work, k is the Boltzmann constant, T is the oxidation temperature, and Vd
Is the activation volume of the oxidizing species diffusion coefficient Deff, p is the hydrostatic pressure, and p = − (σx + σy + σz) / 3. σi (i = x, y, z) is the vertical component of stress.

Next, the interface moving process will be described. After the oxidation concentration C obtained in the oxidizing species diffusion process is obtained, the local oxidation rate F (F is also the flow of oxidizing species) at the interface 4 is obtained. Referring to FIG. 16, it is assumed that the local oxidation rate F of the interface 4 is proportional to the product of the oxidizing species concentration C and the interface reaction rate constant ks. That is, F · n = ks C. Note that n is an outward normal vector of the oxide film.

[0024]

(Equation 2)

Ks0 is an interface reaction rate constant when no stress is applied, LORIENT is a plane orientation factor, and σn is a stress component perpendicular to the interface and has a negative value when the stress compresses the oxide film 2.
Vs is an activation volume having an interface reaction rate constant ks. The distance is calculated by multiplying the oxidation rate F at the interface 4 thus obtained by a predetermined time. Next, a transition region 5 is set below the interface 4 by that distance as shown in FIG.

The flow F of oxidizing species at the vapor phase / oxide film interface 2b is F · n = h (C ^* -C). Here, h is the mass transport coefficient, and C ^* is the equilibrium concentration of the oxidizing species concentration. Lateral boundaries 2a and 2 of the oxide film 2
It is assumed that there is no flow F of oxidizing species at c and no flow F of oxidizing species at the nitride film interface 3a, that is, F · n = 0.

Next, the volume expansion process will be described. The transition region 5 is expanded and the stress generated by the expansion is obtained using the finite element method. FIG. 17 shows an analysis plane by the finite element method. The upper diagram in FIG. 17 is a cross section of the layer structure including the actual oxide film 2, and the lower diagram is an analysis plane corresponding to the cross section. In the finite element method, as shown in FIG. 17, the analysis plane is composed of a number of meshes 6 which are two-dimensional elements of a triangle. Reference numeral 7 is a node which is a corner of the mesh 6. The mesh 6 may be a quadrangle other than the triangle.

[0028]

(Equation 3)

Equation 3 is a governing equation derived from the principle of virtual work. The objective of the simulation is to solve the displacement increment Δam of the node 7 (corner of each mesh 6 on the xy plane) at the m-th time step, which is an unknown number, and obtain the position of each node 7 from the displacement increment Δam. Predict the shape of semiconductors. Ω is the total area of all meshes 6.

B is a strain-displacement matrix, D is an elasticity matrix, Δtm is a time increment at the m-th time step, and Δfm is a nodal load increment at the m-th time step. B ^T is a transposed matrix of B. Further, β is a rate of change of inelastic strain with time and depends on stress.

[0031] When the viscoelastic body, the stress - strain relation, σm = 3K · εm σx ' = 2G · (εx' -εx c ') σy' = 2G · (εy '-εy c') σz '= 2G · become ^{(εz '-εz c') τxy} = 2G · (γxy-γxy c) τyz = 2G · (γyz-γyz c) τzx = 2G · (γzx-γzx c). K is the bulk modulus and G is the shear modulus.

Σm is the average stress, and σm = (σx + σy + σz) / 3.

Εm is an average strain, and εm = (εx + εy + εz) / 3.

Τij = (i, j = x, y, z) is the shear stress.

Γij = (i, j = x, y, z) is the shear strain.

Σi '= (i = x, y, z) is the deviation of the normal stress component, and σx' = σx-σm σy '= σy-σm σz' = σz-σm.

Εi '= (i = x, y, z) is the deviation of the vertical strain, and εx' = εx-εm εy '= εy-εm εz' = εz-εm.

Ε i ^c '(i = x, y, z) is an inelastic component in the deviation component of the vertical strain, and is between the time change rate βi (i = x, y, z). as stream law, βx = d / dt · εx c '= σx' / (2μ) βy = d / dt · εy c '= σy' / (2μ) βz = d / dt · εz c '= σz' / There is a relationship of (2μ). Note that d / dt is a time derivative.

