JPH04216646A - Method for simulating shape of semiconductor integrated circuit - Google Patents

Abstract

PURPOSE:To estimate the cross-sectional shape of a hole after performing a working process in a short calculating time by adding the data of the representative points of the surface shape representing the shape of the hole in addition to the points representing the two-dimensional shape on a section to be analyzed. CONSTITUTION:The detailed two-dimensional shape of a cross section every time step and the rough three-dimensional shape of a whole hole 3 are found by virtually defining a plurality of shielding plates 8 with holes 3 produced by cutting a hole 3 in round slices in the horizontal direction in a plurality of nearly parallel planes every time step in the first stage and calculating the movement of each point representing the surface shape on a section to be analyzed (a surface the cross-sectional shape of which is to be estimated) and the movement of several points representing the shape of the hole 3 on each shielding plate 8 by taking the incident particle interrupting effect of each plate 8 in the second stage. After finding the shapes, the stage is again returned to the first state. The first and second stages are repeated until all time steps are completed.

Description

[Detailed description of the invention]

0001

[Field of Industrial Application] The present invention relates to a method for simulating the shape of a semiconductor integrated circuit, and in particular, to a method for simulating the shape of a large-scale semiconductor integrated circuit (hereinafter referred to as LSI) after a processing process (deposition or etching) is performed. The present invention relates to a simulation technique for predicting the shape of an LSI, and relates to an LSI shape simulation method that improves prediction accuracy and reduces calculation time.

0002

[Prior art] Conventional LSI shape simulation (
For example, Tazawa et al., “Unified Topograph
hy Simulator for Complex
Reaction including both D
“eposition and etching”,Sy
Mposium on VLSI Technology
y, 1989. ), two-dimensional deformation calculations were performed on the assumption that the cross-sectional shape of the simulated object continued indefinitely in the direction perpendicular to the analysis cross-section. However, on actual LSIs, the influence of the surface shape in the direction perpendicular to the analysis cross section cannot be ignored in many cases.
In particular, in hole areas such as through-holes, accurate shape prediction cannot be made unless the effect of shielding incident particles that contribute to deposition or etching by the walls in front and behind the analysis cross section is taken into account. There was a problem.

[0003] As a method to overcome the above problem, LSI
There is a method of treating the shape as three-dimensional data and performing three-dimensional deformation calculations (for example, Yamaguchi et al., "Three-dimensional Shape Simulation", Proceedings of the 36th Japan Society of Applied Physics Association Conference).

0004

[Problem to be solved by the invention] However, usually LSI
Although it is sufficient to be able to predict the cross-sectional shape of the hole when performing pattern design or process design, since the deformation of the entire hole shape is calculated in three dimensions, this method is different from normal two-dimensional simulation. There is a problem in that it takes a huge amount of calculation time to obtain the same level of accuracy.

[0005] An object of the present invention is to predict the cross-sectional shape of a semiconductor integrated circuit after the processing process has been carried out, while taking into account the influence of the surface shape in the direction perpendicular to the analyzed cross-section, and in a short calculation time. Our goal is to provide the technology that makes it possible.

[0006]

[Means for Solving the Problems] In order to solve the above problems, the present invention provides a shape simulation method for a semiconductor integrated circuit that predicts the cross-sectional shape after deposition or etching on the surface of a semiconductor integrated circuit. For cases where the incidence of particles contributing to deposition or etching is affected by the shielding effect of the surrounding three-dimensional shape, as in the part shown in FIG. The first step is to virtually define multiple shielding plates with holes created by cutting them into rings on a plane, and the movement of each point representing the surface shape on the plane whose cross-sectional shape is to be predicted (analytical cross-section). , by calculating the movement of several points representing the shape of the hole on each shielding plate, taking into account the shielding effect of each shielding plate on incident particles, the detailed cross-section after one time step has elapsed. a second stage to obtain the two-dimensional shape and the rough three-dimensional shape of the entire hole, and then return to the first stage again and repeat the first and second stages until all time steps are completed. The most important feature is the repetition of

[0007]

[Operation] According to the above-mentioned means, a simulation can be performed that takes into account the effect that incident particles contributing to deposition or etching are shielded by walls existing in front and behind the analysis section in the hole portion. Furthermore, when making a hole in a membrane or attaching a membrane to a hole, the shape of the hole may change over time, and the corners may gradually become rounded or sharp. In order to re-approximate the shape of the hole in each shielding plate by calculating the movement of the representative point of the surface shape at each time step, we will calculate the phenomenon in which the shielding effect changes due to the hole becoming rounded or pointed. You can perform simulations that take this into account.

