Modern molecular devices are constructed using ultra-thin molecular layers of thickness ranging from nanometers to microns incorporated between metal or semiconductor electrodes.1 Unique properties of charge transport through molecular layers make these systems attractive for several technological applications including molecular wires,1-3 light emitting devices, 4 light absorbers used in solar cells5 (see e.g. Ref. 1 for the review). Injection and transport of charge in the insulating molecular levels are very sensitive to various imperfections in the system. For example, the presence of charge traps is known to lead to qualitative changes in the conduction properties when typical trap depths exceed the scale of thermal energy (0.025eV at room temperature).6 This is a very small scale compared to electronic energies near 1eV and even vibration energies near 0.1eV, so it is not surprising that various structure defects modify the system behavior qualitatively and quantitatively. It is hard and expensive to make perfect molecular structures for molecular electronic devices, intended for room temperature performance. Most experimental techniques used to make molecular layers of several tens of nanometer thickness, including for instance vacuum deposition,7 vapor deposition8 and spin coating,9 lead to the formation of an essentially amorphous organic layer with extensive disordering. Recently developed selfassembly techniques, where the molecular structure is prepared by careful layer by layer covalent bonding9,10 can not yet be conveniently made thicker than a few nano-meters. Even in the self assembled layers the transport of charge can be strongly affected by the presence of defects.11 In addition one recent experimental comparison10 of charge injection through spin-coated and self-assembled layers made from identical molecules show much better performance of the disordered spin-coated layer. Thus the effect of disordering is not always destructive. On the one hand it reduces charge mobility by making traps within the molecular layer.6,12,13 This is certainly a destructive effect for molecular device performance. On the other hand the fluctuations in molecular energies can promote efficient injection of charge, thus increasing the injection current.14-18 How significant is the effect of disordering? To characterize it we can use the electronic (or hole) energies within the molecular layer. For an isolated molecule the relevant energy is the electron affinity or ionization potential of the molecule. If the molecule is within an amorphous structure, the electronic energies fluctuate from molecule to molecule due to fluctuations in neighboring molecule positions, surface defects, etc. Then we can introduce a characteristic average energy EM and its typical fluctuation w, describing the effect of disordering.14-16 If this fluctuation exceeds the thermal energy, molecules with energies below the average one by w become charge traps. The energy of the trapped states has been determined experimentally for various materials. In the widely used organic emitting layer composed of Alq3 (tris-(8-hydroxyquinoline) aluminum) molecules (e.g. Ref. 9,10), these energies are found to be widely distributed within the range from 0.06eV to 0.5eV.19 In the standard hole transport layer TPD (N,N'-bis(3-methylphenyl)N,N'-diphenylbenzidine) these energies range from 0.1eV to 0.55eV.19 These are very large energies compared to the thermal energy kBT ∼0.025eV. A similarly wide distribution of defect energies has been found for another light emitting layer, PPV (poly-phenylene-vinylene) molecules.20 To get some feeling for these numbers, one can estimate the difference in the population probabilities of two molecules with energies different by δE ∼ 0.25 eV that can be less than the typical defect energy.19,20 At low concentrations the population ratio can be estimated as exp(δE/(kBT)) ∼ e10 ∼ 20000. This is a dominant effect for the injection process. Fluctuations of the molecular energies obviously lead to fluctuations of the injection energetics and if some electrons see injection barriers below the average by 0.25eV compared to others, their injection will dominate if their fraction exceeds 0.0001. Thus the disordering is significant for understanding electronic injection and transport in molecular layers. It affects both the charge bulk transport (mobility) and the charge injection. The effect of disordering on the charge transport is described by the theory of traps.6 Disorder generally suppresses the current because a large fraction of carriers is localized in traps and thus the overall moving charge density is smaller than in an ordered system. For specially correlated trap potentials due to the static polarization of molecules, disorder leads to strong mobility-voltage dependence. 21 The effect of energy fluctuations on the injection can be quite different [14-16] because of the possibility to reduce the injection barrier. The rare injection channels composed of molecules with fluctuationally reduced energy can conduct charge from the metal into the bulk of molecular material much more efficiently than injection through the average barrier caused by energy mismatch of metal and molecular layer.16 Bulk transport or surface injection regimes dominate the electronic properties of molecular layers under different conditions in either the injection-limited regime or the space charge limited regime 6,17,18,22-28 (non Ohmic or Ohmic metal-insulator contact). The injection-limited regime is realized at low applied voltage (and internal current), when the density of carriers inside the molecular layer is small enough to ignore its effect on the potential distribution inside the material. In this case the current is defined by the probability for the charge to enter from the metal to the molecular layer; this requires overcoming the injection barrier. The space-charge limited regime is established when the current is large enough so it partially blocks the injection, thus controlling the charge balance and forming an Ohmic contact. It is clear that the perfect injecting contact for any semiconductor device is an Ohmic contact.22 Practically it is often hard to reach the space-charge limited regime because it requires very high current, which can lead to damage of the material. It is easier to become space-charge limited when the injection potential barrier formed by the difference between the metal work function and the molecular electronic level is relatively low,22-23 but it is more difficult with highly stable Al or Au electrodes possessing a large work function. It is interesting that the recent investigation of charge transport through the significant emitting material Alq3 25 gave the evidence that the performance regime there is always injection-limited. Thus both regimes are interesting from the practical point of view and require theoretical analysis. The effect of disordering (traps) is relatively well understood in the space-charge limited regime,6 while the injection into the disordered medium is not so clear. Several studies based on the Monte-Carlo methods and a perturbative analytical approach (see Refs. 14,15,18) show a remarkable increase of the current, arising from fluctuations. An analytical onedimensional hopping model developed in our previous work16 predicts strong field and temperature dependence caused by the disorder. The main purpose of this paper is to extend that model16 to account for disorder effects in real materials. We will combine an analytical treatment with a numerical analysis of the one-dimensional hopping model to compute the charge current dependence on the voltage, temperature and disorder in the injection limited regime. Other important effects will be discussed, including the tun neling injection that can be seen at low temperature2,24,29 and sometimes takes place even at room temperature2,11,30 and the influence of disorder on device damage. The most attention will be paid to the current injection into amorphous organic layers of the thickness about a 100 nm placed between metal electrodes. However under certain conditions the results can also be applied to inorganic semiconducting junctions and molecular wires. We will discuss them briefly. The paper is organized as follows. In section 2 we introduce and discuss the limiting regimes for the charge injection including thermal activation vs. tunneling injection and the injection limited regime vs. the spacecharge limited current. Criteria for crossovers between different regimes will be established. The significance of the interaction of mobile electrons with the conducting electrons from the metal, leading to the formation of the image charge and defining the absolute value of the current and current/voltage characteristics, will be pointed out. Section 3 is devoted to the theory of charge injection into the disordered medium. Following our previous work16 we will consider the injection path optimization problem and derive the current as a function of the applied voltage, temperature and energy fluctuation (disordering). The average current and its fluctuations will be considered as a possible source for the damage caused by the high local current. A brief discussion of the experimental data characterizing the electronic properties of the molecular layer in the light of our theory will be made in Section 4. The results will be summarized in Section 5.
|Title of host publication||Computational Materials Chemistry|
|Subtitle of host publication||Methods and Applications|
|Number of pages||60|
|ISBN (Print)||1402017677, 9781402017674|
|Publication status||Published - Dec 1 2005|
ASJC Scopus subject areas
- Materials Science(all)