Dopant Pairing in a Molecular Semiconductor
- PDF / 88,214 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 60 Downloads / 177 Views
P4.2.1
Dopant Pairing in a Molecular Semiconductor Howard M. Branz and Brian A. Gregg National Renewable Energy Laboratory Golden, CO 80401 U.S.A. ABSTRACT Recent doping experiments in n-type perylene diimide (PPEEB) semiconducting thin films showed an unexpected quadratic dependence of electrical conductivity upon dopant molecule concentration. We propose that singly-ionized dopant pairs outnumber ionized unpaired dopants and dominate conductivity. Random association into dopant pairs during spin coating then explains the quadratic dependence. Classical calculations confirm that dopant pairing reduces the binding energy of the easiest-to-ionize electron. Our model agrees with the measured conductivity activation energy and magnitude, assuming typical electron mobility in the crystal. The random distribution of dopants implies their distribution cannot equilibrate during the spincoating process. INTRODUCTION We propose a random dopant-pairing model which explains recent doping experiments in semiconducting perylene diimide (PPEEB) molecular crystals [1]. PPEEB is a good model system for studying doping because the host has a well characterized crystal geometry [2], the dopant is a derivative of the host molecule which should be accommodated within the normal crystal structure, and a conductivity power law spans many orders of magnitude [1]. Because large dopants cannot readily diffuse, it is hoped stable organic semiconducting pn-junctions can be formed using this approach to doping. Figure 1 reproduces the dependence of room temperature electrical conductivity (σ) on dopant concentration (d) observed in spin-cast thin-film polycrystalline PPEEB. The films are doped n-type by adding a reduced derivative of the same molecule (see Figure 3) into the PPEEB solution from which the films are spun [1]. The best power-law fits to the data of Figure 1 show a remarkably good quadratic dependence of conductivity, σ~dx with x = 2.06 ± .09. This dependence spans five orders of magnitude in conductivity. Conductivity is given by σ=nqµ, where n is the density of π* electrons contributing to dc conduction, µ is their mobility, and q is the electron charge. Variable-range hopping expressions [3] for mobility give unsatisfactory fits to the data, as illustrated by the non-linearity of lnversus (d/d0)-1/2 and lnversus (d/d0)-1/4, shown in Figure 2. Most likely, transport between crystallites, rather than hopping between dopants, controls µ. We therefore assume that charge carrier density, rather than mobility, controls σ(d). The quadratic dependence of σ then requires that n α d2. Figure 3a shows the structure of the PPEEB molecule, with its 7-ring perylene diimide chromophore and two long tails that form 36° angles to the plane of the figure. These chair-like molecules crystallize into a triclinic lattice, in which there is a stack of slightly offset chromophores with a spacing of ∆z=3.4Å between ring planes [2]. Carriers have their highest mobility along this π-interacting column of chromophores, good mobility between adjacent
Data Loading...
