JP2787316B2 - LSI shape simulation method - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a shape simulation technique for predicting a cross-sectional shape of a semiconductor LSI device after processing (etching / deposition). The present invention relates to a simulation method for improving the accuracy of a shape simulation including the above.

[Conventional technology]

In conventional simulation, the shape of the processed surface expressed by a line segment connecting the points, all the points on the working surface, the inclination angle theta ₁ and theta ₂ formed by the both side surfaces of the point _(Figure 12 (a) ~ (Refer to (d)).
With this method, a smoothly changing curved surface can be handled without any problem, but there is a possibility that a large error may occur at a point where the gradient changes steeply. In FIG. 12, P is a point where the gradient changes steeply (singular point), and S is a machined surface.

θ ₁ = 90 °, θ ₂ = 0 ° (FIG. 12 (a) or (d)
FIG. 13 and FIG. 14 show an example of a case where the singular point P is deposited by a deposition apparatus having a combination of a directional deposition component and an isotropic deposition component.
Shown in the figure. FIG. 13 shows the actual shape, and FIG. 14 shows the simulated shape according to the conventional method. 13 and 14, S1 is the initial shape, and S2 is the shape after processing.

[Problems to be solved by the invention]

Since it is basically difficult to correct an error in the shape simulation in the middle, even a small error is accumulated, and there is a possibility that a shape completely different from the actual shape is finally predicted. Therefore, in order to handle a shape including a singular point with high accuracy in the conventional simulation method, the interval between points should be made fine at least as shown in FIG. It is necessary to advance the simulation in a short time step while adding points to the above, which has a disadvantage that the calculation time is greatly increased. In FIG. 15, S3 is the initial shape, and S4 is the shape after processing.

The present invention has been made in view of such a point,
An object of the present invention is to perform a simulation of an LSI cross-sectional shape change including a singular point with high accuracy without increasing calculation time.

[Means for solving the problem]

In order to achieve such an object, the present invention provides an LSI shape simulation method for predicting a processed shape from an initial surface shape of an element cross section, in which an initial surface is approximated by a set of points, and each point includes the point. A first method that treats all the angles between the inclination angles formed by the straight lines on both sides, and a movement that determines the end point of the movement vector of each point when moving each point on the processing surface by the first method. And a second method to be taken on the rear surface.

[Action]

In the LSI shape simulation method according to the present invention, high-precision processing of a singular point can be realized without considering the singular point, that is, by performing the same processing at all points.

〔Example〕

First, a method of calculating a shape change at a singular point will be described. Assuming that the moving speed of the processing surface in the direction perpendicular to the processing surface with the inclination angle θ is v (θ), the singular point is a point having all the angles between the inclination angles θ ₁ and θ ₂ formed by the surfaces on both sides of the point. Therefore, the shape after time t can be regarded as v in the direction perpendicular to the surface with all surfaces having an angle between the inclination angles θ ₁ and θ _2.
(Θ) · A curved surface composed of surfaces that are moved by t (represented by a combination of envelopes formed by the moving surfaces themselves on both sides of the singularity and each moving surface having an angle between both surfaces) Curved surface). The shape change calculation methods in singularity, utilizing this natural laws, n aliquoted angle between the inclination angle theta ₁ and theta ₂ of which both side faces of the singularity forms a fine angle [Delta] [theta], the respective angle It is characterized in that the shape of the singular point after t time is obtained by calculating and joining the movement positions of the holding surfaces after t time. FIG. 1 corresponds to the actual shape of FIG. 12 (a singular point of θ ₁ = 90 ° and θ ₂ = 0 °
FIG. 9 is an explanatory diagram for explaining a shape change calculation method at a singular point when a directional deposition component and an isotropic deposition component are combined (deposited by a certain deposition apparatus). This is an example where the envelope formed by the moving surface has a shape after processing. In FIG. 1, S5 is an initial shape, S6 is a shape after processing, and a to e are straight lines corresponding to equally divided angles.
Equally divided (n = 4). A 'to e' are straight lines a to e
Is a straight line indicating after the movement of.

