Carrier mobility temperature dependence

The temperature dependence of the charge carrier mobility is dependent on the electronic stmcture of the solid. For a pure non-polar semiconductor - as in an ideal and pure covalent semiconductor - the electrons in the conduction band and the electron holes in the valence band can be considered as quasi-free (itinerant) particles. Then the mobilities of electrons and electron holes, Un and Up, are determined by the thermal vibrations of the lattice in that the lattice vibrations result in electron and electron hole scattering (lattice scattering). Under these conditions the charge carrier mobilities of electrons and electron holes are both proportional to T 3/2, e.g. 

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

Carriers and channels may be distinguished on the basis of their temperature dependence. Channels are comparatively insensitive to membrane phase transitions and show only a slight dependence of transport rate on temperature. Mobile carriers, on the other hand, function efficiently above a membrane phase transition, but only poorly below it. Consequently, mobile carrier systems often show dramatic increases in transport rate as the system is heated through its phase transition. Figure 10.39 displays the structures of several of these interesting molecules. As might be anticipated from the variety of structures represented here, these molecules associate with membranes and facilitate transport by different means. 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

Figure 3. (a) Representation of the hexagonal discotic mesophase formed by hexadodecyl substituted HBC 33. (b) The temperature dependence of the intracolumnar charge carrier mobilities for 33 and 34. Phase transition tempera-... 

These different modes of transport result in a dissimilar temperature dependence of the charge carrier mobility, and this often provides a convenient means to investigate which transport regime may apply. In this chapter, due attention is therefore given to experimental approaches that allow for an investigation of the transport mechanism, and concomitantly of the underlying electronic structure. 

Monte Carlo simulations [54], analytical effective medium theory [64], and stochastic hopping theory [46] predict a dependence of the charge carrier mobility as a function of temperature and electric field given in (3) ... 

However, one should be cautious about overinterpreting the field and temperature dependence of the mobility obtained from ToF measurements. For instance, in the analyses of the data in [86, 87], ToF signals have been considered that are dispersive. It is well known that data collected under dispersive transport conditions carry a weaker temperature dependence because the charge carriers have not yet reached quasi-equilibrium. This contributes to an apparent Arrhenius-type temperature dependence of p that might erroneously be accounted for by polaron effects. 

Fig. 8 Temperature dependence of the zero field hole mobility in the low carrier density limit in a polyfluorene copolymer. The data are inferred from space-charge-limited current experiments and analyzed in terms of the extended Gaussian disorder model (see Sect. 4.1). From [90] with permission. Copyright (2008) by the American Institute of Physics...

The conclusion that polaron effects contribute only weakly to the temperature dependence of the charge carrier mobility is supported by a theoretical study of... 

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...

As the mobilities are likely to depend on temperature only as a simple power law over an appropriate region, the temperature dependence on conductivity will be dominated by the exponential dependence of the carrier concentration. We will have more to say about carrier mobility in the section on semiconductors. 

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