Richardson-Dushman

The analytic theory outlined above provides valuable insight into the factors that determine the efficiency of OI.EDs. However, there is no completely analytical solution that includes diffusive transport of carriers, field-dependent mobilities, and specific injection mechanisms. Therefore, numerical simulations have been undertaken in order to provide quantitative solutions to the general case of the bipolar current problem for typical parameters of OLED materials [144—1481. Emphasis was given to the influence of charge injection and transport on OLED performance. 1. Campbell et at. [I47 found that, for Richardson-Dushman thermionic emission from a barrier height lower than 0.4 eV, the contact is able to supply... 

From Fig. 6.14 it becomes clear why one must heat filaments to very high temperatures to see electron emission in electron guns. Only the part of the electron distribution that has obtained energies above 0 can be utilized. The occupation number at the vacuum level can be approximated by e hT leading to the well known Richardson-Dushman formula, which describes the fluxj of electrons evaporating from a surface with work function 0 at temperature T ... 

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

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]. 

When a metal sample is heated, electrons are emitted from the surface when the thermal energy of the electrons, kT, becomes sufficient to overcome the work function O [53]. The probability of this electron emission depends on work function O and temperature T as expressed in the Richardson-Dushman equation ... 

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... 

Electron emission current density (A/m ) can be calculated by the following Richardson-Dushman equation (Chodorow and Susskind, 1964) ... 

Richardson-Dushman equation An equation of electron saturation emission current density from a heated cathode. It states that the emission electron current density is proportional to the square of the cathode temperature and an exponential of negative constant times a reciprocal of the absolute temperature of the cathode. The proportionality constant is 6.02 x 10" and the negative constant depends on the cathode material. 

X 10 V m would be sufficient for this. The emission would follow the Richardson-Dushman law for thermionic emission, namely the current density would be... 

The thermionic electron emission current jT is described by the Dushman-Richardson relation [93,95] ... 

Table 2.4 Constants in the Dushman-Richardson and Fowler-Nordheim Formulas [95]...

Richardson equation (Rlchardson-Dushman equation) SeexHERMioNic emission. 

According to the Dushman-Richardson equation, the electron current upon heating a substrate of work function O is given by... 

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