A Figure of Merit for Transparent Conducting Nanotube Films

  • PDF / 87,388 Bytes
  • 5 Pages / 612 x 792 pts (letter) Page_size
  • 56 Downloads / 229 Views

DOWNLOAD

REPORT


1204-K10-41

A Figure of Merit for Transparent Conducting Nanotube Films Á. Pekker1, K. Kamarás1, N. M. Nemes2 and M. Garcia-Hernandez3 1

Research Institute for Solid State Physics and Optics, P.O. Box 49, Budapest, Hungary H-1525 GFMC. Dpto. Fisica Aplicada III, Universidad Complutense de Madrid, E-28040 Madrid, Spain 3 Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientificas, Cantoblanco, E-28049 Madrid, Spain 2

ABSTRACT We propose a wavelength-dependent figure of merit for transparent conducting nanotube networks, composed of the sheet resistance and the optical density. We argue that this would be more useful than previous suggestions, because it relies on more realistic assumptions regarding the optical parameters of real nanotubes.

INTRODUCTION The use of carbon nanotubes as transparent conductive coatings has been extensively studied in the last years. Several systems were investigated [1] and various manufacturing techniques have been suggested [2-4]. Unique characterization of film quality is imperative if these products are to be manufactured on a large scale. The two parameters to be balanced in a transparent conductive layer are the transmission in a chosen spectral region (for the most important application, in solar cells, this is preferably the visible region) and the dc conductivity (or sheet resistance). Both quantities depend on the optical and electrical properties and the thickness of the film. Sheet resistance has to be minimized and transmission maximized for an optimal product. In the literature, the approaches used so far are either completely practical, bearing in mind the feasibility for applications, or more fundamental, starting from the basic physical quantities of the film material and using optical relationships with realistic approximations. The simplest quality indicator would be of course the ratio of transmission at a given wavelength and the sheet resistance. This indicator was introduced by Fraser and Cook for ITO films [5]. Haacke [6] later showed that this figure reaches its optimum value at a thickness where the transmission is 0.37, way too low for the desired applications; he introduced instead the quantity ΦTC=T10/R□, which shows maximum at T=0.9. The exponent can be tuned for more transmitting samples, but in this case the figure of merit loses its uniform character. Hu, Hecht and Grüner [4] approached the problem from a much more fundamental point of view. They start from a simplified version of the formula introduced by Tinkham [7] for thin metallic films: T (ω ) =

1  ( ) 1 + 2π σ 1 ω   cRsq σ 1 (0 )  

2

,

(1)

where T is the transmittance at frequency ω, σ1 the real part of the optical conductivity (σ1(0) the dc conductivity), c the velocity of light and Rsq the dc sheet resistance. This equation is valid in the microwave and far infrared range, where the real part of the conductivity exceeds the imaginary part, σ1>>σ2. In this case the ratio σ1(ω)/σ1(0) is characteristic of the film and independent of frequency. At h

Data Loading...