Γ ij ^c '(i, j = x, y, z) is an inelastic component of the shear strain, and its rate of change β with time.
As a flow rule between ij (i, j = x, y, z), βxy = d / dt · γxy ^c = τxy / μ βyz = d / dt · γyz ^c = τyz / μ βzx = d / dt・ There is a relation of γzx ^c = τzx / μ.

[0040]

(Equation 4)

Usually, the viscoelastic coefficient μ is normally expressed by the equation (4). Here, V0 is an activation volume having a viscosity coefficient μ. μ 0 is a low stress viscosity coefficient and depends on T. As a function form of f, a hyperbolic function such as Eyring viscosity or an exponential function can be considered.

The mesh 6 in the principle of virtual work
FIG. 17 shows the constraint conditions of No. Left and right boundaries S1 and S
2 The component ux in the x-axis direction of the displacement of one of the nodes 7 above is set to zero (in FIG. 17, the x component ux of the boundary S1 is set to zero). That is, ux = 0. Also on the other boundary (boundary S2 in FIG. 17), ux is set to zero or a linear boundary condition is set. That is, ux1 = ux2 = ux3 = ... fx1 + fx2 + fx3 + ... = 0. fx is a component of the reaction force of the node 7 in the x-axis direction, and FIG.
The subscript i (i = 1, 2, 3, ...) In is the number given in order to the node 7 on the boundary S2.

On the other hand, on the bottom surface S3, the node 7 on the bottom surface S3
The y-axis component uy of the displacement of is assumed to be zero. That is, uy = 0.

When a constraint condition of plane strain is imposed as a constraint condition in the z-axis direction perpendicular to the analysis plane, the z-axis direction component uz of the displacement of all the nodes 7 is zero (in other words, displacement is performed only on the analysis plane). ), That is, uz = 0.

When a plane stress constraint condition is imposed as a constraint condition in the z-axis direction perpendicular to the analysis plane, it is assumed that no stress acts in the z-axis direction at all nodes 7, and the z
The axial component fz is zero (in other words, stress does not work in the direction from the analysis plane to the analysis plane), that is, fz = 0.

However, as explained in the prior art, the above-mentioned constraint condition of plane stress neglects the actual constraint that is apparently present, and the above-mentioned constraint condition of plane strain is stricter than the actual constraint. As a result, the stress is overestimated.

Therefore, in the present embodiment, the constraint condition of displacement and stress from the actually existing analysis plane to the outside of the analysis plane is appropriately imposed to bring it closer to the actual constraint. That is, some of the nodes 7 are the first constraint condition that the nodes 7 are displaced only on the analysis plane, and some of the nodes 7 are outward from the analysis plane to the outside of the analysis plane. A second constraint condition of displacement and a third constraint condition of an outward stress acting on some of the nodes 7 are imposed.

FIG. 1 is a diagram showing an analysis body corresponding to the above-mentioned analysis plane used in the semiconductor shape prediction simulation method according to the first embodiment of the present invention. First, all the meshes 6 shown in FIG. 17 are replaced with the meshes 8 which are the elements as shown in FIGS. 2 and 3, that is, all the meshes 6 shown in FIG. 17 are extruded in the z-axis direction, and as shown in FIG. The analysis body 9 is used. The mesh 8 is a triangular prism element as shown in FIG. 2, an element divided into tetrahedral elements as shown in FIG. 3, or a hexahedral element when the shape of the mesh 6 before extrusion in the z-vertical direction is a quadrangle. Any three-dimensional element may be used.

Next, a semiconductor shape prediction simulation method for predicting the cross-sectional shape of the layer structure including the oxide film 2 using the finite element method will be described. First, an element including a plurality of nodes is set on the analysis plane corresponding to the cross section. Next, the transition area 5 is set. The setting of the transition area 5 is as described above. Next, the mesh 8 is expanded to displace the plurality of nodes 7 of the mesh 8 based on the principle of virtual work as described above. Note that Ω in Expression 3 here is the total volume of all the meshes 8 and imposes the above-described first to third constraint conditions. Next, the stress at each node 7 is calculated by displacing the node 7. The mesh 8 is again expanded based on the stress, and the node 7 is displaced based on the virtual work principle. The expansion of the mesh 8 and the calculation of stress are repeated for a predetermined time step. After the time step ends, the transition area 5 is reset again. By repeating the setting of the transition region 5 and the calculation of the expansion / stress of the mesh 8 between time steps, the shape of the cross section is finally predicted based on the position of the node 7 on the analysis plane.