In other words, in the present invention, in addition to the points representing the two-dimensional shape on the analytical cross section, data on surface shape representative points representing the shape of the hole are only added as graphic data, and surface movement calculation Also, it is sufficient to simply extend the two-dimensional calculation to three dimensions. In other words, complicated processing such as three-dimensional surface movement processing and unnecessary surface deletion processing that requires an enormous amount of calculation time is completely unnecessary.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described in detail below with reference to the drawings.

[0010] In all the drawings for explaining the embodiment, parts having the same functions are given the same reference numerals, and repeated explanations thereof will be omitted.

FIG. 1 is a flow chart for explaining an LSI shape simulation method according to an embodiment of the present invention, and FIG.
A plan view showing an example of defining a representative cross section for explaining the LSI shape simulation method of this embodiment, FIG. 3 is an analytical cross-sectional view for explaining an example of defining a representative cross section, and FIG. 4 shows a shielding calculation plane. FIG. 5 is a plan view for explaining a definition example of a shield calculation plane and surface shape representative points; FIG. 6 is a diagram for explaining a definition example of a shield calculation plane and surface shape representative points. Fig. 7 is a plan view for explaining an example of the definition of a shielding plate, Fig. 8
is an analytical cross-sectional view for explaining an example of the definition of a shielding plate, FIG.
10 is a plan view for explaining an example of redefining the surface shape representative point from the intersection of the closed curve showing the hole in the shield plate and the representative cross section, and FIG. 10 is the intersection of the closed curve showing the hole in the shield plate and the representative cross section. 11 is a plan view for explaining the calculation concept of the shielding effect of incident particles by each shielding plate, and FIG. 12 is a cross-sectional view of each shielding plate. Figure 13 is a plan view for explaining an example of redefining the representative surface curve from each surface shape representative point after movement; FIG. 2 is an analytical cross-sectional view for explaining an example of redefining a representative surface curve from each surface shape representative point after movement.

2 to 14, 1 is an LSI substrate, 2 is an insulating film, 3 is a hole (through hole), 4 is a representative cross section, 5 is a representative surface shape curve, 6 is an analytical cross section, and 7 is a shielding calculation plane. , 8 is a shielding plate.

In the LSI shape simulation method of this embodiment, as shown in FIG. 1, first, as a pre-processing, a bottom surface (referred to as a reference bottom surface, usually a surface parallel to the LSI substrate 1) serving as a reference for analysis is prepared. In addition to setting the analytical cross section 6 (step 101) as a plane perpendicular to
As shown in the analytical cross-sectional view of FIG. (Step 103).

Thereafter, at each time step, representative points of the surface shape are determined (step 104), and approximate values are determined using a closed curve equation (step 105). Next, a new representative point of the surface shape is determined (step 106), and the movement of the surface area of each point is calculated (including calculation of shielding of incident particles) (step 107). Next, a representative surface shape curve 5 is defined (step 108).

[0015] Then, the processes of steps 104 to 108 are repeated until all time steps are completed (step 109).

In the process of step 104, as shown in FIGS. 4 to 6, the points of intersection with each representative surface shape curve 5 (surface (referred to as shape representative points).

In the process of step 105, a closed curve passing through each surface shape representative point (or its vicinity) on each shielding calculation plane 7 is approximated by an equation, and as shown in FIGS. A shielding plate 8 with holes to be defined is virtually defined. For example, when the corners are rounded, the equations used for approximation are:

[0018]

[Formula 1] xn/αn+уn/βn=1 If the corner is sharp,

[0019]

[Math 2] x=α(p1/n+q1/n)

0020
]

[Math 3] y=β(p1/n-q1/n)

0021
]

[Formula 4] |p|+|q|=1 is appropriate. Here, x and y are coordinate variables on the shielding calculation plane, and α, β, and n are constants. In other words, 2≦n<
When ∞, it represents an ellipse (a rounded figure), and when 0≦n≦1, it represents a pointed figure.

In the process of step 106, FIGS.
0, the intersections between the closed curves indicating the holes of each shielding plate 8 and the first defined representative cross sections are found, and these intersections are set as new surface shape representative points.

In the process of step 107, each point on the analytical cross section and each surface shape representative point are moved as shown in FIGS. 11 and 1.
As shown in FIG. 2, the calculation is performed taking into account the shielding of incident particles by each shielding plate 8.

In the process of step 108, as shown in FIGS. 13 and 14, the surface shape representative points after movement are connected by line segments for each representative section to which they belong, or
Or define a new representative surface curve by approximating it with a function.

