Doped hole mobility

The concentration of free holes generated by the p-dopant can be calculated under the assumption that doping does not alter the hole mobility. Doing so, Zhang... 

The mobility of the charge carriers depends on the temperature, dopant concentration, and electric field strength [11, 14]. For the ideal case, when the size of the local centers with radius R is less than the mean distance between them p0, the mobility is given by p p2 exp ( — jp) exp ( — A/kT), where j = R0/2 is the localization parameter. The exponential dependence of the hole mobility on the distance between the doping molecules was established. 

In a FET device with highly doped Si as the gate and Si02 as the gate insulator, the hole mobility of the alternating copolymer 20 was measured.37... 

Rubin et al [21], using a Kaufinan ion gun to produce N2+, report a 300 K hole mobility of 12 cm2/V s for an Mg-doped layer with p = 2 x 1016 cm 3. Surprisingly, however, for an undoped layer grown with a high N2+ flux, they get a 300 K mobility of about 150 cm2/V s, but at a very low hole concentration, p s 4 x 1012 cm 3. For this sample, the dominant acceptor has an activation energy of 0.29 eV, much deeper than that of Mg. 

Figure 97 Arrhenius plot of electron and hole mobilities in the crystallographic c direction of a well-purified anthracene crystal (a) and for a 4x 10 7mol tetracane-doped anthracene crystal (b). After Ref. 442. Copyright 1975 Wiley-VCH, with permission.

Pai et al. (1983) measured hole mobilities of a series of bis(diethylamino)-substituted triphenylmethane derivatives doped into a PC and poly(styrene) (PS). The mobilities varied by four orders of magnitude, while the field dependencies varied from linear to quadratic. In all materials, the field dependencies decreased with increasing temperature. The temperature dependencies were described by an Arrhenius relationship with activation energies that decrease with increasing field. Pai et al. described the transport process as a field-driven chain of oxidation-reduction reactions in which the rate of electron transfer is controlled by the molecular substituents of the hopping sites. 

The concentration dependence of the hole mobility of TPM-E doped PS was described by Magin et al. (1996). TPM-E is a moderately polar molecule with a dipole moment of 2.10 Debye. Figure 5 shows the temperature dependencies for 45% TPM-E. The results are similar to those reported for vapor-deposited TPM glasses and doped polymers described previously. The data in Fig. 5 yield n0 = 2.9 x 10-2 cm2/Vs and a = 0.111 eV. For purposes of comparison, Fig. 6 shows the zero-field data of Fig. 5 plotted versus T-l. From these results, it is clear that the temperature dependence cannot be described by an Arrhenius relationship over an extended range of temperatures. A further problem concerning the use of an Arrhenius relationship is the prefactor mobility. At 272 K, the data in Fig. 6 yields a prefactor mobility of 690 cm2/Vs, a value that is difficult to justify. For all concentrations, plots of ft versus (a/kT)2 were linear with slopes between... 

Figure 5 The temperature dependencies of the hole mobility of TPM-E doped PS.

Hirao (1995) measured hole mobilities of poly(4,4 -cyclohexylidenediphenyl-carbonate) (PCZ) doped with BTAS and a series of related derivatives. The field and temperature dependencies were described as logfj. )3E-f/2 and -(TJT) . 

Novo et al. (1993) measured hole mobilities of EFTP doped PC. In agreement with Veibeek and Verbeek et al., negative field dependencies were observed at high fields. Figure 16 shows field dependencies for 17% EFTP at different temperatures. Figure 17 shows the room temperature field dependencies for different EFTP concentrations. 

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