Mobility of electrons and holes

The conductivity is proportional to the product of the diffusivity and the concentration. To separate these two contributions, the voltage-relaxation [47] and the charge-transfer techniques [25] may be employed to obtain separately the diffusivity and concentration, respectively. 

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Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

At low electric fields v is proportional to E and a mobility /u=er/m can be defined. The mobility of electrons and holes in bulk silicon is shown in the figure on the inner front cover of this book. 

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]. 

A representative example for the information extracted from a TRMC experiment is the work of Prins et al. [141] on the electron and hole dynamics on isolated chains of solution-processable poly(thienylenevinylene) (PTV) derivatives in dilute solution. The mobility of both electrons and holes as well as the kinetics of their bimolecular recombination have been monitored by a 34-GHz microwave field. It was found that at room temperature both electrons and holes have high intrachain mobilities of fi = 0.23 0.04 cm A s and = 0.38 0.02 cm / V s V The electrons become trapped at defects or impurities within 4 ps while no trapping was observed for holes. The essential results are (1) that the trap-free mobilities of electrons and holes are comparable and (2) that the intra-chain hole mobility in PTV is about three orders of magnitude larger than the macroscopic hole mobility measured in PTV devices [142]. This proves that the mobilities inferred from ToF and FET experiments are limited by inter-chain hopping, in addition to possible trapping events. It also confirms the notion that there is no reason why electron and hole mobilities should be principally different. The fact... 

The bipolar single-trap model assumes that both electrons and holes share identical trap centers. Since sequential trappings of the electrons and holes by the identical centers mean the neutralization of the electric charge, the effective space-charge field will depend on the relative power (i.e., the mobilities) of electron and hole transports. The expressions for the writing and erasing diffraction efficiency are [100] ... 

Tables 4.1 and 4.2 show room temperature mobilities of electrons and holes in various organic semiconductors (ordered single crystals as well as disordered structures) from field-effect analyses.

According to the experimental data, the mobility of most ions is around 10" cm V s. These values are about 5-6 orders of magnitude smaller than the mobility of electrons and holes in a semiconductor. In order to achieve sufficient conductance in an electrochemical cell, electrolyte conductivities of o> 1(H (Q cm) , and therefore ion concentrations of c > 10 mole per liter, are required. In investigations of electrode processes it is important that the solution is made sufficiently conductive by the addition of ions which are not involved in the electrode reaction. Such a solution is usually called a supporting electrolyte . 

LUCO of the host and acts as an effective electron trap [49]. In combination with the comparable mobility of electrons and holes, the chemical inertness evidences the potential of diindenoperylene for application in e.g. photovol-taics where a balanced charge transport is required. 

In analogy to the mobility of electrons and holes in crystals, the diffusion coefficient for coherent excitons is determined by the relaxation time r. According to Frolich (13), we have... 

The mobilities of electrons and holes are independent of the electric field over a wide range of carrier velocities, but they change with temperature. If the temperature decreases, the mobility of both carriers increases. The mobility of electrons and holes in pure germanium as a function of temperature is shown in Fig. 7.10. The mobility changes at /x with a 1.5, for T < 80 K. For... 

Although the mobility of electrons and holes decreases with temperature, exactly as in a metal, it is found that the conductivity of an intrinsic semiconductor increases with temperature, as the exponential term in Equations (13.2) and (13.3) dominates the other terms. 

The ratio of the short circuit current to the fully saturated current, as argued, gives directly the ratio of the number of coulomb-pairs versus free carriers at short circuit, which is estimated to be only 60% in the studied MDMO-PPV/PCBM samples. More recently, the model has been expanded to describe the performance of bulk heterojunction solar cells depending on the PCBM concentration. In these recent models, the mobility of electrons and holes determined in independent experiments has been incorporated [103]. 

As new metal oxide semiconductors are identified and explored for water photoelectrolysis, a persistent problem that arises is the low drift mobility of electrons and holes and the short lifetimes of photogenerated carriers. Many materials that seem promising on the basis of bandgap and stability are found inadequate for photoelectrolysis because the low mobility of minority carriers prevents rapid charge transport to the aqueous interface. Metal oxides are also prone to nonstoichiometry, which can result in traps that promote recombination and shorten carrier lifetimes. When short lifetimes and low mobility arise in the same material, device efficiency can drop rapidly and photocurrents are far below those that might be otherwise expected. 

Fig. 5.2-70 Effective mobility of electrons and holes in MOSFET s inversion channel. Qs = gtotai is the charge on the gate electrode. It is seen that mobility decreases at high transverse electric fields. For comparison, bulk mobilities are fin — 1600, fip = 600cm- /V s [2.96]...

The mobility of electrons and holes is affected by two main scattering mechanisms chemical impurities and lattice scattering. The mobility temperature dependence due to... 

We need to say that the requirement of a pure ion for conducting is the most difficult for fulfillment, because, in this case, the level of any electronic contribution to the total electrical conductivity must be negligible. However, this is not at all easy to achieve. Even very low concentrations of electronic carriers will give rise to a significant electronic component because of the very high mobility of electrons and holes in comparison with the ionic mobilities. Therefore, most ion conductors are, in fact, mixed conductors, and only very few are capable of being classed as pme ionic conductors. 

F ure 3,9 Mobility of electrons and holes in germanium as a function of electric field strength and temperature... 

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