JPH03101150A - Formation of coordinate grid in numerical analysis of semiconductor; formation support apparatus of coordinate grid - Google Patents

Abstract

PURPOSE:To shorten the operation time to form a coordinate grid according to an object to be analyzed by a method wherein, instead of the potential distribution of a numerical simulation, a concentration distribution of impurities in an input data is utilized as a physical quantity controlling the concentration of the coordinate grid. CONSTITUTION:A structure of a semiconductor as an object is formed at a geometric- shape data formation part 41 while a numerical value of coordinates of its vertes is input via a pick or an operation panel 6 by using a light pen or the like. An impurity distribution function is selected from predetermined patterns; its parameter is designated; also an impurity distribution in a corresponding substance region over the whole region is formed. Then, a parameter controlling the interval between grid lines on the basis of a previous geometric-shape data is input at a coordinate-grid formation part 42. At a coordinate-grid correction part 43, a coordinate grid formed in a pretreatment is displayed on a display device 2 together with the concentration distribution of impurities; the coordinate grid is added, deleted or the like via the pick by using the light pen or the like.

Description

Detailed Description of the Invention [Purpose of the Invention (Industrial Field of Application) The present invention relates to a coordinate system for generating two-dimensional rectangular coordinate grid points used for discretizing an analysis region in numerical analysis of semiconductors using a computer. This invention relates to a grid creation method and its support device.

(Prior Art) In numerical analysis such as semiconductor device simulation, a potential distribution is determined by discretizing an analysis region using a difference method or a finite element method. Recently, general-purpose numerical analysis programs have been created for this purpose, allowing highly accurate analysis. However, when semiconductor device designers perform numerical analysis using these analysis programs, when the target of analysis becomes complex, the problem is that it takes a lot of time to create coordinate grids and data such as physical property data. be. Therefore, various Buri processors have been developed to save labor in these operations. For example, I
In the matupumetsu in DEAS-S supertab, the geometric shape of the analysis object is created in the computer by using the display in an online interactive format, and based on this, the coordinate grid points inside the shape are determined by interpolation. , automatically creates data such as coordinate grid creation and physical property data creation.

By the way, in numerical analysis, the calculation accuracy improves as the number of coordinate grid points increases, but the required calculation time and storage capacity also increase accordingly. Therefore, due to constraints on calculation time and storage capacity, there is an upper limit to the number of coordinate grid points that can be analyzed. Therefore, in order to improve the accuracy and convergence of numerical analysis with a finite number of grid points, it is necessary to concentrate the coordinate grid in analytically important areas depending on the analysis target. However, in conventional technology, after the geometry of the object to be analyzed is created in a computer, the coordinates are created based on the input data of the number of divisions, regardless of the physical state to be analyzed. The problem is that it is not always possible to obtain

Therefore, a method has been developed that performs numerical simulation using an appropriate initial mesh and semi-automatically corrects the mesh based on the distribution of physical quantities obtained as a result (
For example, IDEA S-S manufactured by 5DRC in the US
(adaptive mesh in uppertab). However, with this method, it is necessary to perform -degree numerical simulation, it is a semi-automatic mesh correction method by inputting parameters, so detailed changes per mesh cannot be made, and it is therefore difficult to control grid concentration based on the user's experience. There were problems such as:

(Problems to be Solved by the Invention) As described above, in the conventional method of creating a coordinate grid in numerical analysis, it is difficult to create a coordinate grid at high speed, and it is difficult to concentrate grid points in areas important for analysis. There was a problem.

The present invention provides a coordinate grid creation method and a coordinate grid that can reduce the work time for creating a coordinate grid, easily create a coordinate grid according to an object to be analyzed, and also enable fine-grained modification of grid points. The purpose is to provide a creation support device.

[Configuration of the Invention (Means for Solving the Problem) The present invention provides an effective method for controlling the concentration of a coordinate grid when creating a coordinate grid on a two-dimensional plane for numerical analysis of semiconductors. As a physical quantity, the impurity concentration distribution, which is input data, is used instead of the potential distribution, which is the result of numerical simulation. That is, in the coordinate grid creation method of the present invention, first, a coordinate grid is generated once by calculation. Then, together with the created coordinate grid, the impurity concentration distribution is displayed on a graphic screen in order to control the concentration of the coordinate grid. The analysis operator creates a desired coordinate grid by repeatedly displaying and inputting correction data while looking at the coordinate grid and impurity distribution displayed on the same screen.

The coordinate grid creation support device according to the present invention includes arithmetic means for determining and correcting grid spacing, display means for displaying the determined grid spacing together with impurity distribution on the same screen, and correction data for grid lines while viewing the display screen. It is possible to create the coordinate grid interactively as described above.

