Scattering charged-impurity

This process describes the scattering of free carriers by the screened Coulomb potential of charged impurities (dopants) or defects theoretically treated already in 1946 by Conwell [74,75], later by Shockley [10] and Brooks and Herring [76,77]. In 1969, Fistul gave an overview on heavily-doped semiconductors [78]. A comprehensive review of the different theories and a comparison to the experimental data of elemental and compound semiconductors was performed by Chattopadhyay and Queisser in 1980 [79]. For nondegenerate semiconductors the ionized impurity mobility is given by [79] ... 

The temperature dependence of the mobility depends on the nature of the scattering centers (acoustical or optical phonons, charged impurities. ..) However, in all cases, it is found that the dependence follows the general law given by Equation... 

Similar calculations were carried out for the single impurity systems, niobium in Cu, vanadium in Cu, cobalt in Cu, titanium in Cu and nickel in Cu. In each of these systems the scattering parameters for the impurity atom (Nb, V, Co, Ti or Ni) were obtained from a self consistent calculation of pure Nb, pure V, pure Co, pure Ti or pure Ni respectively, each one of the impurities assumed on an fee lattice with the pure Cu lattice constant. The intersection between the calculated variation of Q(A) versus A (for each impurity system) with the one describing the charge Qi versus the shift SVi according to eqn.(l) estimates the charge flow from or towards the impurity cell.The results are presented in Table 2 and are compared with those from Ref.lc. A similar approach was also found succesful for the case of a substitutional Cu impurity in a Ni host as shown in Table 2. 

The application of an electric field E to a conducting material results in an average velocity v of free charge carriers parallel to the field superimposed on their random thermal motion. The motion of charge carriers is retarded by scattering events, for example with acoustic phonons or ionized impurities. From the mean time t between such events, the effective mass m of the relevant charge carrier and the elementary charge e, the velocity v can be calculated ... 

More recent work has shown, however, that an exponential decay of the screening potential as in (21) is not correct, and that round any scattering centre the charge density falls off as r 3 cos 2kFr. This we shall now show, by introducing the phase shifts t/, defined as follows (cf. (13)). Consider the wave functions Fx of a free electron in the field of an impurity. These behave at large distances from the impurity as (Mott and Massey 1965)... 

Analysis of Hall-effect data has been one of the most widely used techniques for studying conduction mechanisms in solids, especially semiconductors. For the single-carrier case, one readily obtains carrier concentrations and mobilities, and it is usually of interest to study these as functions of temperature. This can supply information on the predominant charge-carrier scattering mechanisms and on activation energies, i.e., the energies necessary to excite carriers from impurity levels into the conduction band. Where two or more carriers are present, the analysis becomes more complex, but much more information can be obtained from sludies of the temperature and magnetic held dependencies. 

A uniform electric field distribution across the sample is extremely important for achieving device quality materials. Unfortunately, real chromophore materials do not always behave as uniform insulator materials. We have already demonstrated that ionic impurities can dramatically reduce the effective electric field felt by chromophores. The presence of spatially and temporally varying nonuniform space charge distributions leads to nonuniform poling fields. The resulting nonuniform chromophore order can lead to light scattering. 

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