The electronic structure alignment at the interfaces is largely determined by the mismatch between the Fermi level of the substrate and the electron affinity/ionization potential of the adsorbed material. Of course the energetic alignment is also important when carbon nanotubes are interfaced with a metal or with a semiconductor in the development of nanoscale electronic devices.
Surprisingly, the electron affinity (EA) and the ionization potential (IP) have not received much attention, because most of the published theoretical papers are concentrated on ab initio calculations of the work function (WF). Therefore the interplay between these quantities and the presence of edge localized states has not been discussed enough.
Field emission properties also depend on the EA and IP as well. In particular, the huge
aspect ratio (height to diameter) of carbon nanotubes makes them a very promising
material for realizing low threshold voltage field emitters, such as lamps, X-ray tubes
and flat panel displays.
In collaboration with Dr. Fabio Trani, Dr. Giovanni Cantele, Prof. Domenico Ninno and Prof. Giuseppe Iadonisi from the Department of Physics of the University of Naples “Federico II” and Dr. Andrea di Matteo from STMicroelectronics, we investigated the electronic properties of single-wall carbon nanotubes with methods based on the density functional theory. We analyzed two classes of systems: the isolated nanotube and the corresponding periodic array. In the first case we put the emphasis on the dependence of EA and IP on both the nanotube geometry (either armchair or zig-zag) and length. In the second case we calculated the array band structure and the variations of EA and IP with the intertube distance.
We had to use three different definitions of EA and IP. Indeed:
- in periodic systems, the electron affinity is calculated as EA=E_vac-E_LUMO and the
ionization potential as IP=E_vac-E_HOMO, where E_vac is the vacuum level energy calculated from electrostatics;
- in finite systems, the electron affinity is defined as EA=E(N)-E(N+1) where E(N)
and E(N+1) are the total ground-state energies in the neutral (N) and single charged (N+1) configurations. The ionization potential is similarly defined as IP=E(N-1)-E(N);
- in finite systems, also other definitions have been used for comparison, where the electron affinity is calculated as EA=-E_LUMO and the ionization potential as IP=-E_HOMO (in analogy to definitions 1., indeed for finite systems we have E_vac=0).
We have shown that the definition 3. differs from definition 2. for the self-energy correction that is not included in definition 3. On the other hand, in finite systems the electronegativity, defined as EN=(EA + IP)/2, is independent of the definitions used for EA and IP.
We have calculated the electronic orbitals of H-passivated and no passivated (5,5) and (7,0) nanotubes with lengths 18.3 Å and 23.9 Å, respectively. Indeed, as we discussed above, HOMO and LUMO orbitals have some influence on both the EA and IP.
The orbitals of the no passivated (5,5) and (7,0) nanotubes exhibit edge localized states due to dangling bonds.
The localized nature of the HOMO and LUMO orbitals of the (7,0) nanotube induces a weak dependence of EA and IP on the nanotube length, while for the (5,5) nanotube, where HOMO and LUMO are delocalized, the quantum confinement effects plays an important effect. Indeed for the (5,5) nanotube we found strong oscillations of EA and IP due to ‘quantum box’ confinement effect.
In the figures above the self-energy correction is not included. The self-energy correction is defined as the difference between the quasi-particle gap (EA–IP from total energies definition 2.) and the HOMO–LUMO gap and for the (5,5) H passivated nanotube ranges between 3.4 and 1.7 eV going from the shortest to the longest nanotubes. Similarly, for the (7,0) H passivated nanotube the variation ranges from 3.2 to 1.9 eV. We found that the electronegativity EN is independent on the self-energy correction.
We calculated also the EA, IP and WF of nanotube arrays using the definition 2. usually applied to periodic systems, based on the LUMO and HOMO energies. In a recent paper the work function of individual single-wall carbon nanotubes has been measured with photoemission microscopy. By analysing the data coming from a set of nanotubes, the authors have been able to conclude that most of them have work functions ranging within a 0.6 eV window. Although it may be a fortuitous coincidence, the set of calculations presented in our work does give an overall work function variation in the range 0.5–0.6 eV.
The full article “Ab initio calculations of electron affinity and ionization potential of carbon nanotubes” can be found on Nanotechnology 19 025711 (2008).