When the shape of the oxide film predicted by the simulation and the shape of the actual oxide film under these constraint conditions are compared, the shapes are remarkably in agreement with each other as compared with the conventional case. One reason for this is
This is because the constraint condition in the present embodiment is a condition close to the actual situation where the stress is determined by the balance between the stress in silicon and the stress in the oxide film. And the accuracy of the resulting stress distribution is significantly improved compared to the conventional one,
The effect of the stress on the displacement of the nodes is also significantly improved compared to the conventional case.

In the present embodiment, the constraint conditions of displacement and stress from the actually existing analysis plane to the outside of the analysis plane are appropriately imposed, so that the actual constraint can be approximated and the shape of the semiconductor can be predicted. In doing so, it is possible to predict the shape of the semiconductor, which is extremely close to the shape of the actual product. In addition, since the elements are three-dimensional elements, the volume expansion, stress, and displacement of the analysis body 9 can be three-dimensionally analyzed as shown in FIG.

Embodiment 2 In the present embodiment, an example of the first to third constraint conditions described in the first embodiment will be described. 5 to 7 are diagrams showing constraint conditions in the second embodiment of the present invention. As shown in FIG. 5, the constraint condition of one surface (back surface in FIG. 5) of the front surface and the back surface of the analysis body 9 is set so that the component uz of the displacement of each node 7 on the one surface in the z-axis direction is zero ( In other words, it displaces only on the analysis plane),
That is, uz = 0 (first constraint condition).

The other constraint condition (surface in FIG. 5) in the z-axis direction is a boundary condition for plane deformation. That is, uz1 = uz2 = uz3 = ... fz1 + fz2 + fz3 + ... = 0 (second and third constraint conditions). Here, uz is the z component of the displacement of the node 7, fz is the z component of the reaction force of the node 7, and FIG.
The subscript i (i = 1, 2, 3, ...) In is a number given to the nodes 7 on the surface of the analysis body 9 in order.

Other constraint conditions on the boundary are the same as the constraint conditions shown in FIG. That is, referring to FIG. 6, the x component ux of the displacement of one of the nodes 7 on the left and right boundaries S1 and S2 is set to zero (in FIG. 6, the x component ux of the boundary S1 is set to zero). That is, ux = 0. On the other boundary (boundary S2 in FIG. 6),
ux is set to zero, or a linear boundary condition is set. That is, ux1 = ux2 = ux3 = ... fx1 + fx2 + fx3 + ... = 0. Here, ux is the x component of the displacement of the node 7, fx is the x component of the reaction force of the node 7, and the subscript i in FIG. 6 (i = 1,
2, 3, ...) are the numbers sequentially given to the nodes 7 on the boundary S2.

Referring to FIG. 7, the bottom surface S3 is above the bottom surface S3.
The y component uy of the displacement of the upper node 7 is zero. That is, uy = 0.

When the shape of the oxide film predicted by the simulation and the shape of the actual oxide film under these constraint conditions are compared, the shapes are remarkably in agreement as compared with the conventional case. One reason for this is
As described above, the constraint condition of plane deformation that the front surface of the analysis body 9 is kept flat before and after the deformation of the analysis body 9 and the constraint condition that the back surface is also kept flat (displacement is zero) are in silicon. This is because the condition is close to the actual situation where the stress is determined by the balance between the stress in the oxide film and the stress in the oxide film.
The accuracy of the resulting stress distribution is significantly improved as compared with the conventional one, and the influence of the stress on the displacement of the node is also significantly improved as compared with the conventional one.

