Electrons mobility

As electrons move through a solid under the influence of they experience a number of collisions (in a process called scattering) that decreases p. There are three scattering mechanisms  

FIGURE 30.3 Illustration of (a) a large polaron of radius R, formed in a metal oxide MO and (b) a small polaron, showing the distortion of the lattice around an electron trapped at a metal. 

Electron-electron. At room temperature the mean distance between electron-electron collisions is about 10 times that of electron-phonon collisions so electron-phonon scattering is dominant. 

FIGURE 30.4 Conductivity variations with temperature for the different ciasses of electrical conductor. The shading indicates the range of values at room temperature. 

Electron drift velocity— dependence on electron mobility and electric field intensity 

The scattering phenomenon is manifested as a resistance to the passage of an elee-tric current. Several parameters are used to describe the extent of this scattering these include the drift velocity and the mobility of an electron. The drift velocity represents the average electron velocity in the direction of the force imposed by the applied field. It is directly proportional to the electric field as follows  

The constant of proportionality is called the electron mobility and is an indication of the frequency of scattering events its imits are square meters per volt-second (mW-s). 

Until now we have mainly treated electrons and holes analogously to the ionic defects. As far as the mobility is concerned, quantum mechanical eflfects cause severe differences. There is no energy of activation (AH = 0) in the case of perfect band conduction and, formally speaking, the temperature dependence of the mobility is effectively determined by the prefactor. The determining process for the finite mobility is scattering by lattice vibrations and/or imperfections. The T / relation for acoustic phonon scattering is a typical law in this context (see Chapter 3) (see Fig. 6.14). Unless the electronic charge concentration has been fixed by dop- 

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]). 

According to Mott s conception [47] the transition from delocalization to localization (e.g. metal-insulator transition, transition from isolated states within the band gap to impurity bands) occurs when the mean distance exceeds a certain critical value (oc ci/ ) — the distance of the effective Bohr s radius (more precisely 4 x Bohr s radius). The critical behaviour exhibits similarities to that treated in Section 5.7.2. 

In the case of heavy doping, the conductivity can become metallic and comparable to that of the solid metal elements ( one-dimensional metals ). 

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More precise coefficients are available (33). At room temperature, cii 1.12 eV and cii 1.4 x 10 ° /cm. Both hole and electron mobilities decrease as the number of carriers increase, but near room temperature and for concentrations less than about 10 there is Htde change, and the values are ca 1400cm /(V-s) for electrons and ca 475cm /(V-s) for holes. These numbers give a calculated electrical resistivity, the reciprocal of conductivity, for pure sihcon of ca 230, 000 Hem. As can be seen from equation 6, the carrier concentration increases exponentially with temperature, and at 700°C the resistivity has dropped to ca 0.1 Hem. 

TT-Electron materials, which are defined as those having extended Jt-electron clouds in the solid state, have various peculiar properties such as high electron mobility and chemical/biological activities. We have developed a set of techniques for synthesizing carbonaceous K-electron materials, especially crystalline graphite and carbon nanotubes, at temperatures below 1000°C. We have also revealed new types of physical or chemical interactions between Jt-electron materials and various other materials. The unique interactions found in various Jt-electron materials, especially carbon nanotubes, will lay the foundation for developing novel functional, electronic devices in the next generation. 

Here, o=nqp is the channel conductivity, and fi the electron mobility, assumed to be constant all over the channel. The elemental resistance dR of an elemental segment dx of the channel is given by... 

Increasing the electron mobility in the layer near to the electron contact proportionally increases the net injected electron current. The current may not change by exactly the same amount that the mobility is increased by if the density of injected electrons is large enough to change the electric field distribution. 

The upper panel of Figure 11-17 shows the effect of increasing the electron mobility in the layer near to the electron contact of the iwo-polymer-laycr electron-only device. The solid line is the calculated / V characteristic when the electron mobilities ol lhe two layers are the same and given by the value used above. The dotted line... 

Figures 12-12 and 12-13 document that trap-free SCL-conduction can, in fact, also be observed in the case of electron transport. Data in Figure 12-12 were obtained for a single layer of polystyrene with a CF -substituted vinylquateiphenyl chain copolymer, sandwiched between an ITO anode and a calcium cathode and given that oxidation and reduction potentials of the material majority curriers can only be electrons. Data analysis in terms of Eq. (12.5) yields an electron mobility of 8xl0 ycm2 V 1 s . The rather low value is due to the dilution of the charge carrying moiety. The obvious reason why in this case no trap-limited SCL conduction is observed is that the ClVquatciphenyl. substituent is not susceptible to chemical oxidation.

Discuss the conduction of heat by copper (a metal) and by glass (a network solid) in terms of the valence orbital occupancy and electron mobility. 

Improvement of the ionic current by fast transport in the electrodes. High electronic mobility and low electronic concentration favor fast chemical diffusion in electrodes by building up high internal electric fields [14]. This effect enhances the diffusion of ions toward and away from the solid electrolyte and allows the establishment of high current densities for the battery. 

Whereas cuprite is red, tenorite is black, showing that there is some electron mobility in this crystal resonance... 

Device Typical material Electron mobility Resistivity ohm-cm... 

Optoelectronic components produced by CVD include semiconductor lasers, light-emitting diodes (LED), photodetectors, photovoltaic cells, imaging tubes, laser diodes, optical waveguides, Impact diodes, Gunn diodes, mixer diodes, varactors, photocathodes, and HEMT (high electron mobility transistor). Major applications are listed in Table 15.1.El... 

Zinc oxide is a thoroughly studied typical semiconductor of n-type with the width of forbidden band of 3.2 eV, dielectric constant being 10. Centers responsible for the dope electric conductivity in ZnO are provided by interstitial Zn atoms as well as by oxygen vacancies whose total concentration vary within limits 10 - 10 cm. Electron mobility in monocrystals of ZnO at ambient temperature amounts to 200 cm -s". The depth of donor levels corresponding to interstitial Zn and oxygen vacancies under the bottom of conductivity band is several hundredth of electron volt [18]. 

HOMO = highest occupied molecular orbital) is the Fermi limit. Whenever the Fermi limit is inside a band, metallic electric conduction is observed. Only a very minor energy supply is needed to promote an electron from an occupied state under the Fermi limit to an unoccupied state above it the easy switchover from one state to another is equivalent to a high electron mobility. Because of excitation by thermal energy a certain fraction of the electrons is always found above the Fermi limit. 

An alternative approach to electronic conductivity in the polyphosphazenes, utilizes the outrigger approach in which the appropriate functionality for electronic mobility is provided by the substituents.4 A successful... 

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