JPH0437116A - Simulating method for shape - Google Patents

Abstract

PURPOSE:To more accurately perform a shape simulation in lithography and etching steps by moving a straight line passing a line segment in a direction of distance normal direction of the product of a dissolving speed and a time interval at a point having small angle formed between adjacent segments, and using its crossing point as a new point. CONSTITUTION:Means 17 for providing removing speed of a substance to be removed as a function of a position, means 18 for representing the sectional shape of the surface of the substance to be removed similarly to points of definite number, means 23 for obtaining an angle between points representing the sectional shape and two line segments for connecting two adjacent points, means 24 for moving a position of the point, if the angle between the two segments for holding a certain point is smaller than a predetermined angle theta0, after calculation counting time ( t) of the point at a distance of the product of the removing speed and the t in a normal direction and obtaining the segments after moving as an intersection of the two straight lines, and means 25 for obtaining the position of the point after the t, if the angle between the two segments for holding the certain point is larger than the angle theta0, as a position moved at a distance of the product of the removing speed and the t at the position in the direction of the bisecting line of the angle formed between the two segments are provided.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to a simulation method in a lithography process and an etching process.

2. Description of the Related Art Conventionally, this type of shape simulation method is based on the IEEE Transaction on Electron Devices (IEEE Transaction on Electron Devices)
Non-Electron-devices) Magazine, No. E
D-Volume 26, No. 4, April, 1979, Page 717-
SAMPLE disclosed on page 722 is widely used. In this type of program, a string model has been used to develop a resist in a lithography process and to track changes in the shape of a simulated object over time in an etching process.

The string model will be explained using Figure 2.

FIG. 2 is a schematic diagram of a simulation of the resist shape during development, with the right direction being the X direction and the downward direction being the two directions. Second
In the figure, the cross-sectional shape of the surface to be simulated at a certain time t is approximated by a set of points P1(t) placed at appropriate intervals on the surface to be simulated and a set of line segments connecting adjacent points. Ru. In FIG. 2, 1 and 2 indicate one of the points Pi(1) and one of the line segments, respectively.

In the following explanation, the position of point Pi on the X, Z plane is expressed as (xi
.

zi). In Figure 2, the shaded area below the broken line is
Represents unremoved substances. Here, the removal rate of the substance is given in advance as a receding distance of the surface per unit time as a function R(x,z) of X and Z. In the string model, each point P1(t) is expressed as R(x
i, zi) and Δt to find a point Pi(t+Δt) at a time of 10Δt. At this time,
The moving direction 3 of each point P1(t) is the point at both ends (i=1.
N) is determined as the direction of the bisector of the angle formed by the line segment P i 1(t)P 1(t) and the line segment P 1(t)P i + 1(1). There are various methods of determining the moving direction of the points at both ends. For example, it is defined as the normal direction of a line segment.

Problems to be Solved by the Invention In the conventional string model, the direction of movement of each point provided on the surface, excluding both ends, is determined to be the direction of the bisector of adjacent line segments. Therefore, calculation errors become large in portions where the radius of curvature is small, that is, in portions where the angle between adjacent line segments is small. This will be explained using FIG.

In FIG. 3, the part to the left of the solid line is the unremoved substance.

Such an acute-angled shape corresponds to a standing wave that appears on the resist sidewall in a photolithography simulation. Points 6 to 10 represent the surface at time t, and for simplicity, points 6.7.10 and 8.
．． 9.10 are half straight lines 2. Suppose that they are lined up on m. Furthermore, Figure 3 is an enlarged view of a small part.
The dissolution rate R (x, z) is considered to be approximately a constant value R at each point from 6 to 10.

After time Δ, points 6 and 7 are RΔt downward in the normal direction of half-line e, points 8 and 9 are RΔt upward in the normal direction of half-line m, and point 10 is RΔt upward in the normal direction of half-line m.

Move a distance RΔt to the left in the direction of the bisector of m, and move from point 11 to point 15, respectively. However, in reality, the dissolution of resist and the like proceeds in the direction normal to all points on the two-half straight lines e and m representing the surface. For this purpose, in reality, a perpendicular k is drawn from the part on the straight line indicated by A, that is, the bisector C of the half line e2m that sandwiches the point 10, to the half line e1m.

A portion where the distance p of j satisfies p<=RΔt is dissolved. However, when using the conventional model, point 10 is located on the bisector C
It moves along distance RΔt and moves to point 15. However, the portion indicated by A in FIG. 3 is dissolved at time t+Δt. For this reason, when a shape like that shown in FIG. 3 is simulated using a conventional model, the portion with a small radius of curvature melts more slowly than in reality, and the resulting shape differs greatly from the actual shape. In fact, when photolithography is simulated using a conventional string model, protrusions on the resist sidewall due to standing waves are
It appears larger than it actually is, making it impossible to perform accurate simulations. This problem is an essential problem caused by expressing the surface shape with a finite number of points, and the dissolution rate R
Even when (x, z) is not a constant and each point is not arranged on a straight line, this problem becomes noticeable when the angle between certain adjacent line segments is small. In order to reduce this phenomenon, it is possible to increase the number of points Pi and narrow the interval, but this is not practical as it increases calculation time and storage capacity required for calculation.

The conventional model has the above-mentioned problems.

