Thermionic emission equation

The first part of the equation relates to the well-known thermionic emission equation [93]. At low temperatures (up to 400°C), the term IR is more significant than vice versa at high temperatures (above 400°C). Thus, the... 

To determine barrier heights and ideality factors for the nanodiodes, we fit the current-voltage curves of our devices to the thermionic emission equation. For thermionic emission over the barrier, the current density of Schottky contacts as a function of applied voltage is given by [69]. 

For the same the single layer devices based on Alq3, Peyghambarian et al. [83] found that the 1/V characteristics can also be described by an SCL current flow in the low cu ire lit regime. However, in the low current regime the 1/V characteristics can be qualitatively modeled by the Fowler-Nordheim equation (even if, quantitatively, the real device current differs from the calculated by seven orders of magnitude) [83] and thermionic emission ]78]. 

The emission equation is valid for each of the patches on a nonuniform surface, but the total measured current from the various patches depends on the relative magnitudes of the collecting field and patch fields, as well as on the work function. Hence, the effect of some patches may be out of proportion to their area and the average work function of a polycrystalline surface measured thermionically may differ somewhat from the true average work function... 

Millikan s experiment did not prove, of course, that (he charge on the cathode ray. beta ray, photoelectric, or Zeeman particle was e. But if we call all such particles electrons, and assume that they have e/m = 1.76 x Hi" coulombs/kg. and e = 1.60 x 10" coulomb (and hence m =9.1 x 10 " kg), we find that they fit very well into Bohr s theory of the hydrogen atom and successive, more comprehensive atomic theories, into Richardson s equations for thermionic emission, into Fermi s theory of beta decay, and so on. In other words, a whole web of modem theory and experiment defines the electron. The best current value of e = (1.60206 0.00003) x 10 g coulomb. 

From the Richardson-Dushman equation, the current density Je by thermionic emission can be obtained as... 

So far only one specific characteristic of computed surface potentials seems to have an important effect on experimental results. For thermionic emission of surfaces subject to an electric field, the Richardson equation must be modified in two ways. First the potential barrier is lowered by the electric field to give a new work function. In addition the reflection coefficient is altered. The relative current )/ 0 as a function of applied field E becomes... 

Thermionic emission. The number of electrons which escape from the metal surface increases rapidly with temperature (thermionic emission). In general, the higher the temperature and the lower the work function, the higher is the electron emissivity. The current density can be calculated by the Richardson-Dushman equation (in the absence of an external electrical field), according to i — AT exp(—rp/kT), where A is the Richardson constant (A cm K ), T is the temperature (K), and

work function (eV). For pure tungsten A — 60.2 (A cm K ) [1.91]. The thermionic current (A cm ) can then be calculated as i — 60.2r exp(—52230/T) [1.37]. 

By treating surface recombination as a hopping process in the image charge potential, Scott and Malliaras [140] have derived a very simple equation that describes the injected current as a function of electric field, temperature, and measurable parameters of the organic, namely the dielectric constant, the site density, and the drift mobility. The current has the usual form of thermionic emission, but with an effective Richardson constant that is several orders of magnitude lower than that in inorganic semiconductors. The results of the model are in... 

However, experimental ]V curves often deviate from the ideal /scl- In these cases, the measured current /inj is injection limited caused by a nonohmic contact or poor surface morphology. When the MO interface is nonohmic, carrier injection can be described by the Richardson-Schottky model of thermionic emission the carriers are injected into organic solid only when they acquire sufficient thermal energy to overcome the Schottky barrier ((()), which is related to the organic ionization potential (/p), the electron affinity (AJ, the metal work function (O, ), and the vacuum level shift (A) [34,35]. Thus, the carrier injection efficiency (rj) can be calculated by the following equation ... 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

In thermionic emission, the current density / obtained from the electrically heated filament in the presence of an electric field E obeys the modified Richardson-Dushman equation ... 

The thermionic-emission current /th> in amperes, generated by a heated filament is described by the Richardson-Dushman equation... 

The thermionic emission from the clean surface is given by the Bicharclson equation... 

At the start of the migration experiment / = Ojd (p. 349) was 1-77. The strip was then flashed at 1535 or at 1655° K., and its thermionic emission measured periodically at a lower temperature of 1261° K. Fig. 130 shows the observed values of logt /im plotted against time after flashing at 1535 and at 1655° K. In the same figure the full curve has been calculated according to the equation (p. 352) ... 

The forward bias dark current of a Schottky barrier diode has already been demonstrated to be caused by the thermionic emission of majority carriers from the semiconductor to the metal. It can be represented by the equation... 

This value of may be significantly lower than that found from equation 33 for the thermionic emission of electrons. 

Equation (2.31) is identical to Eq. (2.18) derived for a majority carrier device (thermionic emission model). Accordingly, the same type of current-voltage curve is expected as that given in Figure 2.7. The characteristics of the models occur only in the pre-exponential factors, which indeed are different in both cases (compare Eqs. (2.17) and (2.30)). As mentioned before, the jg of the majority carrier device is only determined by the barrier height and some physical constants (Eq. (2.19)), whereas jg of the minority carriers depends on material-specific quantities such as carrier density, diffusion constant, and diffusion length. 

Riess and coworkers at the University of Bayreuth proposed a Schottky barrier model for the operation of ITO/PPV/Al LEDs [70,71,94]. They argue that the current is predominantly carried by holes and that this hole current is limited by the Schottky barrier formed at the PPV/Al interface rather than by any barrier at the ITO/ PPV interface. They model the current-voltage characteristics using the equation for thermionic emission across a Schottky barrier from a semiconductor into a metal. It should be noted that the doping levels estimated for these devices are in the range 10 -10 cm, considerably higher than the values estimated by Marks et al. for their devices. 

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