Three-dimensional calculation of field electron energy distributions from open hydrogen-saturated and capped metallic (5,5) carbon nanotubes

A. Mayer, N. M. Miskovsky, P. H. Cutler
2001 Applied Physics Letters  
We present three-dimensional simulations of field emission from open and capped ͑5,5͒ carbon nanotubes, with consideration of hydrogen saturation of the open structure. The transfer-matrix methodology used for the calculations reproduces appropriate band-structure effects due to the periodic repetition of a basic unit of the nanotubes and the use of Bachelet pseudopotentials. The total-energy distributions of field-emitted electrons contain peaks, which are related to standing waves in the
more » ... g waves in the shell of the nanotubes and to resonant states at the apex of the closed structure. These peaks move to lower energies with increasing electric field. The results indicate that field emission is more efficient with the open structure and that hydrogen saturation of the dangling bonds results in a further enhancement of the current. This letter reports a three-dimensional transfer-matrix calculation of field emission from a carbon nanotube, which includes atomic discreteness for open hydrogen saturated and capped ͑5,5͒ structures. The Bachelet pseudopotentials 1,2 are used in the calculation to introduce band-structure effects, which are manifested in the calculated energy distributions. Like other forms of nanostructured carbon, the nanotubes show interesting field-emission properties such as low extracting field, high current density, and long operating time. [3] [4] [5] In general, the current-voltage characteristics of the nanotubes are found to follow a Fowler-Nordheim type tunneling law 6 with an emitter work function around 5 eV depending on the type of nanotube. Electronic states localized near or at the apex of the nanotube influence the current emission profile. 7 The localized states are relatively well documented for various kinds of tube termination 8-11 and can be induced by extracting electric field, as shown by recent ab initio calculations. 12 To study field emission from metallic ͑5,5͒ carbon nanotubes, we used the transfer-matrix technique developed in previous publications. [13] [14] [15] This methodology predicts emission currents by treating, in the same framework, threedimensional aspects of the atomic structure of the carbon molecule as well as the potential barrier associated with the field-emission process. For the latter application, the potential energy was obtained using techniques developed in Ref. 13 to calculate the atomic polarization. Pseudopotentials 1,2 were used to represent ion-core potentials and the electronic exchange energy was evaluated using the local density approximation 4 3 C X 1/3 , where (r) is the local electronic density. 14 In order to reproduce appropriate band-structure effects in the distribution of incident states, a basic unit of the carbon nanotubes was repeated periodically in an intermediate region between the supporting metal cathode and the volume containing the extraction field. This geometry is illustrated in Fig. 1 . In this letter, we consider a fixed bias of 12 V and different values of the distance D between the cathode and anode to change the extraction field. For the properties of the supporting metal to reflect those of an infinite nanotube, the metal is given a work function of 5.25 eV ͑the value corresponding in our model to the middle of the metallic plateau in the distribution of incident states͒ and, second, electron energies extend 16 eV below the top of the potential barrier. The field-free region zр0 includes Nϭ16 units of the ͑5,5͒ molecule ͑320 carbon atoms͒, which are connected to seven units ͑140 carbon atoms͒ in the region zу0 where the extraction field is present ͑the last carbon atoms are 1.66 nm above the plane zϭ0 separating the parts of the nanotube, respectively, inside or outside the field region͒. This structure is completed either by hydrogen atoms to saturate the dangling bonds of the open structure or by half a C 60 molecule to close the nanotube. The situation depicted in Fig. 1 is that corresponding to the hydrogen-saturated open structure. The total-energy distributions calculated for the open hydrogen-saturated structure are illustrated in Fig. 2 . The four curves correspond to the incident distribution at zϭ0 and to the transmitted distributions at zϭD for local electric fields of 2, 2.5, and 3 V/nm. These fields should be considered as already amplified by a micron-long body to account for the difference by 3 orders of magnitude with fields applied macroscopically. 8 The sharp peak at the edge of the metallic plateau in the distribution of incident states is due to a van Hove singularity. 16 The other oscillations are related to standing waves in the structure. The separation between these oscillations is inversely proportional to the length of the nanotube and is typically 0.2 eV in the vicinity of the Fermi level for a 16-nm long nanotube ͑64 basic units instead of 16 here͒. The unnormalized values as well as the width of the distributions associated with the transmitted states increase a͒
doi:10.1063/1.1418456 fatcat:os5bmyvaffdtva557kehihfiga