FIG. 2 shows that the singular points of θ ₁ = 90 ° and θ ₂ = 0 ° are singular points when the singular points are etched by an etching apparatus having a combination of a directional etching component and an isotropic etching component. FIG. 4 is an explanatory diagram for describing a shape change calculation method in FIG. This is an example of a case where the processed shape is constituted only by the moving surfaces themselves on both sides of the singular point. In FIG. 2, S7 is the initial shape, and S8 is the shape after processing.

Further, FIGS. 3 and 4 show that θ ₁ = 0 ° and θ ₂ =
This shows an example of deposition and etching for a singular point of 90 ° (see FIG. 12 (a) or (c)), respectively. 3 and 4, S9 and S11 are initial shapes, and S10 and S12 are shapes after processing.

A processing method for such a singular point has never been considered in a conventional simulation. In FIGS. 1 to 4, there are a case where the shape after processing is the initial shape as it is and a case where it changes from the initial shape.
This will be described later in a method of calculating a movement vector of each point on the processing surface.

Next, a shape change calculation method when the initial surface shape is represented by a set of points will be described. Usually, in a shape simulation, a surface shape is represented by a line segment connecting points. In this case, as shown in FIG. 5, except for points (A and B) on a flat plane where there is no gradient change, a smooth curved surface whose gradient is actually continuously changed also has a gradient at each point. Changes discontinuously (points C to G). The present invention is characterized in that these points are treated in the same way as the singular points described in the shape change calculation method at the singular points described above. For a flat plane having no gradient change, the plane moved by v (θ) · t in the direction perpendicular to the plane becomes the plane after t time. Can be applied as an extended interpretation (it is sufficient to consider that the surface of the point has only one inclination angle). In FIG. 5, S13 is a real surface shape, and S14 is a surface shape expressed by a set of points.

As described above, in this method, all points on the surface can be regarded as singular points and treated in a unified manner, and the introduction of singular point processing does not complicate the configuration or control of the simulator at all. Absent. The overall shape after the time t is obtained by connecting these surfaces. FIG. 6 is an explanatory diagram for explaining the present method. Note that this method (the same applies to the shape change calculation method at the singular point described above)
The moving speed v (θ) of all points on the processing surface to be simulated is the expected angle (above the horizontal line passing through that point).
In the case of an angle of 180 degrees, an angle which is independent of an obstructing substance (in the case of isotropic etching or deposition) is applicable regardless of the length of the time t. In FIG. 6, S15 is the initial shape, and S16 is the shape after processing.

Next, a method of calculating a movement vector of each point on the processing surface will be described. When a point at which v (θ) changes depending on the estimated angle is included, the present invention is used because v (θ) at each point may change with the temporal change of the shape. Also in this case, as in the conventional simulation method, it is necessary to divide the entire processing time into minute times and change the shape little by little (repeat the simulation with the shape after the minute time as the next initial shape). In this case, it is convenient to adopt a method of gradually moving a set of points representing the initial shape (calculating and moving a movement vector for each point) as in the conventional method. In the present invention, at this time, for all points on the processing surface, the end point of the movement vector (that is, the end point of the movement vector on the surface after processing obtained by the shape change calculation method when the above-described initial surface shape is represented by a set of points) By taking the (destination), the shape after processing is represented with high accuracy. Hereinafter, one method for obtaining the end point of the movement vector on the above-described processing surface will be described.

