JPS6158234A - Method for developing simulation - Google Patents

Abstract

PURPOSE:To enable to precisely form the surface of resist after developing by a method wherein the vector of developing is selectively increased on the necessary places only, or the developing vector on the unnecessary places is eliminated. CONSTITUTION:In the region surrounded by a boundary 1, a numerical operation is performed with a plurality of points, contained in the line 2 located on the initial surface of resist, as the starting point, and the locus 3 of the developing vector till the finishing time of developing is obtained. When the intervals between the tips of the adjoining developing vector is calculated, the intervals at two places are widened. At this point, the smallest integral number N4, which is not smaller than the quotient obtained by dividing the tip interval of the developing vector by the reference value, is calculated and the point at which the part between said two vectors will be divided into N4 sections is calculated. A numerical operation is performed with these points as new starting point, and the locus 4 of the new developing vector is calculated. By repeatingly performing the above-mentioned procedures on the entire initial surface of the resist, the number of developing vector can be suppressed to the minimum, thereby enabling to reduce the time necessary for numerical operation to the minimum.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to semiconductor process simulation, and particularly to a simulation method suitable for efficiently calculating a precise shape.

[Background of the invention]

Regarding development simulation methods, Jewett et al. discuss the advantages and disadvantages of various methods.

(R, E, Jewett, P, 1.) Iagouel
, A.R., Neureuther.

andT., Van Duzer, “Line-Pro
file Resist Development Si
mulation Techniquas”, Pol
ymarEngineering and 5cien
ce, vol, 17. No, 6. pp381-384.
(1977), the ray-tracing model is cited as a method suitable for three-dimensional development calculations. However, in development simulation using a ray-tracing model, if the distance between the tips of adjacent development vectors is too wide (the broken line connecting the tips of the development vectors represents the resist surface, in this case it is difficult to accurately display the resist shape). This problem is inherent in development simulation, since development generally increases the resist surface area.

[Purpose of the invention]

An object of the present invention is to provide a method for efficiently and precisely determining the resist surface after development in development simulation using a ray-tracing model.

[Summary of the invention]

In order to precisely determine the resist shape, a large number of development vectors may be generated at the start of the development simulation, but this method is disadvantageous in terms of calculation time. Therefore, the number of initial development vectors is kept relatively small and the distance between the tips of adjacent development vectors is measured every time a predetermined development time elapses, and if the distance is longer than a predetermined standard, the initial resist surface An appropriate number of development vectors are generated from Alternatively, if the distance is short, by deleting unnecessary development vectors, a precise resist shape can be obtained with the minimum necessary development vectors (and hence calculation time).

[Embodiments of the invention] The present invention will be explained below using examples.

Example 1 According to the ray-tracing model, the locus of the position vector r representing the development vector is described by a linear equation.

ds ds Here, S is the length along the trajectory, n is the virtual refractive index defined by the following equation, and the right side is the gradient of the virtual refractive index.

n = R + a a * / R... (2) Here, R
is the development rate at the position [r] in the resist film, Raa
m is its maximum value. The distribution of n is given separately, so the distribution of n is also known.

As shown in Figure 1, in the area surrounded by boundary 1, numerical calculations are performed based on the above equation using multiple points included in line segment 2 on the initial surface of the resist as starting points, and development is started from time 0 seconds. Locus 3 of the development vector up to the end time was obtained.

When the distance between the tips of adjacent development vectors was calculated, the distance was wider than the reference D1 at two locations, and the resist shape was also rough. Here, the distance D l between the starting points of the development vector (that is, the interval between the starting points on the line 2°) was used as the reference.

Therefore, find the minimum integer N that is not smaller than the quotient obtained by dividing the tip interval of the development vector by the reference value, and
We determined points that divide the starting points of the book vector into N4 sections. Using these points as new starting points, the same numerical calculations as described above were performed to obtain a new development vector locus 4.

By performing this operation, new development vectors were inserted into areas where the interval between development vectors had become wide with just one development calculation, and a precise resist shape could be drawn.

By repeating the above process for the entire initial surface of the resist, a three-dimensional precise resist image is created in the entire area surrounded by boundary 1, and the number of development vectors is uniformly increased over the entire area from the initial stage of development. This could be obtained in a short calculation time.

Note that if the intervals between all the development vectors do not fall within 3 of the reference value even in the second development calculation, the process may be repeated until one condition is satisfied.