As described above, according to the present embodiment, by imposing the constraint condition that the plane displacement is on the front surface of the analysis body 9 and the displacement in the z-axis direction is zero on the back surface, the shape of the real object is predicted in predicting the shape of the semiconductor. It is possible to predict the shape of a semiconductor extremely close to

Embodiment 3 FIG. In the first embodiment, the stress components are x-axis, y-axis, z-axis, xy plane, yz plane, zx.
Although the six-component analysis handles six components on the plane, the four-component analysis may handle four components on the x-axis, y-axis, z-axis, and xy plane. In this case, as shown in FIG. 8, x is about three nodes arranged in the z-axis direction with respect to the analysis plane.
Pseudo three-dimensional analysis is performed assuming that the displacement amounts in the axial direction and the y-axis direction are the same. If the displacements of the nodes p1 and p1 'in the x-axis and y-axis directions, the displacements of the nodes p2 and p2' in the x-axis and y-axis directions, and the displacements of the nodes p3 and p3 'in the x-axis and y-axis directions are the same. To do.
That is, the outward displacement from the analysis plane to the outside of the analysis plane is
Displace only in the direction perpendicular to the analysis plane. Note that the nodes pi (i = 1, 2, 3, ...) Are the nodes on the back side of the analysis body 9, and the nodes pi ′ (i = 1, 2, 3, 3, ...) Are the nodes on the front side of the analysis body 9. .

[0059] stress-strain relationship, σm = 3K · εm σx ' = 2G · (εx' -εx c ') σy' = 2G · (εy '-εy c') σz '= 2G · (εz' -εz c ') Τxy = 2G · (γxy−γxy ^c ).

[0060] Flow law, βx = d / dt · εx c '= σx' / (2μ) βy = d / dt · εy c '= σy' / (2μ) βz = d / dt · εz c '= σz '/ (2μ) βxy = d / dt · γxy ^c = τxy / μ.

As described above, according to this embodiment, the number of variables can be reduced and the calculation can be simplified. Further, it is not necessary to actually make the node 7 in the z-axis direction by extrusion.

Embodiment 4 In the first embodiment, the governing equation (Equation 3) is an example in which an explicit method is used, but an implicit method may be used instead.

[0063]

(Equation 5)

Equation 5 is a governing equation using the explicit method (reference 4: OC Zhengiewitz, translated by Yoshiki and Yamada,
Matrix finite element method, Baifukan). D0 is pseudoelastic ^{matrix, D0 = [D -1 + Δtm} θS0] is ^-1 S0 = ^dβ / ^dσ. θ is a parameter indicating the time integration scheme and is 0
Takes a value from 1 to 1.

Solving Δam based on the explicit method puts a heavy burden on the computer of the simulation main body.
The simulation takes a long time. However, if Δam is solved based on the implicit method, the load on the computer of the simulation body is reduced, and the time required for the simulation is shortened.

Embodiment 5 FIG. 9 is a diagram showing the configuration of the simulation system according to the fifth embodiment of the present invention. In FIG. 9, 10 is a computer which is the main body of the simulation system, 11 is a photograph showing the oxide film shape of an actually manufactured semiconductor, 12 is a scanner for outputting the oxide film shape of Photo 11 to the computer 10, and 14 is a scanner. A mouse that is a pointing device. Photo 11 is SEM
(Scanninng Electron Microscope) photograph and TEM (Transmission Electron Microscop)
e: Transmission electron microscope) Any type of photograph such as a photograph may be used. The pointing device may be something other than the mouse 14.

Next, a semiconductor shape prediction simulation method using the simulation system shown in FIG. 9 will be described. First, an actual semiconductor oxide film shape is prepared, and the oxide film shape is photographed. In addition, in the photograph 11, a scale is baked in parallel with the main surface of the oxide film shape on the photograph 11 (for example, the interface between the silicon and the oxide film other than the bird's beak). Next, the simulation of the computer 10 is used to predict the oxide film shape, and the computer 1
It is displayed on the display of 0. Next, referring to FIG. 9, the scanner 12 converts the photograph 11 into image data and captures it in the computer 10. Next, by displaying the oxide film shape according to Photo 11 on the display of the computer 10 based on the image data, the oxide film shape and Photo 11 according to the simulation are displayed on the display of the computer 10.
Oxide film shape due to.

By the way, normally, when the captured image data is displayed as it is on the display of the computer 10, the main surface of the oxide film shape shown in Photo 11 is not displayed in parallel with the main surface of the oxide film shape by simulation. in addition,
The scale of the oxide film shape shown in Photo 11 on the display does not match the scale of the oxide film shape by simulation. Therefore, it is not easy to compare the oxide film shape shown in Photo 11 with the oxide film shape obtained by simulation.