For each point on the processing surface, as shown in FIGS. 7 to 10, first, a point Q is set on the side where the angle between both sides of the point P is an inferior angle. The point Q is, for example, as shown in FIGS.
As shown in the figure, a bisector L of an angle formed by both sides of the point P is drawn, and the distance from the point P on the bisector L is set to be longer than the maximum movement distance in the unit time step. Although the processing is simple, the method of determining the point Q is not limited to this. Next, the post-movement positions of the surfaces on both sides of the point P are obtained, and the intersection R of both surfaces after the movement is obtained. Then, the position after movement of all surfaces having an angle between the inclination angles θ ₁ and θ ₂ (calculation is performed by equally dividing the angle between θ ₁ and θ ₂ by n at a fine angle Δθ) is obtained.
A point S closest to the point Q is an end point (ie, a movement destination) of the movement vector of the point, of the intersections formed by the surfaces after the movement and forming a straight line QR (PS is a movement vector). 7 and 8 show the case of deposition, and FIGS. 9 and 10 show the case of etching. S17 is the initial shape, and S18 is the shape after processing.

If theta ₁ and theta ₂ are equal (the case of a point on the flat surface)
Cannot find the intersection after the movement of both sides of the point P. In this case, the point P is simply set as v (θ
₁ ) · t may be moved, but it is preferable to move the point P in a direction in which the inclination of θ ₁ (= θ ₂ ) is preserved.

In particular, if it is desired to further increase the shape approximation accuracy after the movement of a point having a large difference between θ ₁ and θ ₂ (which is considered to be an actual singular point), the number of points at the movement destination may be increased. For example, as shown in FIG. 11, the points at which the straight lines drawn perpendicular to the respective surfaces on both sides of the point P intersect with the surfaces after the movement of the respective surfaces are defined as T and U, and between the inclination angles θ ₁ and θ ₂ . After the movement of all the surfaces having the angles of, each of the intersections between the line QT and the point closest to the point Q (in this case, the point T) and the point Q among the intersections with the line QU Accuracy can be improved by performing processing of adding the closest point (in this case, point U) to a point representing the processed surface. If you want to further improve accuracy, between ST, SU
A similar process may be performed with more points taken in between. In addition,
Although this drawing is an example of deposition, the same applies to etching.

〔The invention's effect〕

As described above, the LSI shape simulation method according to the present invention approximates the initial surface with a set of points, and treats each point as having all angles between the inclination angles formed by straight lines on both sides including the point. 1 and a second method in which the end point of the movement vector of each point when moving each point on the processing surface is obtained on the surface after movement obtained by the first method. High-precision processing of singular points, which was not considered at all in simulations up to this point, can be realized without being aware of singular points, that is, by performing the same processing at all points, complicating the configuration and control of the simulator Without this, there is an effect that a highly accurate simulator can be made.

Further, the method according to the present invention eliminates the necessity of taking a time step finely in order to treat a singular point with high accuracy unlike the case of using the conventional simulation method, so that there is an effect that the simulation time can be reduced.

[Brief description of the drawings]

1 to 4 are explanatory diagrams for explaining a shape change calculation method at a singular point. FIGS. 5 and 6 show a shape change calculation method when an initial surface shape is represented by a set of points. 7 to 11 are explanatory diagrams for explaining a method of calculating a movement vector of each point on the processing surface, and FIG. 12 is each point on the processing surface and both sides of each point. FIG. 13 to FIG. 15 are explanatory views showing an inclination angle formed by a surface, and FIG. 13 to FIG. 15 are views showing shapes after processing by a conventional simulation method. S5, S7, S9, S11 ... initial shape, S6, S8, S10, S12 ... shape after processing.

──────────────────────────────────────────────────続 き Continued on the front page (72) Akira Yoshii, Inventor Nippon Telegraph and Telephone Corporation, 1-6, Uchisaiwaicho, Chiyoda-ku, Tokyo (58) Field surveyed (Int.Cl. ⁶ , DB name) H01L 21 / 302

Claims (1)

(57) [Claims] In an LSI shape simulation method for predicting a shape after processing from an initial surface shape of an element cross section, the initial surface is approximated by a set of points, and each point is an inclination angle formed by straight lines on both sides including the point. And a second method in which the end point of the movement vector of each point when each point on the processing surface is moved is determined on the surface after movement obtained by the first method. An LSI shape simulation method comprising: