1. Carbon nanocones- calculation of electronic properties
ANNA ŁAPIŃSKA – University of Bialystok
TOMAS KADAVY- Charles University in Prague
Supervisor: Vsevolod Katkov, Ph.D.

2. contents The aim of the project An equipment description
A experminent description
Obtained results

3. The aim of the project
The aim of project was to become acquainted with basics information about carbon nanostructures, method of their study and calculation of electronic properties of one of allotropes of carbon – nanocones.

4. An equipment description
Calculation was made by using „Wolfram Mathematica” program.

5. An experiment description
The task was to calculate electronic properties of carbon nanocones using tight binding method.
Electronic properties, which was considered: energy spectrum and density of electron in every atom.

6. An experiment description – carbon nanocones
Conical, zero dimensional structure.
They have height and base diameter of the same order of magnitude.
The opening angle (apex) of the cones is not arbitrary, but has preferred values of approximately 20°, 40° and 60°.
The absolute value of the cone wall thickness varies between 10 and 30 nm, but can be as large as 80 nm for some nanocones.

7. An experiment description
Structure, which were used during calculation.
SEM image of carbon nanocones

8. Tight binding method
The tight binding (TB) method is a method used for calculation of electronic band structures of solids.
The idea of TB method is taken to account direction between the nearest neighbour.
To find energy spectrum and density of states one can calculate eigenvalues and eigenvectors respectively of matrix:

9. Results HOMO (Highest Occupied Molecular Orbital) – -1.51 eV
LUMO (Lowest Unoccupied Molecular Orbital)– eV
HOMO is connected with top of valence band of semiconductor
LUMO is connected with the bottom of conductivity band.

10. results Plot of gained energy spectrum of carbon nanocones:
Vertical axis: eigenvalues

11. results Density of electron for LUMO level for atom type A:
Vertical axis: eigenvector
Horizontal axis: the number of atom

12. results Density of electron for atom type B,C:
Vertical axis: eigenvector
Horizontal axis: the number of atom

13. Conclusion
It was calculated enegry spectrum for carbon nanocone. (It was also find HOMO and LUMO level).
It was found that LUMO level double generated.
Density of electron states for LUMO level was calculated.
It was found that periodical oscilations of DOS appear for second, third rings.
DOS for top ring is constant.

14. Thank you for attention!