Hole mobility electric field

The application of a small external electric field A to a semiconductor results in a net average velocity component of the carriers (electrons or holes) called the drift velocity, v. The coefficient of proportionality between E and is known as the carrier mobility p. At higher fields, where the drift velocity becomes comparable to the thennal... 

Figure 6 shows the field dependence of hole mobiUty for TAPC-doped bisphenol A polycarbonate at various temperatures (37). The mobilities decrease with increasing field at low fields. At high fields, a log oc relationship is observed. The experimental results can be reproduced by Monte Carlo simulation, shown by soHd lines in Figure 6. The model predicts that the high field mobiUty follows the following equation (37) where d = a/kT (p is the width of the Gaussian distribution density of states), Z is a parameter that characterizes the degree of positional disorder, E is the electric field, is a prefactor mobihty, and Cis an empirical constant given as 2.9 X lO " (cm/V). ...

The reason for this can be seen as follows. In a perfect crystal with the ions held fixed, a positive hole would move about like a free particle with a mass m depending on the nature of the crystal. In an applied electric field, the hole would be uniformly accelerated, and a mobility could not be defined. The existence of a mobility in a real crystal derives from the fact that the uniform acceleration is continually disturbed by deviations from a perfect lattice structure. Among such deviations, the thermal motions of the ions, and in particular, the longitudinal polarisation vibrations, are most important in obstructing the uniform acceleration of the hole. Since the amplitude of the lattice vibrations increases with temperature, we see how the mobility of a... 

Our picture of the transport process in these thick oxide layers is that there is a uniform concentration gradient of defects (cation vacancies and positive holes) across the layer. But it is important to notice that the oxidation flux is exactly twice that to be expected if diffusion alone were responsible for the transport of cation vacancies. The reason for this is, of course, that the more mobile positive holes set up an electric field which assists the transport of the slower-moving cation vacancies. 

Figure 12-27. Temperature dependence of the hole mobility in DPOP-PPV at different electric fields Dale for T= 0 have been obtained by extrapolation. The inset shows the intersection of Arrhenius plots at T()=465 K (Ref. 1831).

Studies of double carrier injection and transport in insulators and semiconductors (the so called bipolar current problem) date all the way back to the 1950s. A solution that relates to the operation of OLEDs was provided recently by Scott et al. [142], who extended the work of Parmenter and Ruppel [143] to include Lange-vin recombination. In order to obtain an analytic solution, diffusion was ignored and the electron and hole mobilities were taken to be electric field-independent. The current-voltage relation was derived and expressed in terms of two independent boundary conditions, the relative electron contributions to the current at the anode, jJfVj, and at the cathode, JKplJ. 

One has to consider that in Eqs. (9.15)—(9.17) the mobility /t occurs as a parameter. As it will be pointed out below, // shows a characteristic dependence on the applied electric field typical for the type of organic material and for its intrinsic charge transport mechanisms. For the hole mobility, //, Blom et al. obtained a similar log///,( ) const. [E dependency [88, 891 from their device modeling for dialkoxy PPV as it is often observed for organic semiconductors (see below). 

Figure 12-30. The electric field dependence of the hole mobility in McLPPP ut different lem-peralures.

It is important to realize that the migration in an electric field depends on the magnitude of the concentration of the charged species, whereas the diffusion process depends only on the concentration gradient, but not on the concentration itself. Accordingly, the mobility rather than the concentration of electrons and holes has to be small in practically useful solid electrolytes. This has been confirmed for several compounds which have been investigated in this regard so far [13]. 

Charge transport The holes and electrons must move through the device under the influence of the applied electrical field. The mobility of holes in typical hole transport organic materials is approximately 10 cm2/(V s) [65], For electrons the mobility is usually one or more orders of magnitude lower [66],... 

At low electric fields v is proportional to E and a mobility /u=er/m can be defined. The mobility of electrons and holes in bulk silicon is shown in the figure on the inner front cover of this book. 

Fig. 8 Electron (a) and hole (b) mobilities of EHO-OPPE films as a function of electric field at various film thicknesses open triangles L=6.5 pm, filled circles L=8 ]im, open squares L=12 p.m). Reproduced with permission from [61]...

Application of an external electric field causes the charges generated in the bright regions of the pattern to migrate (in polymers mobile charge carriers are holes)... 

Fig. 11 Temperature dependence of the hole mobility in PMPSi at different electric fields. Full curves are calculated using the theory by Fishchuk et al. [70], The fit parameters are the width a of the density of states distribution, the activation energy (which is p/2), the electronic exchange integral J, and the intersite separation a. From [70] with permission. Copyright (2003) by the American Institute of Physics...

Fig. 17 Temperature dependence of the hole mobility measured in an FET with (a) pentacene and (b) P3HT as active layers. Parameter Is the gate voltage. Data fitting using the Fishchuk et al. theory in [102] yields values for the mobility and the disorder potential extrapolated to zero electric field and zero carrier concentration. To is the Meyer-Nedel temperature (see text). From [102] with permission. Copyright (2010) by the American Institute of Physics...

Gambino S, Samuel IDW, Barcena H, Bum PL (2008) Electric field and temperature dependence of the hole mobility in a bis-fluorene cored dendrimer. Org Electron 9 220... 

Warta W, Karl N (1985) Hot holes in naphthalene high, electric-field-dependent mobilities. Phys Rev B 32 1172... 

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