JPH06209101A - Device/process simulating method - Google Patents

Abstract

PURPOSE:To enable a device/process simulating method to be applied even in the rapid change in the physical quantity by a method wherein discrete lattice points and regions are formed as it filling up the space between adjacent contour lines or surfaces in arbitrary physical quantity in analytic region with polygons or polyhedrons to be analyzed. CONSTITUTION:Discrete lattice points 10 are determined along contour lines 9 while triangular discrete regions 10a are formed as it filling up the spaces between adjacent contour lines 9. That is, since the concentration distribution of the contour lines 9 is to be densified in the parts where the distribution rapidly changes, respective discrete regions 10a are made inevitably smaller so as to increase the density thereof. Accordingly, the device/process simulating method faithfully following after the change in physical quantity with high precision can be applied even within the analytic region including the parts in the rapid change in the physical quantity.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a device / process simulation method for analyzing the influence of a variable of an arbitrary physical quantity on a physical characteristic of a semiconductor device or a manufacturing process, and more particularly to a device / process simulation method. The present invention relates to improvement in accuracy of a simulation method for generating and analyzing a lattice point and a discretized region.

[0002]

2. Description of the Related Art Generally, in a device / process simulation method, it is necessary to generate discretized grid points and discretized regions in an analysis region in order to discretize and solve equations.

FIG. 4 is a schematic sectional view of a MOSFET having discretized lattice points and discretized regions generated in a conventional device / process simulation method. In this figure, a region surrounded by a thick solid line 1-2-3 and a region surrounded by a thick solid line 4-5-6 represent source / drain regions. Thick solid line 2-3-6-5-8
The region surrounded by -7 is the semiconductor substrate region. The intersections 10 of the thin solid lines are the discretized grid points, and the region 10 surrounded by the thin solid lines connecting the discretized grid points adjacent to each other.
a is a discretized area. In this case, the discretized area 10a has a triangular shape.

[0004]

DISCLOSURE OF THE INVENTION In the conventional device / process simulation method, the discretized lattice points 1
0 and the discretized region 10a are the respective regions 1-2-3, 4-5, 2-3-, without considering the change of the physical quantity.
In order to conveniently divide each of 6-5-8-7 into a plurality of discretized regions, the discretized grid points and the discretized regions are generated according to the shape of the boundary between those regions. However, if the density of the discretized lattice points is small and the area of each discretized region is large in the portion where the physical quantity changes greatly, a highly accurate simulation cannot be expected. Therefore, in the conventional device / simulation method, it is necessary to correct the once generated grid points and the discretized area in the portion where the physical quantity changes greatly.

The present invention has been made in order to solve the above-mentioned problems of the prior art, and generates a discretized grid point and a discretized region in consideration of the degree of change of the physical quantity in the analysis region. It is intended to provide a highly accurate device / process simulation method.

[0006]

A device / process simulation method according to the present invention for analyzing the influence of a variable of an arbitrary physical quantity on a physical characteristic of a semiconductor device or a manufacturing process is performed by an arbitrary method within an analysis area. It is characterized by generating and analyzing discretized grid points and discretized regions so that adjacent contour lines or contour surfaces of physical quantities are filled with polygons or polyhedra.

[0007]

In the device / process simulation method according to the present invention, the interval between the contour lines or contour surfaces of the physical quantity becomes small in the region where the physical quantity changes rapidly.
Therefore, since the discretized grid points and the discretized regions are generated so as to fill the space between these contour lines or contour surfaces, it is possible to obtain a highly accurate simulation result including a region where the physical quantity changes rapidly.

[0008]

FIG. 1 shows a device / device according to an embodiment of the present invention.
It is a block diagram which shows schematically the simulation apparatus for performing a process simulation method. This simulation device includes a reading device 11, a central processing unit 12, an output device 13, and a storage device 14. The reading device 11 reads the shape of the analysis area and changes in physical quantities in the area. Based on the input data read by the reading device, the central processing unit 12 checks the input format rule of the input data, obtains contour lines of physical quantities, generates discretized grid points, and generates discretized regions. Output device 1
3 outputs the simulation result calculated by the central processing unit. The storage device 14 stores input data, physical quantity data, data representing contour lines, data representing generated discretized grid points, data representing generated discretized areas, and the like in a data storage unit.

FIG. 3 shows the M analyzed in the device / process simulation method according to one embodiment of the present invention.
Figure 2 shows a schematic cross section of an OSFET. Regions 1-2-3 and 4-5-6 surrounded by thick solid lines are source / drain regions. Thick solid line 2-3-6-5-8-
The area surrounded by 7 is the substrate area. The curve 9 represented by a broken line represents a contour line of the impurity concentration. As can be seen from this figure, the discretized grid points 10 are generated along the contour lines 9, and the triangular discretized regions 10 a are formed so as to fill up between the adjacent contour lines 9.