Further, the measurement at one interval is not limited to the development end time, but may be performed at any time or any number of times during the development.

The value of D may be set to an appropriate value depending on the situation.

Embodiment 2 A method for further shortening the calculation time than in Embodiment 1 will be described using FIG. 2. Figure 2 is a diagram in which the boundary of the calculation area and the locus of the development vector are projected onto a plane perpendicular to the resist surface. After performing development calculations in the same manner as in Example 1 up to (referred to as the first stage development calculation), the tip distance of the development vector 3 is measured at this time, and if the value is smaller than the reference value, The two development vectors in question are deleted, and in the next development calculation stage (the following stages are referred to as the second stage, third stage, etc. as necessary).

The appropriate value of IID& for generating a new development vector 5 from an appropriate position between the two erased development vectors is approximately 0.1 to 0.7 times the value of Di in Example 1. It is.

For other development vectors, development calculations were continued using the results of the first stage as they were.

According to this method, shape calculations are not performed with unnecessary precision, so calculation time can be shortened without sacrificing precision.

Note that in this example, both of the two development vectors are deleted, but it is also possible to delete one and leave the other.

Embodiment 3 A method for further shortening the calculation time compared to the case of Embodiment 2 will be described with reference to FIG.

The differences between the method of this example and the method of Example 2 are as follows. That is, in this method, in the first stage development calculation, regarding two development vectors that are too far apart, instead of inserting the development vectors from the initial surface of the resist, the development vectors are inserted between the end points of the two vectors. from a suitable position.

In the second stage of development, a new development vector 7 is generated.

This process eliminates the need to insert development vectors many times in the first stage of development, thereby reducing calculation time.

In this embodiment, the number of newly generated development vectors is one in the wide part with nine intervals, but this number can be increased as necessary.

〔Effect of the invention〕

According to the present invention, when obtaining a precise resist shape, the number of development vectors can be minimized by selectively increasing development vectors only in necessary locations or deleting development vectors in unnecessary locations. Therefore, it is possible to perform simulations that minimize the time required for numerical calculations.

[Brief explanation of the drawing]

The first @ is a sketch of the development calculation area and the development vector. FIG. 2 is a diagram showing a development calculation area and a development vector when viewed from a direction in which the vertical direction is the depth direction of the resist. FIG. 3 is a diagram using the same display method as FIG. 2. 1... Boundary of the calculation area, 2... Line segment on the initial surface of the resist, 3... Trajectory of the development vector obtained by the first development calculation, 4... Second development Locus of the development vector obtained by calculation, 5... From the midpoint of the two development vectors that were too close as a result of the first stage development calculation, the newly generated development vector in the second stage development calculation. Trajectory, 6: A trajectory of a development vector that progresses by taking over the first-stage development vector as it is in the second-stage development calculation. 7... The interval was too wide as a result of the first stage development calculation 2
21 of the newly generated development vector in the second stage development calculation from the midpoint of the book's development vector. , 60. ,,2□1, Name of the invention: A person who corrects the development method! Relationship with rumors Patent applicant name (510J Hayashi Shikikai>, 1 Hitachi, Ltd. Target of amendment Column of [Detailed explanation of the invention] in the specification. → Contents of Toko-Bunmisaki Kei 71 amendment [(R,E, Jewett, P., 1. Hag
ouel, A.R. Neureuther and T. Van Duz
er @Line-Profile Re5ist
Development SimulationTe
Polymer Engineer
ring and Science, vol. 1?
, &6, pp381-384. 977J [R. E. Jewett, B. I. Haguell, N. R. Nieuwreiter and H. F<-'F/Dautour, "Resist Development Shape Simulation Silane Technology," Polymer Engineering and Science, VO.
l, 17. NcL6. pages 381 to 384,
1977, (R,E, Jewel, P. 1, Hagouel, A+R, Neureuthe
r andT, VanDuzer” Line
-Profile Re5ist Developer
tSimulation Techniques”
, Polymer Engineering and
5science, vol, 17, NG, 6
. I am corrected.

Claims (1)

[Claims] 1. In the process of development simulation, which is performed by advancing multiple development vectors from the resist surface, development calculations are performed while monitoring the calculated shape, and one or more development vectors are created depending on the degree of smoothness of the shape. A development simulation method characterized by generating or deleting a development vector.