(Function) According to the present invention, without looking at the coordinate grid and impurity distribution, it is possible to repeat finely adding grid lines to the part of the analysis target where the coordinate grid should be concentrated and deleting unnecessary grid lines. This makes it possible to create a coordinate grid optimal for semiconductor device numerical simulation. By using this optimal coordinate grid, it is possible to increase the accuracy of numerical simulation. Furthermore, since the impurity concentration distribution is used instead of the potential distribution, there is no need for numerical simulation to obtain the potential distribution, and the working time for creating the coordinate grid is reduced accordingly.

(Example) Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows the configuration of a coordinate grid creation support device according to an embodiment. This support device 1 includes a display device 2 such as a CRT,
It has an image processing device 3, an arithmetic processing device 4 such as a computer, a storage device 5, and an operation panel 6 such as a keyboard. The display device 2 is connected to the arithmetic processing device 4 via the image processing device 3, and the storage device 5 and the operation panel 6 are also connected to the arithmetic processing device 4.

FIG. 2(a) functionally shows the internal configuration of the arithmetic processing device 4. As shown in FIG. That is, the arithmetic processing unit 4 includes a geometrical shape creation section 41 that interactively creates the initial geometrical shape of the upper conductor;
A coordinate grid creation unit 42 performs calculations to create an initial coordinate grid based on the geometrical shape created here, and a coordinate grid creation unit 42 performs calculations to create an initial coordinate grid, and performs corrections such as adding and deleting grid lines based on the created coordinate grid to determine optimal coordinates. It is composed of a coordinate grid correction unit 43 that creates a coordinate grid.

An overview of the processing by the support device according to this embodiment will be explained. First, in the geometric data creation section 41, a target semiconductor structure is created by picking the coordinates of its vertices with a light pen or the like or by inputting numerical values from the operation panel 6. Also, by selecting one or more impurity distribution functions from among predetermined patterns and specifying its parameters, the impurity distribution of the corresponding material region such as silicon among the entire region is also created.

Next, in the coordinate grid creation section 42, a coordinate grid is created by inputting parameters for controlling the spacing of grid lines based on the previously created geometric data.

Then, the coordinate grid correction unit 43 displays the coordinate grid created in the previous process on the display device 2 together with the impurity concentration distribution, and adds the coordinate grid.

Corrections such as deletion are made by picking with a light pen or the like.

FIG. 2(b) shows a specific program processing flow of the arithmetic processing unit 4. As shown in FIG. As a major process, the second
A structure data definition section (S3) corresponding to the geometrical shape creation section 41 in FIG. )
There are three sections. It is selected in step S1 whether or not all of these steps are to be performed. If only the mesh data is to be modified, it is read from the input format file (S8) and the process jumps to the mesh modification section S8.

When it is selected to perform all sections, the user then selects whether to change the already created structural data or create data from the beginning (S2). If change is selected, the file name of the structural data is specified (S9), and then the structural data definition section S3 is entered. If you choose to create
The structure data definition section S3 is immediately entered. When the process of the structural data definition section S3 is completed, the user is asked whether or not to write the structural data to a file, so if the structural data is to be written, specify a file name (S10). Next, the mesh generation section S5 is entered, and then the mesh correction section S6 is entered.

When the mesh correction is completed, you will be asked whether you want to export the mesh data to a file, so if you want to export it, specify the file name (Sll). With the above steps, execution of all programs is completed.

Next, specific processing at each stage in the outline explained above will be explained in detail using an actual graphic screen as an example.

First, the geometric shape creation section 41 will be explained.

When the range of the two-dimensional analysis region is specified in the X direction and the X direction, a screen as shown in FIG. 3 is displayed on the display device 2. Here, scales are displayed on the X-axis 31 and the y-axis 32, respectively. The increment width of this date marking can be changed, for example, in units of 10 times.

0 Also, when picking a coordinate value, the value is rounded so that the coordinate closest to the picked value among the carved coordinates is the coordinate value that is finally adopted in the program. for example,
If the scale is marked in units of 10 degrees, and if the picked coordinate value is PO and the coordinate value adopted in the program is PI, then Pl-[PO/10' +0.5] *10"
becomes. However, [Xl is the largest integer not exceeding X.

By adopting this method of picking coordinates, the digits below a certain number are "0" just like when inputting numerical values.
You can easily specify the coordinates. In addition, desired geometric shape data is created using functions such as inputting numerical values, setting impurity distribution functions, deleting already set shape data and impurity distribution functions, and zooming display of regions.

