Temperature dependence of the mobility

Figures 12-17 and 12-18 show the temperature dependencies of the mobility in a hopping system with a Gaussian DOS of variance <7=0.065 eV as a function of the relative concentration c of traps of average depth ,=0.25 eV and as a function of the trap depth E, at a fixed concentration < =0.03, respectively. For c=0...

Figure 12-18. The temperature dependencies of the mobility simulated for different nap depths. The trap concentrations were 3x1 O 2 and the field 2xl05 V em 1 (Ref. 72J).

Figure 14-26. Temperature dependence of the mobility of pen-lacenc-evaporalcd film. Data are shown for three devices grown under similar conditions (data taken from Ref. [961).

A celebrated derivation of the temperature dependence of the mobility within the hopping model was made by Miller and Abrahams 22. They first evaluated the hopping rate y,y, that is the probability that an electron at site i jumps to site j. Their evaluation was made in the case of a lightly doped semiconductor at a very low temperature. The localized states are shallow impurity levels their energy stands in a narrow range, so that even at low temperatures, an electron at one site can easily find a phonon to jump to the nearest site. The hopping rate is given by... 

Notice that the energy of the ion is the same at the beginning and the end of the jump the energy required to make the jump, E, is known as the activation energy for the jump. This means that the temperature dependence of the mobility of the ions can be expressed by an Arrhenius equation ... 

The experimental temperature dependence of the mobility parametric in the apphed electric field (Fig. 9) allows for calculating a and g for different values of the electric field. Because a scales hnearly with /e the value can be determined by plotting a vs yE and then determining the intersection of the hnear fit of the data with E=0. Knowing allows one to determine the width of density of states a from the relation... 

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. 

Results are shown in Figs. 12 and 13. All blend specimens were set iso-thermally above LCST and kept there for a maximum of 5 min. As will be seen, this corresponds only in some cases to an early stage of spinodal decomposition depending on temperature. The diffusion coefficients governing the dynamics of phase dissolution below LCST are in the order of 10"14 cm2 s"1. Figure 12 reflects the influence of the mobility coefficient on the phase dissolution. As can be seen, the apparent diffusion coefficient increases with increasing temperature of phase dissolution which expresses primarily the temperature dependence of the mobility coefficient. Furthermore, it becomes evident that the mobility obeys an Arrhenius-type equation. Similar results have been reported for phase dis-... 

Fig. 3.15. The temperature dependence of the mobility for constant drift time (solid lines) and constant drift distance (dashed line).

The analysis of the experimental data in Section 7.1 found a conductivity prefactor of about 100 Q" cm", but without any correction for the temperature dependence of the mobility edge. The comparison with the predicted value of o , suggests that Yc is less than 1 and is positive, which corresponds to a shift of Ec into the gap with increasing temperature. Similarly the free carrier mobility found in... 

On average, a carrier located at can continue its motion only after thermal excitation. If all carriers were located at and a transport level existed at e = 0, the center of the DOS, the temperature dependence of the mobility should follow a non-Arrhenius dependence of the form exp[-(a/ 7)-2]. This temperature dependence has been recovered by both EMA studies and Monte Carlo simulations, although with a constant in the exponent of less than unity that accounts for the statistics of occupational energies. The predicted temperature dependence of the zero-field mobility is... 

From Eqs. (8), (9), and (10), the important predictions of the formalism are the field and temperature dependencies of the mobility and the temperature dependence of the field dependencies of the mobility. The simulations predict (1) logjU versus El/2 is linear with slopes that decrease with increasing temperature, (2) logjU versus T 2 is linear with slopes that decrease with increasing field, and (3) /J versus (o/kT)2 is linear with a slope given as C. Since C is an empirical constant that contains no adjustable parameters, it provides a stringent test of the theory. 

Bassler (1984) reexamined Pfister s (1977) data for TPA doped PC. Bassler suggested that the field and temperature dependencies of the mobility could be explained by arguments based on energetic disorder. Bassler extended the same argument to a series of arylalkane derivatives doped into a PC and PS (Pai et al., 1983), and charge-transfer complexes formed between 2,4,7-trinitro-9-fluorenone and poly(N-vinylcarbazole) (Gill, 1972,1976). 

Abkowitz and Stolka (1990, 1991) compared hole mobilities of poly-silylanes and polygermylenes containing aliphatic pendants with compounds that contain only aromatic side groups. While transport occurred via states associated with the backbone chain in both compounds, the nature of the side groups was shown to influence the temperature dependence of the mobility. The results were described by a small-polaron argument, based on the assumption that the polarizability increases when an aromatic pendant group was substituted... 

Enokida et al. (1991) measured hole mdbilities of PMPS before and after ultraviolet exposures. The exposures were of the order of 1 erg/s-cm2. Prior to the exposures, the mobilities were approximately 10-4 cm2/Vs and weakly field dependent. Following the exposures, a decrease in the mobility was observed. Under vacuum exposure conditions, a decrease of approximately 40% was observed for a 1 h exposure. Under atmospheric conditions, however, the decrease was approximately a factor of 4. Enokida et al. attributed the decrease in mobility to the formation of Si-O-Si bonds in the Si backbone chain. A similar study of PMPS was described by Naito et al. (1991). While the field and temperature dependencies of the mobility were not affected by the ultraviolet exposures, the dispersion in transit times increased significantly. The change in dispersion could be removed by subsequent annealing. The authors attributed the increase in transit time dispersion to a reduction in the hole lifetime, induced by Si dangling bonds created by the ultraviolet radiation. 

Ulanski et al. (1992) measured hole mobilities of PVK doped PC between 220 to 370 K. With decreasing temperature, the results show a transition from nondispersive to dispersive transport at 250 K. From the temperature dependence of the mobility in the nondispersive regime, the width of the DOS was determined as 0.116 eV. This yields a predicted nondispersive to dispersive transition of 305 K, considerably higher than the value determined experimentally. A comparison of thermally stimulated current, thermoluminescence, isothermal time-of-lflight, and thermally stimulated time-of-flight... 

Figure 98 The temperature dependence of the mobility of DEASP doped PS.

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