Therefore, by rotating, enlarging, reducing, or moving the oxide film shape shown in Photo 11 on the display or the oxide film shape by simulation, the main surface of the oxide film shape by Photo 11 and the oxide film by simulation are shown. Overlap with the main surface of the shape. That is, the conventional superimposing work is performed on the display of the computer 10.

As one of the methods, as shown in FIG. 10, by selecting two points on the above-mentioned scale with the mouse 14, the coordinates of the two points are input to the computer 10. Next, a distance setting window as shown in FIG.
0 is displayed on the display and the actual distance between the two points is input by the keyboard which is the input means of the computer 10. The computer 10 corrects the image data based on the coordinates of the two points so that the simulated oxide film main surface and the two points are parallel (that is, parallel to the oxide film main surface shown in Photo 11).

Further, based on the coordinates of the two points and the input distance between the two points, the image data is corrected so as to be equal to the scale of the oxide film shape by simulation. Next, based on the corrected image data, the oxide film shape shown in Photo 11 is displayed again on the display of the computer 10.

However, although the main surface of the oxide film shape by simulation and the main surface of the oxide film shape shown in Photo 11 are parallel to each other, they may not overlap each other. In that case, as shown in FIG. 11, the oxide film shape by simulation or the oxide film shape by Photo 11 is used for mouse 1
4 is used, the selected oxide film shape is moved in parallel, and both are superposed.

As described above, according to the present embodiment, the work of making the scale of the oxide film shape according to the photograph 11 and the scale of the oxide film shape by the simulation performed when setting the parameters the same on the display is performed by the user. Labor can be reduced. Further, the hard copy output machine 13 which is conventionally used only for shape comparison is not necessary.

In the present embodiment, the case where the oxide film shape obtained by the oxidation simulation and the oxide film shape obtained by the photograph 11 are compared has been described, but the present invention can be applied to other simulations such as etching, deposition and lithography simulation. .

Further, the semiconductor shape prediction simulation system according to the present embodiment can be applied to the semiconductor shape prediction simulation method in the first to fourth embodiments and other semiconductor shape prediction simulation methods.

Embodiment 6 FIG. FIG. 12 is a diagram showing a simulation system according to the sixth embodiment of the present invention. Reference numeral 15 in FIG. 12 is a table for displaying parameters,
16 is a screen of a specific example of the result of the simulation displayed on the display of the computer 10, and other symbols are shown in FIG.
And 21 correspond to the respective symbols. As shown in FIG. 12, a table 15 having the oxidation temperature T as a variable is displayed. The parameters displayed in Table 15 are low stress viscosity coefficient μ
0, activation volume V 0 with viscosity coefficient μ, interfacial reaction rate constant k
Parameters such as activation volume Vs of s, activation volume Vd of diffusion coefficient of oxidizing species Deff, time step of stress calculation, etc., which are difficult for the system user to set, and numerical values of parameters at each oxidation temperature T are displayed. To do.

First, the computer 10 calculates the optimum parameters at each oxidation temperature T set by comparison with the actual shape in advance.
It is stored in the internal storage device. The computer 10 displays the parameter at each oxidation temperature T in the table 15 on the display of the computer 10. The user selects the desired oxidation temperature T
The parameter in 1 is selected by the keyboard of the computer 10, the mouse 14 or the like. The shape of the oxide film is predicted based on the selected parameters.

Conventionally, the viscosity coefficient μ is obtained from the equation 4. The function f in Expression 4 is usually an exponential function expression, and the activation volume V0 is used as a variable. Conventionally, the activation volume V0 to be substituted into the equation 4 has been constant. Therefore, the value of the viscosity coefficient μ at each oxidation temperature T was not optimum. In the present embodiment, the optimum activation volume V according to each oxidation temperature T
By substituting 0 into the function f, the derived viscosity coefficient μ can also take an optimum value according to each oxidation temperature T. The same applies to the activation volume Vs of the interface reaction rate constant ks obtained from the equation 2 and the activation volume Vd of the oxidizing species diffusion coefficient Deff obtained from the equation 1. The low stress viscosity coefficient μ 0 is preset at the oxidation temperature T.

Further, the governing equation (Equation 3) of the first embodiment
The stress analysis is performed by the sequential solution method (reference document 4) in which a time step is usually set and the time change of the stress is sequentially tracked, and the computer 10 performs the sequential solution method. In this iterative solution method, if the time step is made too large, the vibration phenomenon of the solution occurs and the accuracy of the solution deteriorates (reference document 5: Uchida et al., IEICE Tech. ED94-48, SDM94-45, VL).
D94-45). Conversely, if the time step is too small, the calculation time will increase. Therefore, there is a time step in which the solution oscillation phenomenon does not occur and the calculation time is the shortest, and its value varies depending on the oxidation temperature T.

There is also a method of dynamically setting the time increment Δtm of the time step according to the increment of the inelastic strain, but in the case of the oxidation simulation, an appropriate method has not been established yet, and the simulation executor has tried. It is often decided by mistake. This time increment Δ
tm is also a parameter that is difficult for the user to set, and the optimum time increment Δtm is displayed in advance in the table 15 and the user selects it.

As described above, according to this embodiment, the optimum parameters set in advance are displayed in a table and the user is allowed to select the optimum parameters, so that the general user who is not very familiar with the simulation can obtain the best simulation result. Therefore, the work of the user can be simplified and the labor can be reduced.

In FIG. 12, one table 1
Although 5 parameters are displayed in 5, each parameter may be divided into another table and used in combination in the calculation.

Further, the semiconductor shape prediction simulation system according to the present embodiment can be applied to the semiconductor shape prediction simulation method in the first to fourth embodiments and other semiconductor shape prediction simulation methods.

[0084]

According to the first aspect of the present invention, by appropriately imposing the constraint condition of the displacement and stress from the actually existing analysis plane to the outside of the analysis plane, it is possible to bring the condition closer to the actual constraint. In predicting the shape of, the effect of being able to predict the shape of the semiconductor that is remarkably close to the actual shape is obtained.

According to claim 2 of the present invention, the constraint condition is simple, and in predicting the shape of the semiconductor, it is possible to predict the shape of the semiconductor which is remarkably close to the actual shape.

According to claim 3 of the present invention, the number of variables can be reduced and the calculation can be simplified.

According to claim 4 of the present invention, the load on the computer of the simulation main body is reduced, and the time required for the simulation is shortened.

According to claim 5 of the present invention, it is possible to reduce the labor of the user when setting the parameters.

According to claim 6 of the present invention, it is possible to obtain a semiconductor shape prediction simulation system in which it is possible to easily display the first and second semiconductor shapes on the display in the same scale and superimpose them.

According to claim 7 of the present invention, there is an effect that the work of the user can be simplified and the labor can be reduced when setting the parameters.

[Brief description of the drawings]

FIG. 1 is a diagram showing an analysis body according to a first embodiment of the present invention.

FIG. 2 is a diagram showing an example of elements according to the first embodiment of the present invention.

FIG. 3 is a diagram showing another example of elements in the first embodiment of the present invention.

FIG. 4 is a diagram showing three-dimensional expansion of elements according to the first embodiment of the present invention.

FIG. 5 is a diagram showing a constraint condition in the second embodiment of the present invention.

FIG. 6 is a diagram showing a constraint condition in the second embodiment of the present invention.

FIG. 7 is a diagram showing a constraint condition in the second embodiment of the present invention.

FIG. 8 is a diagram showing a pseudo three-dimensional analysis of elements according to the third embodiment of the present invention.

FIG. 9 is a diagram showing a configuration of a semiconductor shape prediction simulation system according to a fifth embodiment of the present invention.

FIG. 10 is a diagram showing a semiconductor shape prediction simulation method according to a fifth embodiment of the present invention.

FIG. 11 is a diagram showing a semiconductor shape prediction simulation method according to a fifth embodiment of the present invention.

FIG. 12 is a diagram showing a semiconductor shape prediction simulation system according to a sixth embodiment of the present invention.

FIG. 13 is a diagram showing a flow of a conventional semiconductor shape prediction simulation.

FIG. 14 is a diagram showing a flow of a conventional semiconductor shape prediction simulation.

FIG. 15 is a diagram showing a flow of a conventional semiconductor shape prediction simulation.

FIG. 16 is a diagram showing an oxidation rate in a conventional analysis plane.

FIG. 17 is a diagram showing an analysis plane in the conventional finite element method.

FIG. 18 is a diagram showing stress caused by volume expansion.

FIG. 19 is a diagram showing volume deformation when an oxide film is treated as a viscoelastic body.

FIG. 20 is a diagram showing shear deformation when an oxide film is treated as a viscoelastic body.

FIG. 21 is a diagram showing a conventional semiconductor shape prediction simulation system.

[Explanation of symbols]

1 silicon, 2 oxide film, 3 nitride film, 4 interface, 5
Transition area, 6 mesh, 7 nodes, 8 mesh,
9 analysis object, 10 computer, 11 scanner, 12 photograph, 13 hardcopy output machine, 14 mouse, 15
Table, 16, 17 Simulation screen.

Claims (7)

[Claims] 1. A semiconductor shape prediction simulation method for predicting a cross-sectional shape of a layer structure including an oxide film by using a finite element method, wherein an element including a plurality of nodes is set on an analysis plane corresponding to the cross section. The first step of expanding the element, the second step of displacing a plurality of nodes of the element based on the principle of virtual work, based on the position of the node on the analysis plane, A third step of predicting the shape of a cross section, the constraint condition imposed on the element in the principle of the virtual work is that some of the nodes are displaced only on the analysis plane. 1 constraint condition, some of the nodes are displaced in the outward direction from the analysis plane to the outside of the analysis plane, and some of the nodes are In the outward direction Semiconductor shape prediction simulation method and a third constraint which forces act, the. 2. The node under the third constraint condition is the same node as the node under the second constraint condition, and is a node other than the node under the first constraint condition, and the second node Among the displacements under the constraint conditions, the component of the displacement in the direction perpendicular to the analysis plane is the same for all the nodes under the second constraint conditions, and among the stresses under the third constraint conditions, The semiconductor shape prediction simulation method according to claim 1, wherein the stress component in the direction perpendicular to the analysis plane has a sum of all the nodes under the third constraint condition being zero. 3. The semiconductor shape prediction simulation method according to claim 1, wherein the outward direction is a direction perpendicular to the analysis plane. 4. The semiconductor shape prediction simulation method according to claim 1, wherein in the second step, the node is displaced based on a governing equation derived from the virtual work principle and using an implicit method. 5. A semiconductor shape prediction simulation system for predicting the shape of a semiconductor, comprising: a scanner that captures the first semiconductor shape, which is a photograph of the first semiconductor shape that is the actual semiconductor shape, and a display. And including the predicted shape of the actual semiconductor, and displaying the captured first semiconductor shape and the second semiconductor shape obtained by predicting the actual semiconductor shape on the display. A semiconductor shape prediction simulation system including the main body of the system. 6. The photograph has a scale imprinted thereon, the system selecting the position of two points on the scale displayed on the display or the first display on the display. A second semiconductor shape is selected by the user of the system, or the selected first or second semiconductor shape is selected.
A pointing device for selecting a destination of the semiconductor shape, and an input means for inputting an actual distance between the two points,
The main body further receives the one selected by the pointing device and the actual distance, and rotates the first or second semiconductor shape to display on the display, or the selected first or second semiconductor shape. The second semiconductor shape is moved to the destination and displayed on the display, or the first or second semiconductor shape is enlarged or reduced based on the actual distance and the position of the two points. The semiconductor shape prediction simulation system according to claim 5, wherein the scales of the first and second semiconductor shapes are the same and are displayed on the display. 7. A semiconductor shape prediction simulation system for predicting the shape of an oxide film, comprising activation of a low stress viscosity coefficient and an oxidation species diffusion coefficient that are preset at each oxidation temperature when the oxide film is formed. Parameters such as volume, activation volume of interfacial reaction rate constant, activation volume of viscosity coefficient or time step of stress are set in advance, the parameters are displayed on the display, and the user of the system is allowed to select, A semiconductor shape prediction simulation system for predicting the shape of the oxide film based on the selected parameters.