Method for reconstructing two-dimensional chemical maps from electron spectroscopy line scans

1. A method comprising:

fast two-dimensional scanning a layered nanostructure with a scanning electron microscope to form a structure image having multiple layers;

slow-rate scanning the nanostructure along selected lines, collecting characteristic spectra;

extracting chemical profiles of the nanostructure from the spectra;

transforming the structure image into a warped structure image by flattening each of the layers in the structure image;

aligning the coordinates of the chemical profiles to those of the warped structure image;

averaging the chemical profiles obtained from different line scans;

expanding the averaged profiles into warped chemical maps; and

inversely transforming the warped chemical maps respectively into two-dimensional chemical maps.

2. The method according to claim 1 , comprising slow-rate scanning the nanostructure along a few selected scanning lines.

3. The method according to claim 2 , wherein each chemical profile includes one or more chemical elements.

4. The method according to claim 3 , comprising transforming the structure image into a warped structure image by defining the morphology of the layers in the structure image by a criteria of equal signal levels, wherein the warped structure image shows no structural change along an axis within the plane of each of the layers.

5. The method according to claim 4 , comprising:

transforming the structure image into the warped structure image using a transformation formula; and

inversely transforming the deformed chemical maps into the two-dimensional chemical maps using a reverse transformation formula corresponding to the transformation formula.

6. The method according to claim 5 , wherein the transformation formula is a warping matrix that continuously transforms the structure image while preserving a topology of the structure image.

7. The method according to claim 6 , wherein the warping matrix transforms the structural image by warping in one or two spatial directions.

8. The method according to claim 6 , comprising transforming the chemical profiles into one averaged chemical profile by:

aligning the chemical profiles to the coordinates of the warped image; and

summing and averaging the chemical profiles.

9. The method according claim 8 , wherein expanding the averaged chemical profiles forms warped chemical maps having no chemical change along one axis within the plane of each layer.

10. The method according to claim 1 , comprising slow-rate scanning the nanostructure along selected scanning lines with employing electron energy loss spectroscopy, energy-dispersive X-ray spectroscopy, or cathode luminescence spectroscopy.

11. The method according to claim 1 , comprising minimizing the electron dose required for the chemical characterization of a nanostructure.

12. A method comprising:

fast two-dimensional scanning a layered nanostructure with an electron probe, with registering an ADF or BF detector signal to provide an image of the nanostructure, the image having multiple layers;

generating a warped image by aligning the layers in the image using a warping matrix;

collecting spectra of the nanostructure along selected scan lines;

extracting chemical profiles from the collected spectra;

aligning and averaging the chemical profiles;

generating warped chemical maps from the averaged chemical profiles, the warped chemical maps having no chemical change along one axis within the plane of each layer; and

applying an inverse of the warping matrix to the warped chemical maps to form two-dimensional chemical maps of the nanostructure.

13. The method according to claim 12 , comprising extracting chemical profiles from the spectra collected when scanning along a few selected lines.

14. The method according to claim 13 , wherein each chemical profile includes multiple chemical elements.

15. The method according to claim 14 , comprising:

generating warped chemical maps by: aligning and averaging the profiles for each chemical element; and

expanding the averaged chemical profiles to generate warped chemical maps having no chemical change along one axis within the plane of each layer.

16. The method according to claim 15 , wherein the warping matrix continuously transforms the image of the nanostructure while preserving a topology of the image.

17. The method according to claim 16 , wherein the warping matrix transforms the structural image by warping in one or two spatial directions.

18. The method according to claim 12 , comprising extracting chemical profiles from the electron probe scanned along the predetermined lines while employing electron energy loss spectroscopy, energy-dispersive X-ray spectroscopy, or cathode luminescence spectroscopy.

19. A method comprising:

fast two-dimensional scanning a layered semiconductor nanostructure with an electron probe to form an image having multiple layers;

slow-rate scanning the nanostructure along a predetermined number of scan lines to form chemical profiles, each chemical profile corresponding to one of the scan lines and including multiple chemical elements;

transforming the image into a warped image by:

defining a morphology of the layers in the image with a criteria of equal signal levels; and

forming a warped image using a warping matrix that continuously transforms the image while preserving a topology of the image, wherein the warped image shows no structural change along each of the layers;

averaging chemical profiles from different line scans;

expanding an averaged chemical profile into the warped chemical maps;

aligning coordinates of the chemical profiles with those of the warped image;

averaging chemical profiles from different line scans for each chemical element;

expanding an averaged chemical profile into warped chemical maps, wherein each of the warped chemical maps exhibits no chemical change along an axis within the plane of each layer; and

inversely transforming the warped chemical maps into two-dimensional chemical maps using a reverse warping matrix corresponding to the warping matrix.

20. The method according to claim 19 , comprising fast two-dimensional scanning the semiconductor nanostructure with registering the signal from an ADF or BF detector to form an image of the nanostructure.