Means for Solving the Problems In order to solve the above-mentioned problems, the present invention provides means for providing a removal rate of a substance to be removed as a function of position;
A means for expressing the cross-sectional shape of the surface of the substance to be removed by approximating it with a finite number of points, and a means for determining the angle between two lines connecting each point expressing the cross-sectional shape of the surface and two points adjacent thereto. When the angle between two line segments that sandwich a point is smaller than a given angle, the position of the point after the calculated step time is calculated as the product of the removal speed at that position and the calculated step time in the direction normal to the two line segments. means to move the distance and obtain the intersection point of the 2M line passing through each line segment after the movement, and if the angle between two line segments that sandwich a certain point is larger than a given angle, the calculation step time after the point is calculated. The lithography process and the etching process are performed using means for determining the position as a position moved in the direction of the bisector of the angle formed by the two line segments by a distance equal to the product of the removal rate at that position and the calculated step time. Perform shape simulation.

At a point Pi(t) where the angle between adjacent line segments is small,
A straight line passing through these line segments is moved in the normal direction by a distance equal to the product of dissolution rate and time interval Δt, and the intersection point is moved to a new point Pi (
t+Δt) approximately corresponds to performing a simulation by setting the interval between points Pi in that part infinitely small.

As a result, since the shape of the simulated object is approximated by a finite number of points, the part with a small circumference radius, that is,
It is possible to prevent delays in the progress of points representing the material surface that occur where the angle between adjacent line segments is relatively small. Also, at a point P1(t) where the angle between adjacent line segments is large,
The point P1 (
By setting the moving direction of t), 2 at all points
There is no need to find the intersection of straight lines, and calculation time can be reduced.

Embodiment FIG. 1 shows an example of a flowchart of shape simulation using a string model using the present invention.

In FIG. 1, the removal (dissolution) rate is determined by the routine shown by the dissolution rate calculation means 17 as a multiplier R(x, z) of x and z.

In a routine indicated by initial setting means 18, the initial position of point Pi is determined based on the initial shape of the object to be simulated. Here, the number of points Pi is assumed to be N.

A time variable initializing means 19 and a variable i initializing means 20 initialize the time variable t and the point number variable i.

The means 21 for determining the position of point Pi determines whether point Pi is an end point (i-1orN).

If it is an end point, it is necessary to move the point depending on the direction of movement, so the end point processing means 22 moves the point Pi to the position of time t+Δt.

The means 23 for determining the angle formed by a line segment determines whether the angle between the line segments sandwiching the point Pi is less than or equal to the angle θ0 given as a parameter in advance.

When the angle is less than θ0, the line segment moving means 24 moves the point Pi to a position of t+Δt using the method according to the present invention. Here, the moving distance of the straight line PiPi1 is the point Pi
Removal rate R(xi.

zi) and the removal rate R(x
i-1, zi-1) and the time interval Δt. Similarly, regarding the moving distance of straight line PiPi+1, point P
Removal rate R(xi, zi) at i and its adjacent point P
Let it be the product of the simple average of the removal rate R(xi+1.zi+1) at i+1 and Δt.

If the angle exceeds θ0, the means 25 for moving on the bisector of the angle formed by the line segment moves the point Pi in the direction of the bisector of the line segment that sandwiches the point by R(xi).

zi) Move a distance of Δt.

A means 26 for counting variable i increments i. A means 27 for determining the end of processing determines whether i>N. If i>N, the time calculation is complete, and the process proceeds to the time counting means 28. If i>N, means 21 for determining the position of point Pi in order to calculate the next point
Return to

A time counting means 28 increments t by Δt. t> end time, means 30 for ending the calculation
Proceed to. t> If it is not the end time, the process returns to the means 20 for initializing the variable i.

Note that the angle θ0 is a fitting parameter, and is optimized based on experimental results.

Effects of the Invention According to the present invention, shape simulation in the lithography process and the etching process can be performed more accurately than before. In particular, in photolithography simulation, it is possible to make the unevenness of the side wall of the resist pattern caused by standing waves close to the unevenness of the actual resist pattern. This allows for more accurate process prediction and evaluation through simulation.
Improved efficiency in process development.

[Brief explanation of drawings]

FIG. 1 is a flowchart of a shape simulation that is an embodiment of the present invention, FIG. 2 is a diagram for explaining a conventional string model, and FIG. 3 is a diagram for explaining problems in the conventional string model. . 17... Means for calculating dissolution rate, 18...
・Initialization means, 19...means for initializing the time variable, 20...means for initializing the variable i,
21... Means for determining the position of point Pi, 22.
... End point processing means, 23 ... Means for determining the angle formed by a line segment, 24 ... Means for moving a line segment, 25 ... Means for moving a line segment Means for moving on the bisecting angle of the formed angle, 26... Means for counting variable 1, 27... Means for determining the end of processing, 28
...Means for counting time, 29...
・Means for determining whether the time has ended, 30... Means for ending. Name of agent: Patent attorney Shigetaka Awano and one other person Figure 1 Figure 2 Figure I. Figure 3

Claims (1)

[Claims] means for giving a removal speed of the substance to be removed as a function of position; means for expressing the cross-sectional shape of the surface of the substance to be removed by approximating it with a finite number of points; and expressing the cross-sectional shape of the surface of the substance to be removed. A means for determining the angle between two lines connecting each point and two adjacent points, and a means for determining the position of the point after a calculation step time when the angle between the two lines sandwiching a certain point is smaller than a given angle. Means for moving the two line segments in the normal direction by a distance equal to the product of the removal speed at that position and the calculated step time, and obtaining the intersection of two straight lines passing through each line segment after the movement, and the two line segments sandwiching a certain point. If the angle is larger than a given angle, the position of the point after the calculation step time is calculated by the removal speed at that position and the calculation step time in the direction of the bisector of the angle formed by the two line segments. A shape simulation method characterized by comprising means for determining a position moved by a distance of the product.