JP2991140B2 - Reflow shape simulation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of simulating a reflow shape of a semiconductor device or the like, and more particularly to a method of simulating a reflow shape of a metal material film or an insulating film thereof.

[0002]

2. Description of the Related Art As a conventional method of simulating a reflow shape of a semiconductor device or the like, a method of analyzing a region by a finite element method using a Stokes equation is generally used.
However, when simulating the reflow shape of a thin film, it is necessary to consider the surface diffusion, it is difficult to form a fine mesh near the boundary between the surface diffusion layer and the bulk diffusion layer, and the calculation time is long. There was such a problem.

[0003] As a reflow model of the prior art, F.S.
A. According to Leon, "IEEE Trans.
CAD "7 (2) PP.168-173 (1988) (hereinafter referred to as a reference). This reflow model is shown in FIGS.
This will be described below. As shown in FIG.
BPSG (B, P
The surface shape of the oxide film 1 containing the string segment 2
4 (b) is a partially enlarged view of FIG. 4 (a), and the radius of curvature of the corner of BSPG1 is R. In this reflow model, a substance flows by diffusion from a portion having a large radius of curvature to a portion having a small radius of curvature, but has a negative radius of curvature on the surface of the concave portion.

Here, the free energy F of the surface is expressed by the following formula (4) as a surface area A and a surface tension constant γ: F = γA (4) The flow rate density (flux) J is expressed by the following equations (5) and (6), respectively.

[0005]

Where N is the number of particles, Ω is the volume of the molecule, D
Is the surface diffusion coefficient, k is the Boltzmann coefficient, T is the temperature, ν is the surface concentration of the molecule, ▽ s is the differential along the surface, R ₁ (S), R
₂ Let (S) be the radius of curvature of two sides that are orthogonal to each other.

[0007] As here D ₀ = DγνΩ ^2, flux J _{i-1, i} flowing from the string node P _i-1 to P _i is represented by the following formula (1),

[0008]

Note that R _i and R _i−1 are the radii of curvature of the contact points P _i and P _i−1 .

In the same manner, fluxes J are obtained for all the nodes 2. Then, as shown in the arrangement view of FIG. 5, △ and the node P amount of BPSG1 flowing from _i-1 to the node _{P i △ t · J i-} 1, i in the diffusion time t, nodes from the node P _i P _{i +} B flowing to ₁
The amount of PSG1 △ t · J _i, the difference between the _{i + 1,} i.e. the movement distance m from node P _i to node P _i 'is determined by the volume change V from the following formula (7) V = △ t ( J i _{-1, i} −J _{i, i + 1} ) (7) A new node Pi ′ is determined.

In this example, only the material on the surface of the fluid material film mainly composed of a metal material film or an insulating film is diffused during the reflow, and the mass transfer inside the bulk is negligible. Therefore, only the flux J on the surface due to surface tension need be calculated. Therefore, the shape after easy reflow can be calculated from the shape represented by the two-dimensional string model using this model. Therefore, there is an advantage that a calculation time is shortened and a program can be easily created.

[0012]

In the prior art described above, the surface diffusion has a low activation energy due to the temperature dependence of the diffusion coefficient, and the diffusion in the bulk cannot be ignored at high temperatures, so that the actual shape can be reproduced. There is a problem that will not be.

Further, when this reflow model is used,
Since the boundary between the flowable material film and the underlying substrate is not taken into account, the calculation is performed when the thickness of the flowable material film partially becomes 0 or less. In this conventional reflow model, only surface diffusion is taken into account, so that if bulk diffusion at high temperature increases, the actual shape cannot be reproduced.

An object of the present invention is to solve these problems,
An object of the present invention is to provide a reflow shape simulation method having high simulation accuracy and short calculation time.

[0015]

The structure of the present invention simulates the shape during reflow of a fluid material film formed on a base substrate of a semiconductor device and comprising a low-viscosity surface diffusion layer and a high-viscosity bulk diffusion layer. A step of extending a bisector of an outline of the material film shape from a node on the surface of the fluid material film to obtain an intersection with the outline of the undersubstrate; 1 on a straight line connecting the upper node and the intersection of the outline of the base substrate.
Calculating the amount of movement of the nodes on the surface by a volume change due to a two-dimensional Stokes flow.

