JPH0367126A - Measurement position determining method - Google Patents

Abstract

PURPOSE:To correctly measure the place dependency of homogeneity by defining a circular area to be measured on a plane, dividing the area to be measured into sections to be measured which have equal area, and setting one measurement point each nearly in the centers of the respective sections to be measured. CONSTITUTION:The area A to be measured is divided radially into four by internal circles I1-I3, and the area to be measured outside the internal circle I1 is divided into eight at an equal rotational angle in the rotational angle direction of the internal circle I1. When the area is divided in the rotational angle direction, the area encircled with the internal circles I1 and I2, the area encircled with the internal circles I2 and I3, and the area outside the internal circle I3 are divided by different methods. Then the measurement points Sij(S23) are set at intersections of auxiliary circles L1-L3 which are so defined as to bisect the area of the sections to be measured and an auxiliary straight lines (h) which is so defined to bisect the area of the sections to be measured and pass the center of the area A. Thus, the measurement points Sij are set, so the surface density at the measurement points in the area A, i.e. the number of the measure ment points per unit measured area becomes uniform without deviation, so that the area A can be measured uniformly by using the measurement points.

Description

Detailed Description of the Invention [Industrial Field of Application] The present invention provides a method for measuring an object to be measured at the center of a plurality of sections divided into equal areas within an arbitrary plane of the object to be measured. The present invention relates to a method of measuring the characteristics of an object to be measured uniformly and without bias by providing points.

[Prior Art] According to this type of conventional measurement method, for example, in a circular measurement head area having a radius R as shown in FIG. 2, two concentric circles Jl and Measurement points are set on J2 and at the center of those circles. In Figure 2, A is the area to be measured, and Jl and J2 are the areas to be measured A.
concentric circles with a common center, S ij (i = 0.l, 2, 3; j = O, l
, 2°...19) are: measurement points.

In this prior art, the radius of the concentric circles is 0°4R and 0.8R, respectively, where R is the radius of the measurement area A.
It is set to be R. Therefore, the circumference of the concentric circle J2 with the larger radius is twice the circumference of the concentric circle J1 with the smaller radius, so the number of measurement points on the concentric circle J2 with the larger radius is accordingly: The radius is set to twice the number of measurement points of the smaller concentric circle Jl.

According to such a method of setting the fixed points 1j, the areal density of the measurement points in the measurement target area ViA, that is, the number of measurement points per unit area of the measurement target area, is not uniform over the entire area of the measurement target area A. Therefore, when measuring the area A to be measured using such measurement points, measurement results for areas having the same area cannot be obtained, so there is an inherent drawback that the measurement results are biased.

[Problems to be Solved by the Invention] It is an object of the present invention to provide a method that eliminates the drawbacks of the conventional measurement position determination methods described above and uniformly measures the plane of any object to be measured without bias. shall be.

[Means for Solving the Problems] In order to solve the above problems, in the present invention, a measurement area is divided into a plurality of measurement sections having equal areas, and one measurement area is placed approximately in the center of each measurement section. Set the measurement point.

[Operation] If the object to be measured is a circle, it is divided in the radial direction by concentric circles, and the area outside the innermost circumference is divided in the rotation angle direction. The area set by these divisions is defined as a section to be measured, and the radius of each concentric circle and the number of sections are set so that the areas of the sections to be measured are equal to each other. In addition, for each section to be measured except for the innermost circumference, the intersection of auxiliary lines dividing the area into two in the radial direction and rotational angle direction is set as a measurement point.

[Example] FIG. 1 is a diagram for explaining the present invention in detail,
A is a circular measurement area defined in the plane of the object to be measured, If, I2 and I3 are inner circles having a common center with measurement area A, and Ll, L2° and L3 are common to the measurement area. In the auxiliary with the center of S ij (i = 0.1.2, 3
; j=0. l, 2. ..., 9) are measurement points.

In the embodiment of FIG. 1, the measurement area A includes three inner circles If, 12. and I3ζ are divided into four in the radial direction, and the innermost circumference 1 with the smallest radius among these inner circles
The area to be measured outside 1 is divided into eight parts at equal rotation angles in the rotation angle direction of the innermost part 1.

The above division in the rotation angle direction is divided into a measurement area surrounded by the inner circle 11 and I2, a measurement area surrounded by the inner circles I2 and I3, and a measurement area outside the inner circle I3. It is done in a way.

A measurement area surrounding a part of the concentric circle outside the innermost periphery divided by the above method and a measurement area inside the innermost periphery are defined as the measurement partitions, and each of the measurement partitions is The areas of are set to be equal.

