Methods of measuring patterns and methods of manufacturing semiconductor devices including the same

1. An image processing method of inspecting patterns, the method comprising:

capturing a pattern image of patterns by irradiating the patterns with a beam providing unit and detecting resulting emissions from the patterns, wherein the patterns contained in the pattern image each correspond to a respective one of patterns being inspected and each have first and second boundaries;

enhancing the first and second boundaries in the pattern image to produce a boundary-enhanced image including first and second boundary patterns corresponding to the first and second boundaries, by processing the pattern image using an image processor;

combining the pattern image and the boundary-enhanced image, using the image processor, to produce an overlapping image including overlapping patterns in which images of the patterns contained in the pattern image occupy regions between the boundary patterns;

binarizing the overlapping image, using the image processor, to produce a binary image including binary patterns corresponding to the overlapping patterns; and

graphically analyzing the binary image, using the image processor, to determine whether patterns used to produce the pattern image have a defect.

2. The method of claim 1 , further comprising producing a pixel value distribution representative of the overlapping image, and extracting a threshold value for use as a binarization reference value for producing the binary image,

wherein the threshold value is extracted from the pixel value distribution representative of the overlapping image.

3. The method of claim 2 , wherein the pixel value distribution comprises a first gray pixel value distribution and a first bright pixel value distribution,

the threshold value corresponding to a minimum pixel value of a valley between the first gray pixel value distribution and the first bright pixel value distribution.

4. The method of claim 3 , wherein the valley conforms to a quadratic function whose leading coefficient is equal to or greater than 1.

5. The method of claim 2 , further comprising producing a pixel value distribution representative of the pattern image and a pixel value distribution representative of the boundary-enhanced image,

wherein the pixel value distribution representative of the overlapping image is produced by adding the pixel value distribution representative of the pattern image to the pixel value distribution representative of the boundary-enhanced image.

6. The method of claim 5 , wherein the pixel value distribution representative of the pattern image comprises a second gray pixel value distribution, a second bright pixel value distribution, and a second valley between the second gray pixel value distribution and the second bright pixel value distribution, and

the pixel value distribution representative of the boundary-enhanced image comprises a third gray pixel value distribution, a third bright pixel value distribution, and a third valley between the third gray pixel value distribution and third bright pixel value distribution,

each of the second and third valleys conforming to a quadratic function whose leading coefficient is less than 1.

7. The method of claim 1 , wherein producing the overlapping image comprises:

multiplying each of pixel values of pixels of the pattern image by a first weight;

multiplying each of pixel values of pixels of the boundary-enhanced image by a second weight; and

adding the pixel values of pixels of the pattern image to the pixel values of pixels of the boundary-enhanced image.

8. The method of claim 7 , wherein each of the first and second weights is 0.5.

9. The method of claim 1 , wherein producing the overlapping image comprises:

adding pixel values of first pixels of the pattern image to pixel values of second pixels of the boundary-enhanced image, respectively, to obtain sums of pixel values; and

dividing each of the sums in half.

10. The method of claim 1 , wherein each of the patterns contained in the pattern image is annular, and

the first and second boundaries respectively comprise inner and outer boundaries each being annular.

11. A method of manufacturing a semiconductor device, the method comprising:

forming a thin-layer structure on a substrate;

etching a portion of the thin-layer structure to form channel holes; and

inspecting the channel holes to determine whether the channel holes have been formed normally,

wherein inspecting the channel holes comprises:

using an electron microscope having an electron beam source, a secondary electron detector, and a controller including an image processor to capture a pattern image of patterns by irradiating the channel holes with an electron beam from the electron beam source and capturing secondary electrons emitted from the channel holes with the secondary electron detector, wherein the patterns contained in the pattern image each correspond to a respective one of the channel holes and each have first and second boundaries,

enhancing the first and second boundaries in the pattern image to produce a boundary-enhanced image including first and second boundary patterns corresponding to enhanced images of the first and second boundaries, by processing the pattern image using an image processor,

combining the pattern image and the boundary-enhanced image, using the image processor, to produce an overlapping image including overlapping patterns in which images of the channel holes contained in the pattern image occupy regions between the boundary patterns,

binarizing the overlapping image to produce a binary image including binary patterns corresponding to the overlapping patterns, and

graphically analyzing the binary image, using the image processor, to determine whether patterns used to produce the pattern image have a defect.

12. The method of claim 11 , further comprising:

determining whether the binary patterns are symmetrical; and

when the binary patterns are asymmetrical, outputting an abnormal detection signal to denote a failure in a process of forming the channel holes,

wherein the method further comprises removing the thin-layer structure.

13. The method of claim 11 , further comprising:

determining whether the binary patterns are symmetrical; and

when the binary patterns are asymmetrical, outputting a normal detection signal to denote the channel holes have been formed normally,

wherein the method further comprises forming vertical insulators and first semiconductor patterns on the substrate and along sides of the channel holes.

14. The method of claim 13 , wherein the normal detection signal is output when the binary patterns each have a circular shape.

15. The method of claim 12 , wherein the abnormal detection signal is output when at least one of the binary patterns has an oval shape.

16. A method of manufacturing a semiconductor device, the method comprising:

forming patterns on a substrate; and

inspecting the patterns including by:

imaging the substrate to produce a pattern image containing images representative of the patterns, respectively, each of the images having discernible regions demarcated by first and second boundaries,

enhancing the first and second boundaries in the pattern image to produce a boundary-enhanced image, wherein the boundary-enhanced image includes first and second boundary patterns as image enhancements of the first and second boundaries demarcating the regions of the images contained in the pattern image,

digitally combining the pattern image and the boundary-enhanced image to produce an overlapping image, wherein the overlapping image includes overlapping patterns representative of a superimposing of the images contained in the pattern image with the boundary patterns, respectively,

processing the overlapping image to produce a binary image of the overlapping image, wherein the binary image includes binary patterns corresponding to the overlapping patterns, and

graphically analyzing the binary image to determine whether the patterns on the substrate have been formed according to specifications.

17. The method of claim 16 , wherein the inspecting of the patterns comprises pixelating the overlapping image, producing a histogram of a distribution of values of pixels of the overlapping image, and extracting a threshold value for use in producing the binary image from the histogram.

18. The method of claim 16 , wherein the pattern image includes grey-scale images representative of the patterns on the substrate, and

the analyzing of the binary image determines whether each of the binary patterns of the binary image has a specified symmetry.

19. The method of claim 16 , further comprising selectively performing a manufacturing routine or a re-fabricating routine depending on results of the analyzing of the binary image, wherein the manufacturing routine when performed completes the semiconductor device and the re-fabricating routine when performed removes the patterns on the substrate and subsequently forms new patterns on the substrate.

20. The method of claim 19 , wherein the forming patterns on a substrate comprises forming a stack of layers on the substrate, and etching a portion of the stack to form channel holes extending vertically in the stack,

the analyzing of the binary image determines whether each of the binary patterns of the binary image have a specified symmetry, and

the selectively performing the manufacturing routine and the re-fabricating routine comprises forming vertical insulators and first semiconductor patterns on the substrate and along sides of the channel holes when the binary patterns are determined to each have the specified symmetry, and removing the stack from the substrate when at least on the binary patterns is determined to not have the specified symmetry.