In the present invention, when calculating the volume change V due to the Stokes flow, first, the node P due to surface diffusion is calculated.
_i-1, the following equation flux J _{i-1, i} by surface diffusion between P _i (1)
Asked by

[0017]

[0018] Here, the curvature of the node P _i the R _i, D surface diffusion coefficient, temperature T, | and the flux J _i-1 and the distance between the nodes _{a, i | P i -P i-} 1 V is obtained from the diffusion time Δt by the following equation (2).

[0019]

Here, the volume change V where μ ₁ and ₂ are the surface diffusion layer and the viscosity coefficient of the bulk diffusion layer, and d ₁ and ₂ are the surface diffusion layer and the thickness of the bulk diffusion layer, are the volume changes V at each node P _i−1 , The distance between the nodes P _i , P _i ′ is determined by geometric calculation from the area of this quadrilateral, assuming that the distance between the nodes P _i , P _{i +1} and the movement point P _i ′ is equal to a rectangle. And the calculation of the volume change V due to the Stokes flow is applied to an axially symmetric model of the distance ρ _i from the central axis to the node, and can be obtained by the following equation (3).

[0021]

According to the structure of the present invention, the analysis is performed not only by the surface diffusion but also by the diffusion of the bulk. The feature is that the simulation accuracy can be greatly improved.

[0023]

FIG. 1 is a flowchart for explaining a reflow simulation of a metal material film in a two-dimensional shape as one embodiment of the present invention. FIG. 2 shows a simulation shape of the metal material film portion in FIG. It is sectional drawing explaining. In this reflow simulation, first, the shape and outline data 102 of the metal material film 101 before reflow is read (step S1). This shape outline data 102 is created using a string model.

Next, a method of calculating the shape after reflow will be described with reference to FIG. First, a straight line 104 is extended in an equiangular direction from two sides adjacent to the node 103 of the shape / profile data 102 of the metal material film 101 (step S2). The distance d between the extended straight line 104 and the intersection 106 of the base substrate 105 is calculated (step S3).

Next, the flow between the node 103 and the intersection 106 is calculated, and the movement amount is obtained (step S).
4). When calculating this flow, the metal material film 101 is composed of a low-viscosity surface diffusion layer and a high-viscosity bulk diffusion layer, and the flow velocity is 0 on the surface of the base substrate 105, and the flow velocity is proportional to the distance. Further, the shear stress generated between the two layers was equal, and the surface diffusion rate due to the surface tension was calculated in consideration of the Stokes flow. Next, a specific calculation method will be described.

First, the flux J _i−1 , _i due to surface diffusion between the nodes P _i−1 , P _i is calculated using the Einstein relation according to the above-mentioned document, taking into account the diffusion due to surface tension. It is calculated by equation (1).

[0027]

[0028] Here, the curvature of the node P _i the R _i, surface D diffusion coefficient, temperature T, | and the distance between nodes | P _i -P _i-1.

Next, a boundary condition is given to the one-dimensional Stokes equation from the flux J _i−1 , _i and the diffusion time Δt, and the Stokes flow μ ▽ ² v = 0 (v is The velocity (flow velocity) is given the conditions shown in FIG. 3 (shear stresses are equal) to obtain v _1, and μ ₁ (v ₀ −v ₁ ) / d ₁ = μ ₂ · v ₁ / d ₂ And the volume change V is determined by the following equation (2) from the law of conservation of mass.

[0030]

Here, μ ₁ and ₂ are the viscosity coefficients of the surface diffusion layer and the bulk diffusion layer, and d ₁ and ₂ are the film thicknesses of the surface diffusion layer and the bulk diffusion layer.

This volume change V is calculated at each of the nodes P _i-1 and P _i-1 in FIG.
_Since a square having a unit thickness of _i , P _{i + 1} and the moving point P _i ′ is formed, the distance between the nodes P _i , P _i ′ is the moving distance m. Since this movement distance m becomes a triangle with the distance between each of the nodes P _i−1 , P _i , P _{i + 1} , its volume change V (area) is known. Can be. As a result, as shown in FIG. 1, the node 103 on the external shape data 102 is
It is moved to the node 107 after the reflow. As described above, the present invention is characterized in that the moving amount of the contact can be easily calculated by the one-dimensional Stokes flow on the straight line 104.

