Field-effect mobility expression

The model describes the transport of individual injected carriers at zero/small carrier concentrations (i.e., in principle, it should not be directly applicable to the relatively high carrier concentrations p = 10 -10 cm present in the accumulation layer of FETs).Vissenberg [97] has developed a percolation model for variable range hopping transport in the accumulation layer of an FET assuming an exponential DOS with width Tq. An expression for the field-effect mobility as a function of carrier concentration p was derived ... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

The operation principle of these TFTs is identical to that of the metal-oxide-semiconductor field-effect transistor (MOSFET) [617,618]. When a positive voltage Vg Is applied to the gate, electrons are accumulated in the a-Si H. At small voltages these electrons will be localized in the deep states of the a-Si H. The conduction and valence bands at the SiN.v-a-Si H interface bend down, and the Fermi level shifts upward. Above a certain threshold voltage Vth a constant proportion of the electrons will be mobile, and the conductivity is increased linearly with Vg - Vih. As a result the transistor switches on. and a current flows from source to drain. The source-drain current /so can be expressed as [619]... 

In a capillary tube, the applied electric field E is expressed by the ratio VILj, where V is the potential difference in volts across the capillary tube of length Lj (in meters). The velocity of the electro-osmotic flow, Veo (in meters per second), can be evaluated from the migration time t of (in seconds) of an electrically neutral marker substance and the distance L, (in meters) from the end of the capillary where the samples are introduced to the detection windows (effective length of the capillary). This indicates that, experimentally, the electro-osmotic mobility can be easily calculated using the Helmholtz-von Smoluchowski equation in the following form ... 

Recently, we have investigated in detail the steady state and transients of the photoinduced polar order and its related anisotropy in both trans and cis molecular distributions [70]. The effect of all the physical parameters involved in the PEP phenomena has been considered. These include molecular anisometry, pump intensity, pump polarization, strength of the poling field, molecular mobility, and retention of memory of the molecular orientation. Here, we discuss the photostationary state of the PEP process by means of analytical expressions. 

First, the concept of mobility must be defined for weak electrolytes. The initial Tiselius perceptions serves as the basis and it can be expressed as follows the substance, present in the solution in more forms, whose molar fractions are x , Xj,... x , mobilities Uj>, Uj,... u and individual forms are in a rapid dynamic equilibrium with one another, migrates through the electric field as the only substance with a certain effective mobility, u, defined by the relationship... 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

In the ideal case, the ionic conductivity is given by the product z,Ft/ . Because of the electrophoretic effect, the real ionic mobility differs from the ideal by A[/, and equals U° + At/,. Further, in real systems the electric field is not given by the external field E alone, but also by the relaxation field AE, and thus equals E + AE. Thus the conductivity (related to the unit external field E) is increased by the factor E + AE)/E. Consideration of both these effects leads to the following expressions for the equivalent ionic conductivity (cf. Eq. 2.4.9) ... 

The migration in CE is obviously influenced by both the effective and the electroosmotic mobility. Therefore, the proportionality factor in the relationship of the migration velocity and the electric field strength in such a case is called the apparent electrophoretic mobility (/iapp) and the migration velocity the apparent migration velocity (vapp). The /iapp is equal to the sum of /migration velocity is expressed as... 

This expression is the general Wagner factor which includes the influence of all the motion of the other species on the motion of species i by the effect of the internal electric fields. W may be larger than 1 which indicates an enhancement of the motion by the simultaneous motions of other species, or W may be smaller than 1 which means that the species are slowed down because of the immobility of other species which are therefore unable to compensate for the electrical charges. The first situation is desirable for electrodes whereas the second one is required for electrolytes in which mobile species should not move except when electrons are provided through the external circuit. Since the transference numbers in Eqn (8.27) include the partial and total conductivities (tj = OjlYjk or the products of the diffusivities (or mobilities) and the concentrations, Eqn (8.27) shows that W depends both on kinetic... 

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] ... 

For a cylindrical particle oriented at an arbitrary angle between its axis and the applied electric field, its electrophoretic mobility averaged over a random distribution of orientation is given by pav = /i///3 + 2fjLj3 [9]. The above expressions for the electrophoretic mobility are correct to the first order of ( so that these equations are applicable only when C is low. The readers should be referred to Ref. [4-8, 10-13, 22, 27, 29] for the case of particles with arbitrary zeta potential, in which case the relaxation effects (i.e., the effects of the deformation of the electrical double layer around particles) become appreciable. 

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