Method of determining the irregularities of a hole

• US 20050090999A1
• Filed: 09/29/2004
• Published: 04/28/2005
• Est. Priority Date: 10/27/2003
• Status: Active Grant

• Current Assignee: Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: Kang, Hyo-Cheon
• Granted Patent: US 7,398,178 B2
• Time in Patent Office: Days
• US Class Current: 702/155
• CPC Class Codes: G01B 15/08 for measuring roughness or irregularity of surfaces

Abstract

In a method of calculating irregularities of a hole, a center coordinate of an actual hole is set. Inner wall coordinates of the actual hole are obtained from the center coordinate of the actual hole. An area of the actual hole is determined based on the inner wall coordinates of the actual hole. A radius of a virtual hole is determined based on the area of the actual hole. A center coordinate of the virtual hole is determined based on the inner wall coordinates of the actual hole to obtain a circumference line of the virtual hole. A standard deviation of the inner wall coordinates of the actual hole relative to the circumference line of the virtual hole is calculated, thereby obtaining the irregularities of the actual hole.

Claims

1. A method of determining irregularities of an actual hole having an irregular circumference, comprising:

obtaining an area of the actual hole having the irregular circumference;

determining a radius and a center of a virtual hole that has a regular circumference, based on the area of the actual hole; and

obtaining the irregularities of the actual hole by determining a standard deviation of the circumference of the actual hole relative to the radius of the virtual hole.

2. The method of claim 1, wherein determining the area of the actual hole comprises:

setting a center coordinate of the actual hole;

obtaining inner wall coordinates of the actual hole measured from the center coordinate of the actual hole; and

determining the area of the actual hole based on the inner wall coordinates of the actual hole.

3. The method of claim 2, wherein determining the area of the actual hole comprises:

providing lines from the center coordinate of the actual hole to the inner wall coordinates of the actual hole to segment the actual hole into a plurality of triangles;

determining the area of each of the triangles; and

summing the areas of the triangles.

4. The method of claim 3, wherein angles formed between the lines are substantially identical.

5. The method of claim 1, wherein the actual hole is located in a semiconductor device.

6. The method of claim 1, wherein the radius and the center of the virtual hole that has a regular circumference is calculated based on the area of the actual hole;

and

the irregularities of the actual hole are determined by calculating said standard deviation of the circumference of the actual hole relative to the radius of the virtual hole.

7. The method of claim 1, wherein determining the area of the actual hole comprises calculating the area of the actual hole based on the inner wall coordinates of the actual hole.

8. The method of claim 2, wherein determining the area of the actual hole comprises drawing said lines from the center coordinate of the actual hole to the inner wall coordinates of the actual hole to segment the actual hole into a plurality of triangles.

9. A method of determining irregularities of an actual hole having an irregular circumference located in a semiconductor device, comprising:

obtaining an area of the actual hole in said semiconductor device having the irregular circumference;

determining a radius and a center of a virtual hole that has a regular circumference, based on the area of the actual hole in said semiconductor device; and

obtaining the irregularities of the actual hole in said semiconductor device by determining a standard deviation of the circumference of the actual hole relative to the radius of the virtual hole.

10. The method of claim 9, wherein determining the area of the actual hole in said semiconductor device comprises:

setting a center coordinate of the actual hole in said semiconductor device;

obtaining inner wall coordinates of the actual hole in said semiconductor device measured from the center coordinate of the actual hole; and

determining the area of the actual hole in said semiconductor device based on the inner wall coordinates of the actual hole.

11. The method of claim 10, wherein determining the area of the actual hole in said semiconductor device comprises:

providing lines from the center coordinate of the actual hole in said semiconductor device to the inner wall coordinates of the actual hole in said semiconductor device to segment the actual hole in said semiconductor device into a plurality of triangles;

determining the area of each of the triangles; and

summing the areas of the triangles.

12. The method of claim 11, wherein angles formed between the lines are substantially identical.

13. The method of claim 9, wherein the radius and the center of the virtual hole that has a regular circumference is calculated based on the area of the actual hole in said semiconductor device;

and

the irregularities of the actual hole in said semiconductor device are determined by calculating said standard deviation of the circumference of the actual hole in said semiconductor device relative to the radius of the virtual hole.

14. The method of claim 9, wherein determining the area of the actual hole in said semiconductor device comprises calculating the area of the actual hole in said semiconductor device based on the inner wall coordinates of the actual hole in said semiconductor device.

15. The method of claim 10, wherein determining the area of the actual hole in said semiconductor device comprises drawing said lines from the center coordinate of the actual hole in said semiconductor device to the inner wall coordinates of the actual hole in said semiconductor device to segment the actual hole into a plurality of triangles.

16. A method of determining irregularities of a hole comprising:

setting a center coordinate (x_c′

,y_c′

) of a actual hole;

obtaining n inner wall coordinates (x₁,y₁), (x₂,y₂), (x₃,y₃), . . . , (x_i,y_i), . . . , (x_n,y_n), wherein n is a positive integer, of the actual hole from the center coordinate of the actual hole;

drawing lines from the center coordinate of the actual hole to the inner wall coordinates of the actual hole to divide the actual hole into triangles, the lines having substantially equal angles between thereof;

summing an area of each of the triangles to obtain an area of the actual hole;

determining a radius r of a virtual hole based on the area of the actual hole;

obtaining a center coordinate (x_c,y_c) of the virtual hole by summing the inner wall coordinates of the actual hole and then dividing the summed inner wall coordinates by n;

determining distances l_i between the center coordinate of the virtual hole and the inner wall coordinates of the actual hole; and

obtaining the irregularities of the actual hole by determining a standard deviation σ

of the distances relative to the radius of the virtual hole using following equation;

$\mathrm{\sigma <br><br>}=\frac{\sqrt{\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(l_i-r\right)}^2}}{n}$