ANNA ŁAPIŃSKA – University of BialystokTOMAS KADAVY- Charles University in

Prague

Supervisor: Vsevolod Katkov, Ph.D.

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

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.

Calculation was made by using „Wolfram Mathematica” program.

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.

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.

Structure, which were used during calculation. SEM image of carbon nanocones

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:

ˆmn m nH H

HOMO (Highest Occupied Molecular Orbital) –-1.51 eV

LUMO (Lowest Unoccupied Molecular Orbital)– 0.75 eV

HOMO is connected with top of valence band of semiconductor

LUMO is connected with the bottom of conductivity band.

Plot of gained energy spectrum of carbon nanocones:Vertical axis: eigenvalues

Density of electron for LUMO level for atom type A:

Vertical axis: eigenvectorHorizontal axis: the number of atom

Density of electron for atom type B,C:

Vertical axis: eigenvectorHorizontal axis: the number of atom

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.