In this section the ELA taking place at interfaces between electrodes and COMs will be described and the concept of surface charge transfer doping will be introduced.
Vacuum level alignment vs vacuum level shift
Vacuum level alignment, also known as Schottky-Mott limit [70], is one of the first models used to calculate the ELA across electrode/OSC interfaces (see Fig. 2.11a,b). In this description, upon contact of an electrode with
an OSC, the energy levels of the organic material (IE and EA) determined separately (in gas phase measurements) were used to calculate the ELA occurring at the interface. In this case, the determining factor for the align-ment of the energy levels after contact is the work function of the electrode.
This implies that the determination of the hole/electron injection barriers (HIB/EIB), which are typically defined as the energy difference between the Fermi level (EF) of the electrode material and the HOMO- or LUMO-charge transport threshold of the adsorbed COM respectively, are given by the simple equations as follows:
HIB =IE −Φ, (2.11)
and
EIB = Φ−EA . (2.12)
However, Evac alignment, in many cases gives erroneous values even by more than 1 eV [61, 71], since it does not take into account physical or chemical interactions that take place at the interface.
One of the first understood deviations from the Evac alignment rule was assessed theoretically for closed-shell noble atoms [72], such as xenon (Xe) adsorbed on metal surfaces. Since then, various studies have shown the deviation from the commonly assumedEvacalignment in many other cases [61,73,74].
For example, when molecules only physisorb on atomically clean Au, the work function of the system was different than the work function of the individual gold electrode [75]. A qualitative picture of the interface energetics of the electrode/metal surface before contact with a COM is shown in Fig. 2.11c. In this illustration, the IE and EA of the COM are assumed for simplicity to remain constant before and after adsorption on the metal, with the parameter µb being the bulk chemical potential. SD is the surface dipole due to a large density of electron cloud spilling outside the surface of the metal and into vacuum. When COMs are deposited out of the surface of the metal, the ”spilling out” electron cloud of the metal is pushed back into the bulk, altering the surface dipole and thus the overall work function of the metal. Thus, the work function of the metal/COM system differs from the work function of the individual metal
Figure 2.11: Schematic energy level diagram of an organic semiconductor (OSC) before (a) and after (b,c) adsorption on an electrode. In (b) the energy levels be-tween the electrode and the organic layer are drawn considering that vacuum-level alignment takes place while in (c) the energy vacuum-levels drawn in such a way that the vacuum level shifts after contact, due to the alteration of the surface dipole (SD) that leads to a work function shift (∆Φ). The corresponding hole injection barriers (HIB) and electron injection barriers (EIB) are depicted, together with the ionization energy (IE) and electron affinity (EA) of the organic material.
alone, giving different HIB and EIB values than estimated by assuming Evac alignment. This phenomenon of Pauli repulsion is termed ”push-back” effect or ”cushion” effect [61,76].
The ”push-back” effect, that causes the formation of interface dipoles (ID) and results in different energy level alignment than what is described in eq. 2.13 and eq. 2.14, results in the following equations for HIB and EIB:
HIB =IE −Φ +ID , (2.13)
EIB = Φ−EA+ID . (2.14)
Fermi level pinning
Fermi level pinning is the phenomenon where for a range of electrode work functions, the final work function reached after deposition of a molecular acceptor or donor is independent of the work function of the pristine electrode. Most of the organic (opto)electronic devices are fab-ricated in atmospheres such as high vacuum, controlled gas or ambient in order to reduce the manufacturing costs. Thus, materials used for the devices include a certain degree of surface contamination which turns their surfaces chemically inert, rendering their electronic coupling with COMs weak. Studies using such kind of chemically inert substrates with different work function to create interfaces with COMs [64, 77, 78] have shown that the energy level alignment at the interfaces follow, in general, the rule shown in Fig. 2.12. Since graphene is also a rather chemically inert material, it follows naturally that this rule will apply for graphene/COMs interfaces.
The dependence of HIB and EIB on Φ is characterised by the S-parameter [80], with S given by the following equation:
S= dEFgap
dΦ , (2.15)
giving the shift of the Fermi level into the energy gap of the OSC (EFgap), as Φvaries [79,80].
In the range where S∼1, the HIB and EIB follow the decrease/increase of the work functionΦ, i.e.,Evac alignment can be used to predict the
en-Figure 2.12: Schematic illustration showing the dependence of electron and hole injection barriers (EIB and HIB, respectively) of organic semiconductors on the work function of electrodes that are chemically inert. The inlets show the posi-tion of the Fermi levelEFwith respect to the HOMO-LUMO gap of the organic semiconductor. Φcrit,low indicates sufficiently low work function to induce elec-trons to flow fromEF into the LUMO of the organic semiconductor, resulting to pinning of the LUMO aroundEF.Φcrit,highcorresponds to sufficiently high work function, to induce electrons to flow from the HOMO to theEF, resulting in the pinning of the HOMO aroundEF.Adapted from [79].
ergy positions of HIB and EIB. In this range, theEF of the electrode falls within the HOMO-LUMO gap of the OSC, as shown schematically in the inlet in Fig. 2.12.
At S ∼ 0, Fermi level pinning controls the ELA. At these positions, the HIB and EIB do not change with alteration of the work function of the electrode. This phenomenon occurs, for electrodes with critically high (Φcrit,high) or critically low (Φcrit,high) work function, resulting in the EF to fall into the unoccupied or occupied states of the organic semiconductor, respectively, if Evac alignment were assumed, as shown in the inlets in Fig. 2.12, for the regions where S ∼ 0. When this occurs, the system is in the so called Fermi-level-pinned regime. This would bring the system out of thermodynamic equilibrium and interfacial charge transfer between substrate and organic semiconductor spontaneously takes place in order to guarantee thermodynamic equilibrium.
The pinning of EF has been observed by ultraviolet photoemission (UPS) and inverse photoemission (IPES) [81,82] to occur at energies large compared to the frontier energy levels of the organic semiconductors. This
results to minimised, but non-zero HIB and EIB values, different than what is expected if theEF would be allowed to fall into the HOMO/LUMO of the neutral molecule.
The reason for Fermi level pinning occurring a few meV away from the frontier energy levels (HOMO or LUMO) of the OSC is not yet clearly re-solved. One of the explanations is the integer charge transfer model (ICT) [83,84]. Under the assumption that the surfaces are chemically inert, only integer charge could be transferred between substrate and COM (as partial charge transfer requires hybridisation and, thus, chemisorption). Conse-quently, cations (or positive polarons) form as a result of the migration of an electron from the HOMO to the substrate whereas, anions (or negative polarons) form when electrons enter the LUMO from the substrate.
Theoretical modelling has shown that the energy levels of the charged species follow the rule depicted in Fig. 2.13, i.e. a renormalisation of the energy levels occurs that reduces the HOMO/LUMO gap of the charged species with respect to the neutral species. Thus, the energy levels that these positive or negative polarons are occupying, will be the energy lev-els where Fermi level pinning will occur. Another possible explanation involves the presence of defect- or impurity- states that are present in the gap of the OSC. These states broaden the density of states (DOS) of the OSC and this causes a tailing of the distribution extending close to theEF. Thus, the Fermi level pinning could occur at these electronic states [85].
Figure 2.13:Scheme showing the energy levels of the ground state of (a) a nega-tively charged molecule (anion or negative polaron), (b) a neutral molecule, and (c) positively charged molecule (cation or positive polaron). Adapted from [79].