Next, details of the coordinate grid creation section 42 will be explained. The operator sets the parameters necessary to generate the coordinate grid (maximum spacing,
Specify the minimum interval and base line position of coordinate grid line generation). First, the entire area of the geometric data created in the previous process is displayed on the graphic screen 1, and input of reference lines for generating coordinate grid lines is requested in the X direction and then in the X direction. For example, up to nine reference lines can be specified in each of the X and X directions. By setting this reference line, the system generates coordinate grid lines in silicon.

Next, the X direction.

Input of the maximum and minimum spacing between grid lines in the X direction is required. These intervals can be specified separately for each range in the X direction and in the X direction.

Once all these specifications are completed, the system generates a coordinate grid according to the following three steps (a) to (c),
Based on that coordinate grid, the coordinate grid data (impurity concentration,
(electrode flag, material flag) and ask the operator to confirm whether or not this coordinate grid is suitable. If the operator does not like this coordinate grid in terms of the fineness of the grid lines in the silicon, etc., he specifies it again from the beginning in the coordinate grid creation section, and if he is satisfied with it, proceeds to the next coordinate grid modification section.

(a) Generating a mesh of IX rays to each group First, find the coordinates of the boundary of the substance on the reference line and the name of the substance. Next, for the layer whose material name is silicon, the impurity concentration on the reference line is calculated using the minimum mesh width specified by the user as the step width. A mesh is generated when this density difference becomes DX (default) 3.0) times in the X direction and DY (default 3.0) times in the X direction. However, the mesh width is a pre-prepared length (1, OXI
O"μm, 1.4 x 101μm, 3.OXIOI
Illm, 5. OXIO1lItm7, OXIO'μ
m) that satisfies the conditions.

(b) Merging of a plurality of generated meshes A virtual mesh interval interpolated at an arbitrary point on a certain mesh as shown in FIG. 4 is defined by the following equation.

When L I = X 141
/ 2. However, 3 m=2 (x-XI) / (XIn Xl)■P
When ≦X≦X1+1, L=nL+ + (1-n)(L+ +L+o)/2. Then, n=2 (Xm - x) / (x1 + 1 - Xl) Using the interval thus defined, the mesh with the smallest L is selected from the plurality of meshes and connected. However, where the selected meshes are exchanged, the meshes may become thinner than necessary, so if the spacing is less than 1/3 of the smaller spacing on both sides, the two meshes may become thinner than necessary. Replace the mesh with one mesh in the middle.

(c) Merge with vertex coordinates of +M structure data Mesh must be generated at the vertices of structure data. Therefore, go to 11 in the mesh (Ml) created in the previous step.
The Tfi point coordinates (M2) of the structural data are merged. In this case as well, the mesh may be finer than necessary, so
Similarly to (b), 1/3 of the smaller spacing between both sides.
If the interval is as follows] 4, delete Ml.

The above procedure is applied to each of the X direction and the X direction.

Next, details of the coordinate grid correction section 43 will be explained. In the coordinate grid correction unit 43, when you want to add grid lines for areas that are not generated in the coordinate grid creation unit 42 (for example, 5iOz, electrodes, air), or for areas that are automatically generated (for example, silicon), you can add more grid lines. .

If you want to delete grid lines, the operator can add or delete grid lines by themselves.
Perform deletion. Functions that can be used by the coordinate grid correction unit 43 include adding and deleting grid lines, zooming display, changing the accuracy of coordinate axes, checking the number of grids, etc.

In addition, in order to check whether the grid lines are appropriate, the impurity distribution in any cross section in the X direction and in the Options are available. by this,
Perform the final check and correction of the grid lines, and output the final grid line data to a file.

Here, regarding the specific display method of impurity distribution, 5. Some examples will be explained.

The first method is to graphically display the impurity concentration in the X direction and at arbitrary coordinates in the X direction within the analysis region. −
For example, if there is a display screen as shown in FIG. 3, the impurity concentration distribution is displayed on the screen as shown in FIG. 5 by inputting the coordinates on the X axis from the operation panel or by picking with a light pen.

In this example, the scale is displayed on a logarithmic scale, but a linear scale may be used. Furthermore, in this example, the impurity concentration distributions 51 and 52 in the two directions of X+Y for a certain cross section in the X direction are displayed on the same screen in alignment with the display screen 53 of the coordinate grid, so the concentration values are You can check and correct the value by comparing it with the value. Furthermore, the grid lines can be confirmed and corrected in the same manner in the X direction as well.