A comparison result when the simulation method of the present invention and the method of the prior art are applied to reflow of aluminium will be described. At a temperature of 300 ° C., the ratio of the diffusion coefficient between the bulk diffusion layer and the surface diffusion layer is one million times, but the film thickness ratio in this case is 1/2000, and this is applied to equation (2). By calculation, the ratio of the two becomes five times, and about five times the surface diffusion occurs. If this is converted into a shape, a difference of about 25% is predicted, and a difference of 25% occurs between the two. This is mainly because the prior art does not consider bulk diffusion. As described above, by using the reflow shape simulation method of the present invention, the calculation time to be increased is only the calculation of d and the equation (2). Therefore, the simulation accuracy is greatly improved only by increasing the calculation time by about 10%. There is a feature that can be.

Further, according to the reflow shape simulation method of the present invention, since the distance from the surface of the underlying substrate is calculated, the thickness of the metal material film partially becomes 0 or less as in the prior art. It can be seen that the calculation accuracy is improved.

Next, as a second embodiment of the present invention, a reflow shape simulation method using an axisymmetric model will be described. Although the concept of this embodiment is similar, the amount of movement of the nodal point can be calculated in consideration of the axial symmetry, and the point is that the above equation (2) is replaced by the following equation (3).

[0036]

Here, ρ _i is the distance from the central axis of the axisymmetric model to the node. This embodiment can be applied to a case of performing a shape simulation of an axially symmetric model such as embedding of a contact hole, and has an advantage that its practicality can be expanded.

[0038]

As described above, according to the reflow shape simulation method of the present invention, the accuracy of the shape simulation can be greatly improved in almost the same calculation time as compared with the prior art. is there.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a simulation process according to an embodiment of the present invention.

FIG. 2 is a cross-sectional view illustrating the shape of the simulation of FIG.

FIG. 3 is a schematic diagram showing a relationship between Stokes flows in FIG. 2;

FIG. 4 is a cross-sectional view illustrating a shape of a simulation according to the related art and an enlarged view thereof.

FIG. 5 is a node arrangement diagram for performing the simulation calculation of FIG. 3;

[Explanation of symbols]

1 oxide film (BPSG) 2 Suroringu segment 101 on the metal thin film 102 outer shape data 103 outer shape data of the node (P _i) linearly extending from 104 node 105 ground substrate outline 106 contour line of intersection 107 contacts after reflow ( P _i ')

Claims (3)

(57) [Claims] 1. A reflow shape simulation method for simulating a shape at the time of reflow of a fluid material film formed on a base substrate of a semiconductor device and comprising a low-viscosity surface diffusion layer and a high-viscosity bulk diffusion layer. A step of extending a bisector of the outline of the material film shape from a node on the surface of the material film to obtain an intersection with the outline of the undersubstrate; and a node on the surface and the outline of the undersubstrate. And calculating a movement amount of a node on the surface by a volume change due to a one-dimensional Stokes flow on a straight line connecting the intersections of the two. 2. When calculating the volume change V due to the Stokes flow, first, the flux J _i−1 , _i due to surface diffusion between the nodes P _i−1 , P _i due to surface diffusion is calculated by the following equation (1). Wherein the curvature of the node P _i the R _i, D surface diffusion coefficient, temperature _{T, | P i -P i-} 1 | this flux J _i-1 and the distance between the nodes, _i and diffusion time Δt From this, V is calculated by the following equation (2). Where μ ₁ and ₂ are the viscosity coefficients of the surface diffusion layer and bulk diffusion layer,
This volume change V where d ₁ and ₂ are the film thicknesses of the surface diffusion layer and the bulk diffusion layer is equal to a square having a unit thickness of each of the nodes P _i−1 , P _i and P _{i + 1} and the moving point P _i ′. 2. The reflow shape simulation method according to claim 1, wherein a distance between the nodes P _i and P _i ′ is obtained as a movement amount m by geometric calculation from the area of the quadrilateral. 3. The calculation of the volume change V due to the Stokes flow is applied to an axially symmetric model of the distance ρ _i from the central axis to the node, and is calculated by the following equation (3). The reflow shape simulation method according to claim 2.