In the example shown in Fig. 1, the radius of the innermost ■1 is rl, the radius of the outer inner circle (concentric circle) I2 is I2, the radius of the inner circle I3 is I3, and the radius of the measurement area A is I4. Then, the area of each measured section can be calculated by the following formula:

Area of inner circle I1: 81 al=π・rl2 Area of measured section outside inner circle I1: a2a2=(π・rl2
I2"-π・rl2)/8=π(I22-r 1")/
8 Area of measured section outside inner circle I2: a3a3=(π・
I32-π・I22)/8=π (I32-I22)/
8 Area of measured section outside inner circle I3: a4a4=(π・
I42-π·I32)/8=π(I42-I32)/8 In the embodiment shown in FIG. 1, the number of sections is eight, but the number is not limited to this number. In the present invention, in short, each section to be measured is determined to have an equal area, so generally, the area of each section to be measured is al=a2=a
Each radius, number of sections, etc. may be selected so as to satisfy the condition 3=a4.

Next, Ll, L2 . and L3, and an auxiliary straight line defined to divide the area of the measured section into two and pass through the center of the measured area (in Figure 1, this is illustrated by an auxiliary straight line passing through point 823). Measurement point s at the intersection
Set lj.

Further, the position coordinates of the measurement point S2j are set to have a rotation angle of 15 degrees counterclockwise around the origin, with the center of the measurement area as the origin, with respect to the position coordinates of the measurement point Slj. The position coordinates of the measurement point S3j are the measurement point S2 like a surface.
It is set to have a rotation angle of 15 degrees counterclockwise around the origin with respect to the position coordinates of j.

Since the measurement points Slj are set in this way, the areal density of measurement points in the measurement area A, that is, the number of measurement points per unit area of the measurement area, is uniform without bias, and by using the 1111+fixed points, The area to be measured A can be uniformly measured.

In this example, the measured section is divided into four circles in the radial direction by three inner circles.
The figure shows a case in which the object is divided into 8 parts and 11 parts in the direction of the rotation angle, but the number of divisions in the radial direction and rotation angle direction can be freely set depending on the uniformity of the object to be measured within the plane. , the measurement point position at this time is determined by the same method as in this example.
can be easily determined.

The apparatus for carrying out the method of the present invention includes a numerical processing device, a memory for storing predetermined calculation procedures and data, and a measurement point set within the plane of the object to be measured based on the calculation results. A measuring point plotter can be implemented as a component. Input the numerical values of the elements necessary for determining the measurement point, such as the radius of the concentric circles and the number of sections, as parameters into such a device, and calculate the coordinates of the measurement point according to the method for calculating the measurement point described above. However, by controlling the coordinate data, it becomes possible to sequentially set specific measurement points.

Since the present invention has the above configuration, for example, measurement points are set on the surface of a silicon wafer and physical measurements such as specific resistance and lattice defect density are carried out over the entire surface. This is suitable for strictly evaluating the quality of wafers. In addition, for example, when conducting physical property tests on the surface of various materials, the recording characteristics of recording media such as optical disks or magnetic disks are determined. It is extremely effective when carrying out.

[Effects of the Invention] As explained above, in the measurement method of the present invention, a circular or rectangular measurement area is defined on the plane of the object to be measured, and the measurement area is divided into measurement sections having equal areas. Since one measurement point is set approximately in the center of each measurement area, the area density of measurement points in the measurement area is uniform, and using this measurement point makes it possible to perform unbiased and uniform measurements. can. Therefore, it is possible to inspect the homogeneity of the region to be measured, and to accurately measure the location dependence of the homogeneity within the region to be measured.

In addition, since the method of the present invention allows measurement points to be set logically and numerically, it has good reproducibility and realizes a device that automatically sets measurement points on the plane of the object to be measured. can do. Furthermore, it is possible to set measurement points by giving elements such as the number of measurement points and their distribution as parameters.

It shows the position of

A...Measurement area Jl and J211...Concentric circles LX, L2 and L3 having a common center with the measurement area...◆@@Auxiliary circle II, 12 having a common center with the measurement area and UI3m−@−−m) Inner circle SiJ (t = o + L 2+ 3: J
=01 11 21 31..., 9)...Measurement point

Claims (1)

[Claims] A method of measuring an object to be measured within an arbitrary plane of the object, in which a circular measurement area is defined on the plane, and the measurement area is divided into multiple measurement sections with equal areas. A method for determining a measurement position, characterized in that one measurement point is set on a plane of the object to be measured and approximately at the center of each of the plurality of sections to be measured.