NANO LETTERS
Energy Conversion Efficiency in Nanotube Optoelectronics
2005 Vol. 5, No. 2 219-222
Derek A. Stewart* and Franc¸ ois Le´onard* Sandia National Laboratories, LiVermore, California 94551 Received September 27, 2004; Revised Manuscript Received November 23, 2004
ABSTRACT We present theoretical performance estimates for nanotube optoelectronic devices under bias. Current−voltage characteristics of illuminated nanotube p-n junctions are calculated using a self-consistent nonequilibrium Green’s function approach. Energy conversion rates reaching tens of percent are predicted for incident photon energies near the band gap energy. In addition, the energy conversion rate increases as the diameter of the nanotube is reduced, even though the quantum efficiency shows little dependence on nanotube radius. These results indicate that the quantum efficiency is not a limiting factor for use of nanotubes in optoelectronics.
Carbon nanotubes (NTs) have been lauded as promising building blocks for a variety of nanoscale applications. Of these, nanoelectronics has perhaps attracted the most interest and has witnessed the development of NT rectifiers1-3 and NT field effect transistors.4-6 These developments have led to recent experimental work7-10 that has extended the realm of possible applications to optoelectronics. Because of their reduced dimensionality and unique electronic structure, NTs are intriguing materials for optoelectronics. Recent theoretical work11 has explored shortcircuit photocurrents in nanotube devices, i.e., the electrical current generated by incoming light in the absence of an applied voltage bias. While the short-circuit photocurrent is of interest for applications in optical communications, for applications in energy conversion, an important measure is the power efficiency. This is a much different problem from the short-circuit photocurrent, because it requires calculating the current-voltage characteristics of illuminated NT devices under bias, a truly nonequilibrium situation. In this work, we explore the power efficiency of fundamental nanotube optoelectronic devices. We consider illuminated nanotube p-n junctions under bias using a selfconsistent nonequilibrium Green’s function formalism. Current-voltage characteristics and power efficiency as a function of photon energy are calculated. We find that energy conversion rates can reach tens of percent, and have a strong dependence on the radius of the nanotube. As shown in Figure 1, the system consists of a singlewall zigzag NT p-n junction under illumination. The NT is described using a tight-binding framework with coupling γ ) 2.5 eV between nearest-neighbor atoms, and the doping is modeled as in ref 12 with a dopant concentration of ( 5 * Corresponding authors. E-mail:
[email protected], fleonar@ sandia.gov. 10.1021/nl048410z CCC: $30.25 Published on Web 01/06/2005
© 2005 American Chemical Society
Figure 1. Sketch of the NT p-n junction under illumination and the calculated self-consistent band-bending at 0.2 V for a (17,0) NT. Dotted lines are the lead fermi levels.
× 10-4 electrons/C atom. The incoming radiation with frequency ω has electric field parallel to the NT axis and Poynting vector perpendicular to the NT surface. The device is made up of an illuminated region 26.74 nm in length (64 unit cells) that is connected to shielded semi-infinite NT leads.13 To apply the nonequilibrium Green’s function formalism14 to this system, we divide the NT into principle layers, with
each layer corresponding to a ring of the zigzag NT. The main quantity of interest is the Green’s function, G
