Carrier, mobility

The carrier mobility, is an alternative measure of the conductivity, the two being related through the density of state by Eq. 

The multiple trapping model of transport in an exponential band tail is described by Eq. (3.20) in Section 3.2.1 and a fit to this expression is given in Fig. 7.8. TTie free carrier mobilities are 13 and 1 cm V s for electrons and holes respectively, with the band tail slopes of 300 °C and 450 C (Tiedje el al. 1981). Implicit in the analysis is the assumption that the exponential band tail extends up to the mobility edge, but the density of states model developed in Fig. 3.16 shows that this is a poor approximation. The band taU changes slope below E. and this may change the estimated values of the mobility. 

It is possible to extract the free mobility and the shape of the band tail from the dispersive transport data without any assumptions about the form of the tail (Marshall, Berkin and Main 1987). The average 

The analysis of the drift mobility is based on the model of an abrupt mobility edge, in which transport only occurs above the energy E. . The 

L is the electrode spacing, the wave velocity and k the wave vector, each of which are given by the experimental configuration. A and B are attenuation coefficients and is the potential at the crystal surface, and these three parameters can also be calculated from the geometry and the material properties. The drift mobihty is measured in this experiment and is defined by 

Electrical characteristics of organic LEDs are inevitably associated with mobility of charge carriers in materials used for their fabrication. The mobility defined as a carrier drift velocity (v) per unit applied electric field 

Time-of-flight experiments have been used for over three decades to characterize carrier mobilities in crystal, and polycrystalline and disordered organic solids including molecularly doped polymers and molecular glasses [28,424,430,431]. Relatively high values (up to several hundreds cm2/V s) and hot carrier effects have been observed in 

The high-field saturation of the carrier velocity can have various origins, e.g. a finite bandwidth of a non-parabolic transporting (here valence) bands, or the emission of optical phonons. It is believed that the high-field saturation of the drift carrier velocity in the crystal directions where the band model concept can be applied is due to the first one. Then [420], 

Provided that real polycrystalline samples are subject of a spatially non-homogeneous distribution of traps near the sample surface and within intergrain boundaries, the pretransit time averaged carrier flux is composed of two comparable parts one due to usual carrier drift in the external field and the second due to carrier diffusion [see Eq. (198) and Sec. 4.4]  

This result is useful in understanding the variation of the field dependence of the TOF measured mobility from sample to sample, following the carrier density gradients (Fc dn/cbc). For example, the role of the diffusion carrier stream would explain the field dependence of jx in single crystals whenever their near-surface layer is strongly populated 

Polymeric semiconductors are usually disordered, so that charge transport is dispersive, i.e. there is a spread in the apparent mobility of the carriers. This results from the presence of the distribution of dopant and host energy states 

Dispersive transport was analysed by Scher and Montroll (1975) for a random array of hopping sites in a regular crystal lattice. The transition rate between sites is an exponential function of both inter-site distance and activation energy. The distribution of transition rates may arise from a variation in separation with fixed activation energy, a variation in activation energy for 

This model predicts that the sum of the exponents of the current decay before and after tT will be 2. As a tends to zero, the temporal distribution j/(2) broadens and the sharp knee seen in Fig. 8.25(b) becomes much less prominent, since the rate of decay of the current is similar both before and after tT. tT will depend on the ratio of the sample thickness to the average displacement of the carrier in the field direction during its random walk through the sample. Use cjf the formal definition of mobility, Equation (4.2), leads to the result that the mobility has a dependence on electric field and sample thickness, L, of the form  

The choice of a Gaussian distribution can be justified by the observation that the optical absorption profiles of well-defined conjugated moieties are Gaussian. Charge transport is treated as a biased random walk amongst the conjugated moieties, which have random site energies described by Equation 

The mobility is concentration dependent, see Table 8.2, since increasing the density of conjugated sites reduces the mean hopping distance. Data for DEH loaded in polycarbonate is shown in Fig. 8.28. The solid line is a fit to the empirical relationship  

---

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... 

In tenns of the carrier mobility, the electrical conductivity c of an n type semiconductor can be written as... 

The carriers in tire channel of an enhancement mode device exhibit unusually high mobility, particularly at low temperatures, a subject of considerable interest. The source-drain current is carried by electrons attracted to tire interface. The ionized dopant atoms, which act as fixed charges and limit tire carriers mobility, are left behind, away from tire interface. In a sense, tire source-drain current is carried by tire two-dimensional (2D) electron gas at tire Si-gate oxide interface. 

The hyperbolic relaxation equation (A-5-2.4.1 a) contains charge carrier mobility as a variable, which should be sensitive to oil viscosity. This is found to be the case for some viscous nonconductive liquids. These have much slower rates of charge dissipation equivalent to an Ohmic liquid whose conductivity is 0.02 pS/m (5-2.5.4). 

The synthesis-driven approach towards material science can be applied to create oligomers and polymers with optimized properties, e.g. maximized carrier mobilities and electrical conductivities or high photo- and electroluminescence quantum yields. It becomes obvious, however, that the ability to synthesize structurally defined -architectures is the key to these high performance materials. 

Figure 9-25. Field-induced tunneling relative t]uanlunt efficiencies of organic LEDs calculated for various carrier mobilities and barrier heights (I KT , ,=,=0.2 2...//,= If) /( =I0"8,...

Two main methods have been used to measure the charge carrier mobility in electroluminescent polymers time of flight (TOF) carrier transit time measurements and analysis of the current-voltage (1-V) characteristics of single carrier devices in the space charge-limited current (SCLC) regime. A summary of the results for the hole mobility of PPV and PPV-related polymers is given in Table 11-1 [24, 27-32]. For... 

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... 

The excellent agreement between the TSC and P1A results has two implications. First, since the TSC method probes the product of mobility and carrier density, while the P1A probes only the carrier density, there seems to be no dominant influence of temperature on the carrier mobility. This was also found in other conjugated polymers like /ra/ry-polyacetylene [19, 36]. Second, photoconductivity (observed via the thermal release of photoexcited and trapped earners) and photo-induced absorption probe the same charged entity [36, 37J. 

The electrical conductivity in the solid state is determined by the product of the carrier concentration and the carrier mobility. In conjugated polymers both entities are material dependent and, i.e., are different for electrons and holes. Electrons or holes placed on a conjugated polymer lead to a relaxation of the surrounding lattice, forming so-called polarons which can be positive or negative. Therefore, the conductivity, o, is the sum of both the conductivity of positive (P+) and negative polarons (P ) ... 

A polymer layer al a contact can enhance current How by serving as a transport layer. The transport layer could have an increased carrier mobility or a reduced Schottky barrier. For example, consider an electron-only device made from the two-polymer-layer structure in the top panel of Figure 11-13 but using an electron contact on the left with a 0.5 eV injection barrier and a hole contact on the right with a 1.2 cV injection barrier. For this case the electron current is contact limited and thermionic emission is the dominant injection mechanism for a bias less than about 20 V. The electron density near the electron injecting contact is therefore given by... 

Figure 12-16. Field dependence of die charge carrier mobility in an undiluted hopping system al various values of the disorder parameter a = a/kT (Kef. [67]).

Currently, there is disagreement concerning the actual magnitude of the conductivity increase, but there is no doubt that an effect, most pronounced for such acceptors as AsFg, does exist (TIO, V13). Models evolved in order to account for the magnitude of the conductivity increase included intergraphite layer-separation (F5), the intercalant concentration (FlO), and carrier-mobility enhancement (F5). 

---