The second method is to display the impurity concentration by placing predetermined marks on grid points as shown in the m6 diagram. In this case, if the n-type impurity concentration on the lattice point P (i, j) is DN (i, j) and the p-type impurity concentration is DP (i, j), then, for example, by the value of DPN given by the following equation, It can be displayed by adding two different types of marks (x, .).

DPN-DP (i, j) -DN (i, j) The third method is to display the impurity concentration on a lattice point by comparing the distance between adjacent lattice points as shown in Figure 7. In this method, a perpendicular bisector is drawn, and the area surrounded by this as a boundary line (the shaded area in the figure) is displayed in different colors. Specifically, in this case, the grid is rectangular, so the point P(i, j
) is the area to be colored by the point P(i,j) when the coordinates are set in the X direction and the X direction as shown in Figure 7.
Let the X coordinate be X(1) and the Y coordinate be y(j), then x
-(x (i) +x (i-1) ] /2x -
(x (i) +x (i +1) ) /2y −(
y (j) 1y (j-1) l /2y -(y
(j) y (j+1) l /2 This is the area surrounded by four straight lines. The number of colors for coloring may be two or more depending on the number of seven colors that the display device can display. By using this display method, whether or not grid lines are generated in sufficient detail at the boundary between the n-type and p-type regions can be expressed as the size of the stepped boundary line. Easy to judge.

The fourth method is to display the impurity concentration on the lattice points.
As shown in FIG. 8, this is a method in which a rectangular region R(i, j) between lattice points is painted differently. As shown in the shaded area of FIG.
P (i, j-1).

Assuming that p (i-i, j>, p (t, j>) is defined by four points, the area is colored differently according to the DPN given by the following formula.

DPN-DP (i-1, j-1) +DP (t, j-1) +DP (i-1, j) +DP (t, j) +DN (i-1, j 1) +DN (i, j-1 ) +DN (i-1, j) +DN (i, j) 8 This π-1 formula is just an example. If only for the purpose of determining two types of positive and negative, a value obtained by multiplying this DPN by an arbitrary constant may be used. For example, multiplying by 0.25 gives the average density value. Alternatively, comparison of the product between DPNs and the product between DNs may be used instead.

[Effects of the Invention] As described above, according to the method and apparatus of the present invention, it is possible to easily create a coordinate grid according to the target area of a semiconductor to be analyzed by numerical calculation in a short working time, and furthermore, the coordinate grid can be created in a short time. Fine-grained corrections can be made to the coordinate grid.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the configuration of a coordinate grid generation support device according to an embodiment of the present invention, FIGS. Figure 3 is a diagram showing the display screen of the display device, Figure 4 is a diagram 9 to explain the definition of the grid spacing, and Figure 5 is a diagram showing the impurity concentration distribution and coordinate grid display screen simultaneously displayed. Figure 6 is a diagram showing an example of displaying the impurity concentration by marking on the grid points, Figure 7 is a diagram showing an example of displaying the impurity concentration on the grid points by coloring, and Figure 8 is a diagram illustrating another example of display where the shaded areas are displayed. 1...Coordinate grid creation support device, 2...Table 7J<device,
3... Image processing device, 4 Arithmetic processing device, 5. Storage device, 6... Operation panel, 4]... Nl shape data creation unit, 42... Coordinate grid creation unit, 43... Coordinate grid correction part.

Claims (4)

[Claims] (1) In a method of creating rectangular lattice points and coordinate grid lines connecting the lattice points on a two-dimensional plane in order to perform numerical analysis of semiconductors using a computer, calculations are performed to determine the lattice spacing. The present invention is characterized by displaying the grid spacing along with the impurity distribution on the same screen, inputting correction data for the grid lines while looking at the screen, and correcting the grid lines by interactively repeating this display and input of the correction data. How to create a coordinate grid. (2) The method for creating a coordinate grid according to claim 1, wherein the impurity distribution is displayed as a graph in an arbitrary cross section as reference data for the correction when inputting the correction data. (3) The method for creating a coordinate grid according to claim 1, wherein when inputting the correction data, the p-type and n-type parts of the impurity distribution are displayed as reference data for correction by coloring areas or markings on the grid points. (4) In a creation support device that creates rectangular lattice points and coordinate grid lines connecting the lattice points on a two-dimensional plane in order to perform numerical analysis of semiconductors using a computer, calculations are performed to determine and modify the lattice spacing. a display means for displaying the lattice spacing determined by the calculation means together with the impurity distribution on the same screen; and an input means for inputting grid line correction data while viewing the screen of the display means; A coordinate grid creation support device characterized in that grid lines are corrected by interactively repeating input of correction data.