Doping metallic and semiconductor carbon nanotubes

Just One Question

We ask our self the following question: is it possible to control the electronic properties of carbon nanotubes by doping?
Indeed one of the most important drawbacks to using carbon nanotubes in microelectronics is the lack of control of their electronic properties. When you grow carbon nanotubes, they can be both metallic and semiconductor, but no control apriori is available for this, at least until present days.
On the other side it is well known that in the consolidated microelectronics based on the solid state physics, where the most used material is silicon, the control of the electronic properties is achieved by means of doping. Doping consists in intentionally introducing impurities into an extremely pure semiconductor. The processes to get doping are diffusion and ion implantation.
Doping seems to be suitable to achieve also the control of the electronic properties of the carbon nanotubes.
The work presented in synthesis in this page illustrates some important theoretical investigations made by me for STMicroelectronics and published in the journal Philosophical Magazine, to explore if carbon nanotubes doping will eventually be used to get control of this fascinating but unruly nano-material.

The Computational Method

Our theoretical investigation on doped SWNTs was carried out with calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA) with the Perdew, Burke and Ernzerhof (PBE) correlation functional. Our calculations are closed shell and were done using the DMol3 program from Accelrys.  All geometry optimizations were performed using a scheme based on delocalized internal coordinates generalized to periodic boundary conditions.

The substitutive impurity positions are shown in figure 1 for both the (5,5) and (8,0) SWNT. It is seen that two possible isomers, AZ and AA’, are considered, in which the two impurities are placed at different or same height along the nanotube axis, respectively.

The unit cells of the N or B doped SWNTs.
The unit cells of the N or B doped SWNTs. In a) and b) AZ and AA’ isomers are shown for (5,5) SWNT, respectively. In c) and d) AZ and AA’ isomers are shown for (8,0) SWNT, respectively.

Doped Semiconductor Nanotubes

The band structure of the pure (8,0) semiconductor SWNT is shown in figure 2 panel b. It is well known that zig-zag (8,0) SWNT is semiconductor with an energy gap of 0.71 eV as calculated within GGA. After the optimization of the geometries we calculated the formation energy of the investigated systems. Very similar results are obtained for the two isomers, for both N and B doping.

Due to the overlap of the impurity orbitals in the periodic structure we expect an impurity band rather than a set of discrete levels as in weak doping. The band structures of the doped (8,0) SWNTs are shown in figure 2. The bands of the pure (8,0) SWNT are not symmetrical with respect to the Fermi energy so for an assigned isomer N and B doping present band structures with distinct features and different occupation. We found that in the N doped (8,0) SWNT the bands are just partially occupied, while in the B doped case the Fermi energy is shifted downward to the top of the new valence band and the doped SWNT exhibit a negligible indirect energy gap. From the analysis of the DOS we deduced that both B doped isomers are metals. This finding let us conclude that holes and electrons have asymmetric behaviors in zig-zag (8,0) SWNT.

One-dimensional band structures of (a) substitutive N doped, (b) pure and (c) substitutive B doped (8,0) SWNT. In (a) and (c) full lines correspond to the AZ isomer and dashed lines to the AA’ isomer (see figure 1). The impurity band labels F and G are referred to both isomers. The Fermi energy is located at EF= 0 eV.

Doped Metallic Nanotubes

Armchair (5,5) SWNT is metallic because valence and conduction bands cross at the Fermi energy and just infinitesimal excitations at finite temperatures suffice to excite carriers in the conduction band. These features are in agreement with the numerical tight binding rules according to which the (n1,n2) SWNT is metallic when n1-n2=3j with j integer and semiconductor otherwise and are confirmed by our DFT calculations. Isomers of B doped (5,5) SWNT demand a formation energy smaller than those for (8,0) SWNT.

We have also calculated the band structure of the (5,5) SWNT with substitutive N and B doping, as shown in figure 3. The formation energies of the two isomers are very similar for any type of doping. Nevertheless band structures of the (5,5) SWNT isomers are different. Indeed, AZ isomer is gapless and exhibit a crossing of fully occupied valence band and empty conduction band, while band structures of AA’ isomer exhibit an energy gap (0.4 eV within GGA) above valence band. Our calculations showed that density of charge associated to the conduction band is more delocalized for AZ isomer, where the distance of the N impurities along longitudinal direction is 4.88 Å, that is the half of same distance in AA’ isomer. Similar results hold for B doping. From the charge density associated to the conduction band we concluded that the band crossing of AZ isomer is due to the delocalization of the density of charge that leads to metallic behaviors, as deduced from the analysis of the DOS.

One-dimensional band structures of (a) substitutive N doped, (b) pure and (c) substitutive B doped (5,5) SWNT. Bands reported as full lines correspond to AZ isomer, while dashed bands corresponds to AA’ isomer with reference to figure 1. The AA’ isomer band structure of both B and N doped SWNT exhibit an energy gap, not present in AZ isomer.

Finally the Answer to the Question We Started

In conclusion we have found that N and B doping of the semiconductor carbon nanotubes considered in this work lead to metallic behaviors for both isomers (this is a good news) but when metallic carbon nanotubes are doped the electrical behavior can be metallic or semiconductor depending on how the impurities are geometrically distributed. Unfortunately the last result is undesired because actual doping technologies cannot achieve a fine control of the geometrical distribution of impurities, and this hinders the control of the electronic properties by means of doping. Probably the electronic properties of carbon nanotubes and silicon cannot be controlled with the same processes.

The full article “Doping effects on metallic and semiconductor single-wall carbon nanotubes” can be found on  Philosophical Magazine Volume 87, Issue 7, Pages 1097 – 1105.

Accelrys reported this work as one of the Case Studies proposed to customers (click here to view).


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