That is, since the contour lines are densely distributed in the portion where the concentration gradient changes abruptly, each of the discretized regions 10a inevitably becomes smaller and the discretized region 10a becomes smaller.
The density of a will increase. As a result, a highly accurate device / process simulation method that faithfully follows the change in the physical quantity is possible even in an analysis region including a portion where the degree of change in the physical quantity is steep.

FIG. 2 is a flow chart showing an example of a procedure for generating the discretized grid points and the discretized regions as shown in FIG. When the procedure in this flowchart starts, first, in step S21, it is determined whether or not the input data satisfies the input format rule. If the input data does not satisfy the input format rule, the process proceeds to step S21a, the fact that the input format rule is not satisfied is displayed on the output device, and the simulation device is stopped. If the input data satisfies the input format rule, the process proceeds to step S22, and the contour lines of the impurity concentration are expressed using appropriate discretized lattice points. At this time, it is needless to say that analysis based not only on the contour line of the impurity concentration as an example but also on the contour line of the potential potential is possible. Further, interpolation such as spline interpolation may be performed on the drawn contour lines.

When the contour lines are determined, the process proceeds to step S23, and the contour points are divided in consideration of the curvature of the contour lines and the distance to the adjacent contour line, and the division points are determined as discretized grid points. If all the contour lines are divided and all the discretized grid points are determined, the process proceeds to step S24.

In step S24, for all the discretized lattice points, from a certain discretized lattice point to the closest discretized lattice point among other discretized lattice points on other contour lines to which the discretized lattice point does not belong. Are connected by a line segment, thereby forming the discretized region 10a. If line segments from all the discretized grid points are formed, the process proceeds to step S25.

In step S25, the discretized area 1
A region other than a triangle is searched for in 0a, and if a region other than a triangle exists, the process proceeds to step S26. Step S2
In 6, the discretized area other than the triangle is divided by the shortest diagonal to generate the triangular discretized area. That is, steps S25 and S are performed until there are no discretized areas other than triangles and all the discretized areas 10a are triangular.
26 is repeated. Then, when all of the analysis regions are divided by the triangular discretized region 10a, the discretized region generation procedure ends.

In the above embodiment, the method of dividing the two-dimensional analysis region into the triangular discretized regions 10a has been described. However, when dividing the three-dimensional region, the "contour line" described above is used. It will be understood that can be replaced by "contour surface" and "triangular discretized region" changed to "polyhedral discretized region". At this time, for example, a tetrahedron or a triangular prism can be used as the polyhedral discretized region 10a.

Further, in the above description of the embodiment, the impurity concentration is taken as an example of the physical quantity defining the contour line, but the contour line representing other physical quantities such as electric potential, magnetic potential, temperature and pressure is analyzed. It will also be appreciated that the contours may not necessarily be evenly spaced.

[0017]

As described above, according to the present invention, the discretized grid points are generated by utilizing contour lines or contour surfaces of arbitrary physical quantities, and the discretized areas are formed accordingly. Highly accurate device that can follow sharp changes /
A process simulation method can be provided.

[Brief description of drawings]

FIG. 1 is a block diagram showing an example of an apparatus that can execute a device / process simulation method according to an embodiment of the present invention.

FIG. 2 is a flowchart showing an example of a processing procedure of a device / process simulation method according to an embodiment of the present invention.

FIG. 3 is a schematic cross-sectional view of a MOSFET showing an example of discretized lattice points and discretized regions generated by the device / process simulation method of the present invention.

FIG. 4 is a schematic cross-sectional view of a MOSFET showing an example of discretized lattice points and discretized regions generated by a conventional device / process simulation method.

[Explanation of symbols]

 1-2-3, 4-5-6 Source / drain region 2-3-3-6-5-8-7 Semiconductor substrate region 9 Contour line of physical quantity 10 Discretized lattice point 10a Discretized region 11 Reader 12 Central processing unit 13 Output device 14 Storage device

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[Procedure amendment]

[Submission date] January 14, 1993

[Procedure Amendment 1]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 1

[Correction method] Change

[Correction content]

[Figure 1]

Claims (1)

[Claims] 1. A device / process simulation method for analyzing an influence of a variable of an arbitrary physical quantity on a physical characteristic of a semiconductor device or a manufacturing process, wherein adjacent contour lines or contours of arbitrary physical quantities in an analysis area are analyzed. A device / process simulation method characterized by generating and analyzing discretized lattice points and discretized regions so that the spaces between high surfaces are filled with polygons or polyhedra.