As can be seen from the above description, according to this embodiment, particles contributing to deposition or etching are not incident on the surrounding area, such as in the hole 3 provided in the insulator 2 on the LSI substrate 1. In the case where the shielding effect of the three-dimensional shape is applied, the first step is to cut the hole 3 into rings in multiple planes approximately parallel to the horizontal direction at each time step. A plurality of open shielding plates 8 are virtually defined, and the second step is to move each point representing the shape of the surface on the analysis cross section (the surface where the cross-sectional shape is to be predicted) 6 and to move each point on each shielding plate 8. By calculating the movement of several points representing the shape of the hole by taking into account the shielding effect of each shielding plate 8 on incident particles, the detailed two-dimensional shape of the cross section after one time step has elapsed. , overall rough 3 of hole 3
Find the dimensional shape, then return to the first step again and repeat the first and second steps until all time steps are completed. Simulations can be performed that take into account the effect of shielding incident particles that contribute to deposition or etching by the wall that exists in the back.

Furthermore, when a film is applied to a rectangular hole 3, the shape of the hole 3 may change over time and the corners may gradually become rounded. However, in the present invention, each time step For each shielding plate 8, the movement of the representative point of the surface shape is calculated.
In order to reapproximate the shape of the hole, a simulation can be performed that takes into account the phenomenon that the shielding effect changes as the hole becomes rounder.

In other words, in the present invention, in addition to the points representing the two-dimensional shape on the analytical cross section, data of the surface shape representative point representing the shape of the hole 3 is only added as graphic data, and the surface movement Calculations can be done by simply extending two-dimensional calculations to three-dimensional ones. In other words, complicated processing such as three-dimensional surface movement processing and unnecessary surface deletion processing that requires an enormous amount of calculation time is completely unnecessary.

Although the present invention has been specifically explained above based on examples, it goes without saying that the present invention is not limited to the above-mentioned examples and can be modified in various ways without departing from the gist thereof. Nor.

[0029]

[Effects of the Invention] According to the present invention, it is possible to easily perform a shape simulation of a semiconductor integrated circuit that takes into account the influence of the surface shape in the direction perpendicular to the analysis cross section, and to calculate the contents of the shape data and deformation. Compared to a completely three-dimensional case, calculation time can be significantly reduced.

[Brief explanation of the drawing]

FIG. 1 is a flowchart for explaining an LSI shape simulation method according to an embodiment of the present invention.

FIG. 2 is a plan view showing an example of defining a representative cross section for explaining the LSI shape simulation method of this embodiment.

FIG. 3 is an analytical cross-sectional view for explaining an example of defining a representative cross-section.

FIG. 4 is a perspective view of a main part for explaining a shielding calculation plane.

FIG. 5 is a plan view for explaining an example of defining a shielding calculation plane and surface shape representative points.

FIG. 6 is an analytical cross-sectional view for explaining an example of defining a shielding calculation plane and surface shape representative points.

FIG. 7 is a plan view for explaining an example of the definition of a shielding plate.

FIG. 8 is an analytical cross-sectional view for explaining an example of the definition of a shielding plate.

FIG. 9 is a plan view for explaining an example of redefining a surface shape representative point from the intersection of a closed curve indicating a hole in a shielding plate and a representative cross section.

FIG. 10 is an analytical sectional view for explaining an example of redefining a surface shape representative point from the intersection of a closed curve indicating a hole in a shielding plate and a representative cross section.

FIG. 11 is a plan view for explaining the concept of calculating the shielding effect of incident particles by each shielding plate.

FIG. 12 is an analytical cross-sectional view for explaining the calculation concept of the shielding effect of incident particles by each shielding plate.

FIG. 13 is a plan view for explaining an example of redefining a representative surface curve from each surface shape representative point after movement;

FIG. 14 is an analytical cross-sectional view for explaining an example of redefining a representative surface curve from each surface shape representative point after movement.

[Explanation of symbols]

1 LSI board 2 Insulator 3 Hole 4　　　　　Surface section 5 Representative surface shape curve 6 Analysis cross section 7 Shielding calculation plane 8 Shielding plate Shielding plate

Claims (1)

[Claims] Claim 1. A semiconductor integrated circuit shape simulation method for predicting a cross-sectional shape after deposition or etching on the surface of a semiconductor integrated circuit, the object being simulated being sliced into rings by a plurality of planes substantially parallel to the horizontal direction. Virtually define multiple shielding plates with holes created by At the same time as calculating the movement of the upper point, the movement of the surface shape representative point on each shielding plate is calculated, and the shape of the hole in each shielding plate is reapproximated, thereby changing the overall three-dimensional shape of the simulation target. A method for simulating the shape of a semiconductor integrated circuit, which is characterized by approximately tracking the shape of a semiconductor integrated circuit.