Free Charge Carrier Mobility

The conductivity o is defined by the product of elemental charge (e), charge carrier mobility (p), and density of charge carriers (n). In case of hole- and electronconducting materials, both charge carriers species contribute according to 

In case of PEDOTPSS, only holes contribute to the charge transport. Injected free electrons will immediately recombine at oxidized PEDOT sites, hence the transport of electrons does therefore not contribute to the overall current. 

The density of holes in PEDOTPSS can simply be calculated using a geometrical consideration. For highly conductive PEDOTPSS, the ratio of PEDOT to PSS is 1 2.5 by weight. The density of solid films is approximately 1 g/cm. Owing to the molecular weight of the monomeric units of PEDOT and poly(styrenesulfonic acid) with 140 and 182 g/mol respectively, the density of EDOT monomer can be estimated to be approximately I ICF cm 3. From electrochemical measurement, the level of oxidation per monomer unit is known to be approximately 1 charge per 3 EDOT units as outlined in Section 9.1. Consequently tire density of holes in PEDOTPSS films can be estimated to be ftp = 3-10 cm 3. 

For highly conductive films a conductivity of 1000 S/cm has been obtained (see Table 9.1). The hole mobility in PEDOT PSS can be calculated to be approximately Pp = 20 cirf/Vs for the given conductivity and the estimated hole density. 

It should be pointed out that for organic semiconductors mobilities of up to 15 cmVVs at room temperature have been reported. However, these high values relate to single crystals with translation symmetry in contrast to PEDOTrPSS as an amorphous solid. Additionally, free-charge carrier interaction can be neglected in such crystalline systems, whereas in PEDOTPSS such an interaction is anticipated due to the high density of oxidized states. This undetermined contribution makes it difficult to translate conductivity models applied for organic semiconductors to PEDOT PSS. 

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In the above consideration it has been tacitly assumed that the charge carrier mobility docs not depend on the electric field. This is a good approximation for molecular crystals yet not for disordered systems in which transport occurs via hopping. Abkowitz et al. [37] have solved that problem for a field dependence of ft of the form p-po (FIFU) and trap-free SCL conduction. Their treatment predicts... 

Figure 4.22 Schematic diagram of a field effect transistor. The silicon-silicon dioxide system exhibits good semiconductor characteristics for use in FETs. The free charge carrier concentration, and hence the conductivity, of silicon can be increased by doping with impurities such as boron. This results in p-type silicon, the p describing the presence of excess positive mobile charges present. Silicon can also be doped with other impurities to form n-type silicon with an excess of negative mobile charges.

Measurements of mobility in PS suffer from the fact that the number of free charge carriers is usually small and very sensitive to illumination, temperature and PS surface condition. Hall measurements of meso PS formed on a highly doped substrate (1018 cm3, bulk electron mobility 310 cm2 V-1 s-1) indicated an electron mobility of 30 cm2 V 1 s 1 and a free electron density of about 1013 cm-3 [Si2]. Values reported for effective mobility of electron and hole space charges in micro PS are about five orders of magnitude smaller (10-3 to 10 4 cm2 V 1 s ) [PelO]. The latter values are much smaller than expected from theoretical investigations of square silicon nanowires [Sa9]. For in-depth information about carrier mobility in PS see [Si6]. 

Electrical conductivity is due to the motion of free charge carriers in the solid. These may be either electrons (in the empty conduction band) or holes (vacancies) in the normally full valence band. In a p type semiconductor, conductivity is mainly via holes, whereas in an n type semiconductor it involves electrons. Mobile electrons are the result of either intrinsic non-stoichiometry or the presence of a dopant in the structure. To promote electrons across the band gap into the conduction band, an energy greater than that of the band gap is needed. Where the band gap is small, thermal excitation is sufficient to achieve this. In the case of most iron oxides with semiconductor properties, electron excitation is achieved by irradiation with visible light of the appropriate wavelength (photoconductivity). 

The basic assumption In conductance measurements Is the Independence of the sample resistance on electric field strength. However a deviation from the linear relation between current density and field strength will be observed If any field effect on the mobility and/or the number of free charge-carriers Is present. 

At high field strengths a conductance Increase Is observed both In solution of strong and weak electrolytes. The phenomena were discovered by M. Wien (6- ) and are known as the first and the second Wien effect, respectively. The first Wien effect Is completely explained as an Increase In Ionic mobility which Is a consequency of the Inability of the fast moving Ions to build up an Ionic atmosphere (8). This mobility Increase may also be observed In solution of weak electrolytes but since the second Wien effect Is a much more pronounced effect we must Invoke another explanation, l.e. an Increase In free charge-carriers. The second Wien effect Is therefore a shift in Ionic equilibrium towards free ions upon the application of an electric field and is therefore also known as the Field Dissociation Effect (FDE). Only the smallness of the field dissociation effect safeguards the use of conductance techniques for the study of Ionization equilibria. 

What is the situation inside the electrode That depends upon whether the electrode is a metal or a semiconductor. What is the most important difference between a metal and a semiconductor Operationally speaking, it is the order of magnitude of the conductivity. Metals have conductivities on the order of about 106 ohm-1 cm-1 and semiconductors, about 102-1(T9 ohm-1 cm"1. These tremendous differences in conductivity reflect predominantly the concentration of free charge carriers. In crystalline solids, the atomic nuclei are relatively fixed, and the charge carriers that drift in response to electric fields are the electrons. So the question is What determines the concentration of mobile electrons One has to take an inside look at electrons in crystalline solids. 

The experimental IRSE data were analyzed assuming an isotropically-averaged effective electron mass parameter of m = 0.28me [135].6 Thereupon, the free-charge-carrier concentration N and the optical mobility parameters p,°pt (i =, L) were obtained [43]. The results of the IRSE-analysis of two sets of Ga-doped ZnO thin films are summarized in Fig. 3.18. 

Fig. 3.18. Free-charge-carrier concentration (a,b) and mobility parameters (c,d) of Ga-doped ZnO thin films on sapphire vs. oxygen pressure during PLD-growth [43]. Triangles and circles correspond to the results determined by IRSE and Hail-effect measurements, respectively. Panels (a,c) and (b,d) contain the results of the films grown with 0.1 and 0.5 mass percent Ga2C>3 powder within the PLD target, respectively. Up- and down-triangles in panels (c) and (d) represent the anisotropic optical mobility parameter /inpt and respectively...

Fig. 3.19. Experimental (dotted lines) and best-model (solid lines) IRSE spectra of two polycrystalline Al-doped ZnO thin films grown by magnetron sputtering on metallized polyimide foil [43], The best-model free-charge-carrier concentration, optical mobility, and thickness parameters are indicated...

The proportionality constant between the applied electric field and the resulting drift velocity is called the charge carrier mobility, jx. For electrons, = q r /ml ), for holes, ftp = 7(Trn/mj ). It should be noted that, owing to differences in the effective masses of electrons and holes, their mobilities within a semiconductor may be markedly different. The electrical conductivity, a, of a semiconductor is related to the free carrier concentrations by ... 

The inherent effective conjugation length of radical ion sites on a jr-chain can only be defined properly if there is no false confinement induced by chemical defects. Chemical defects such as sp -centers within a conjugated chain must also be avoided in view of the charge-carrier mobility. Problems associated with the synthesis of structurally homogeneous, defect-free -systems should be even more serious when going from linear to two-dimensional, so-called ladder structures, which are known to have particularly attractive chemical and physical properties. 

The specific conductivity, a, is related not only to the concentration of free charge carriers, n, but also to the mobility, fi, of the charge carriers (34) ... 

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