Mobility effect orbital overlap

The effects observed for bicyclo[3.1.0]hex-2-ene, 86, were particularly clear-cut, because the H spectrum is fully resolved [218]. The polarization pattern supported a species with spin-density on C3 and C6, indicating the delocalization of spin and charge into the lateral cyclopropane bond. The bicyclohexene system has limited mobility, enabling more significant orbital overlap of the lateral cyclopropane bond with the alkene p-orbitals (86 +). The participation of the lateral bicyclohexene bond is supported by ab initio calculations, carried to the MP2/6-31G level of theory. The lateral cyclopropane bond is lengthened (C1-C6 = 1.748 A), and carbons C3 and C6 carry prominent spin densities, whereas lower spin densities were found at C2 and Cl [220]. 

When orbital overlap is not too marked and the bands are not very broad (cf. band width. Chapter 2) there is significant interaction between the lattice and the electrons. The electrons (or holes) then polarize their environment (see Section 5.3). The electron -I- distortion field state is known as a polaron. The semiconductor InSb is a typical example of a solid containing large polarons . Here the effective mass is increased very slightly, the mobility is not greatly reduced, and the band model for transport is a good approximation, in short the polarization effect is not too strong. Typical mobilities are of the order of 10 (alkaline earth titanates) and... 

As described in detail, electrons and holes can be localized at dopant ions (cf. Section 5.7.1). If the latter are close neighbours, orbital overlap causes band formation and polaron band conductions (see above). In general, since a is proportional to u and c, a distinction must be made between doping effects on the mobility and those that result from the defect concentration (disorder and ionization equiUbria). It is frequently not simple to differentiate between ionization effects from the defect levels with intermediate band conduction and polaron processes from impurity to impurity (see e.g. [377]). 

The second insight that can be obtained from the electronic band structure is the mobility of charge carriers, which is related to the width of the conduction and valence bands. For Si the bands are rather broad, spanning more than 10 eV. This is a direct consequence of the extensive overlap of the sp orbitals on neighboring atoms. More overlap between atomic wavefunctions results in broader bands and easier transport of free charge carriers through the material. This can be quantified via the curvature of the individual bands, which is directly related to the effective mass and mobility of the charge carriers ... 

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