Barrier height

The experiment is performed at various voltages and the barrier height values are corrected for the image charge potential by extrapolating to zero voltage. 

The above technique requires organic layers that are of the order of a few microns thick, considerably thicker than those used in OFEDs. A way to measure charge carrier mobilities directly on an OFED geometry is by time-resolved electroluminescence measurements. The technique is based on the fact that for recombination to take place, the most mobile of the two carriers needs to transverse the sample and meet with the less mobile one [120, 121]. Therefore, the time onset for emission corresponds to the transit time of the most mobile carrier. Blom et al. [122] have described a high sensitivity variation of this technique where the time integrated light output is measured as a fimction of the duration of a voltage pulse and the transit time is extracted by extrapolation to 

13 The Chemistry, Physics and Engineering of Organic Light-Emitting Diodes 

Absolute photoluminescence efficiency measurements in thin solid films are quite difficult, since light-trapping, waveguiding effects and, possibly, distributions in tlie emission dipole moments of individual chromophores modify the angular distribution of the emission. De Mello et al. [126] have described an im- 

It should be mentioned that for p-type materials, usually, a negative space charge is formed because the work function of the semiconductor is below that of the metal. Again assuming an ideal contact, the energy barrier is given by 

A large number of semiconductor metal junctions have been studied. There are various experimental techniques for measuring barrier heights, such as photoelectric and capacity measurements and current-voltage investigations. The first-mentioned technique seems to be the most accurate. These methods are not described here some of them are discussed in Chapters 4 and 5 (see also [7,12,16]). 

Many experimental values for barrier heights at semiconductor-metal junctions have been obtained. Many researchers have also measured the barrier height as a function of the work function of the metal, and have mostly obtained a straight line, as expected from Eq. (2.3). However, in many cases the slope, d j,/ d, of a corresponding plot was much smaller than unity. In 1969, it was shown by Kurtin et al. that the sensitivity of a barrier height to different metals increases with the ionicity of the semiconductor [17]. In order to obtain a better characterization of the experimental data, they defined an index of the interface behavior S which they introduced into Eq. (2.3) as 

The contact between metals and III-V semiconductors has been studied in detail [21, 22]. These semiconductors are of special interest here because many electrochemical experiments have been performed with these materials. In the case of metal-semiconductor junctions, the barrier heights were found to be nearly independent of the type of metal, which was interpreted as strong Fermi level pinning. Various models have been proposed for interpreting the pinning of the barrier height at the surface of several III-V compounds. Besides the metal-induced gap 

When a contact is made between a semiconductor and a metal, the Fermi levels in the two materials must coincide at thermal equilibrium. We will consider here two limiting cases as shown in Fig. 2.3. In the first, we have a somewhat ideal situation (Fig. 2.3a). The semiconductor is assumed to be free from surface states so that the energy bands are flat as far as the surface before contact. In addition, any dipole layer on the metal and on the semiconductor surface is neglected. In the example shown in Fig. 2.3a, the Fermi level of the semiconductor occurs at a higher energy than that of the metal. Accordingly, some electrons are transferred from the semiconductor to the metal after close contact is made between them. This leads to a positive space charge layer after 

This cannot be measured because there are other metal-metal and metal-semiconductor contacts in the measuring circuit, including those of the voltmeter, and the sum of all contact potentials is zero. As can easily be deduced from Fig. 2.3, the barrier height e / 5 at the metal-semiconductor contact is given by 

Oftentimes, the concentration profile follows neither a simple exponential in time nor a discrete combination of exponentials, but a stretched exponential, which is also 

FIGURE 1.3 Concentration profile from a mechanism employing three intermediates, /j, /j, I, plus the initial (dark) state /q. /[(O) = 1 is assumed. The cyclic reaction is started (initiated) by a laser flash. Molecules relax through the intermediate states back to the initial state. The concentration profile of intermediate /j shows all three relaxation times (arrows). 

To retain the analogy with a simple exponential function, it is considered in the cases described by Equations (1.8) and (1.9) that there is a distribution of barrier heights, g(G), each height corresponding to an exponential relaxation (Austin et al. 1975 Nagy et al. 2005). The concentration profile is in this case described by 

By using the normalization condition for the distribution of relaxation times, 

Expressed in terms of the distribntion of relaxation times, gi g). Equation (1.13) reads 

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Adsorbed atoms and molecules can also diflfiise across terraces from one adsorption site to another [33]. On a perfect terrace, adatom diflfiision could be considered as a random walk between adsorption sites, with a diflfiisivity that depends on the barrier height between neighbouring sites and the surface temperature [29]. The diflfiision of adsorbates has been studied with FIM [14], STM [34, 35] and laser-mduced themial desorption [36]. 

The transition from k to on the low-pressure side ean be eonstnieted using iiiidtidimensional unimoleeular rate theory [1, 44], if one knows the barrier height for the reaetion and the vibrational frequeneies of the reaetant and transition state. The transition from to k y ean be deseribed in temis of Kramers theory [45]... 

RRKM fit to microcanonical rate constants of isolated tran.s-stilbene and the solid curve a fit that uses a reaction barrier height reduced by solute-solvent interaction [46],... 

Figure A3.8.1 A schematic diagram of the PMF along the reaction coordinate for an isomerizing solute in the gas phase (frill curve) and in solution (broken curve). Note the modification of the barrier height, the well positions, and the reaction free energy due to the interaction with the solvent.

In prineiple, nothing more is neeessary to understand the infiuenee of the solvent on the TST rate eonstant than the modifieation of the PMF, and the resulting ehanges in the free energy barrier height should be viewed as the dominant effeet on the rate sinee tliese ehanges appear in an exponential fonn. As an example, an error... 

Tredgold R FI and El-Badawy Z I 1985 Inorease of Sohottky-barrier height at GaAs-surfaoes by oarboxylio-aeid monolayers and multilayers J. Phys. D Appl. Phys. 18 103-9... 

Fig. 4. Radial distribution functions between the centre of a test cavity and the (jxygen atom of the surrounding water. The curves correspond to the different barrier heights for the softcore interaction illustrated in Fig. 3...

In the limit that the barrier height is large compared with the thermal energy, it is standard practice to expand the potential n ar the reactant well... 

We can approximate this firaction of states in the reactant well, by expanding the potential in a harmonic approximation and assuming that the tempera ture is low compared with the barrier height. This leads to an estimate for the rate constant... 

For 5=1, the normal transition state theory rate constant is independent of temperature at high temperatures and varies exponentially with temperature in the limit of low temperatures kT small compared with the barrier height U ) as... 

In each of the cases abttvc the total barrier heights are tlivitled by the total II iini her of torsion s counted. For example, ethan e uses a parameter V3=2.0/6 for each ofits six torsions, leading to a total barrier of 2.0 hcal/mol. 

The functional form for dihedral angle (torsional) rotation is identical to that shown in equation (13) on page 175. The barrier heights are in kcal/mol and are in the file pointed to by the Fouri-erTorsion entry for the parameter set in the Registry or the chem. ini file, usually called tor.txt(dbf). If more than one term is... 

Table 6.7 gives a few other examples of torsional barrier heights. That for ethylene is high, typical of a double bond, but its value is uncertain. The barriers for methyl alcohol and ethane are three-fold, which can be confirmed using molecular models, and fhose of toluene and nifromefhane are six-fold. The decrease in barrier heighf on going fo a higher-fold barrier is fypical. Rofafion abouf fhe C—C bond in toluene and fhe C—N bond in nifromefhane is very nearly free. 

Table 6.7 Barrier heights V for some torsional vibrations...

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