Band mobility

Electrons moving in the delocalized state of the liquid collide with density fluctuations. The probability that a collision will take place in the time interval dt is given as dt/x where x is constant. Consider Nq electrons which have made collisions at t = 0. After a time t, N(t) electrons will have remained without a subsequent collision. The probability that they will suffer a collision is dt/x. The number of electrons colliding is then given as 

The number of electrons which have not collided decreases as 

The mean free time t between collisions is given by integration over all times from t = 0 to t = oo  

If we have electrons in thermal equilibrium with the liquid exhibiting an average thermal velocity, then a mean free path. A, is defined as 

In field direction, between two subsequent collisions, an electron is accelerated by the electric field E. At the end of the mean free path it has accumulated a velocity, Vj, such that 

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The distribution of formation energies therefore follows the density of valence band tail states. The dangling bond energy level is estimated to be about 0.8 eV above the valence band mobility edge and the band tail extends at least 0.5 eV into the gap, so that the energies are reasonably consistent with the known defect densities. The only justification for the model is that the creation of the defect occurs without a large... 

The weak bond model assumes a non-equilibrium distribution of weak bonds arising from the disorder of the a-Si H network. It has been proposed that the shapes of the band tails are themselves a consequence of thermal equilibrium of the structure (Bar-Yam, Adler and Joannopoulos 1986). The formation energy of a tail state is assumed proportional to the difference in the one-electron energies, so that the energy, required to create a band tail state of energy Ey from the valence band mobility edge is... 

Trap-Controlled Hopping. In trap-controlled hopping, the scenario described for trap-controlled band mobility applies. However, the microscopic mobility is associated now with carriers hopping in a manifold of localized states. Overall temperature and field dependence reflects the complicated convolution of the temperature and field dependence of both the microscopic mobility and the trap kinetic processes. Glearly, the observed behavior can now range from nondispersive to anomalously dispersive behavior as before, depending on the energy distribution of transport-interactive traps. 

The earliest pictures of the density of states in a-Si H were obtained from field-effect (FE) measurements (Spear and LeComber, 1972 Madan et ai, 1976 Madan and LeComber, 1977). These results indicated a surprisingly low g E), particularly near midgap, and disclosed two distinct defect bands within about 0.4 and 0.6 eV of the conduction- and valence-band mobility edges, respectively, as well as a fairly sharp band tail near E. A major factor in these results, of course, was that hydrogenated amorphous silicon was a new and distinct material compared to other forms of amorphous silicon and that indeed g E) was very different and much lower than for the other kinds of material people had studied. The ability to perform field-effect measure-... 

Fio. 52. Summary of the density-of-states results for five different a-Si H films with differing amounts of phosphorus doping (see description in text). The films have slightly different deduced band gaps, and for purposes of comparison the curves are all normalized to the conduction-band (mobility) edge E. The position of the bulk Fermi level in each film is indicated. [From Lang et at. (1982a).]... 

The relatively weak explicit temperature dependence of the drift mobility in this expression should not be taken too seriously because it is likely that the temperature dependence of the band mobility, which has been ne ected, is equally strong. About all that can be said is that at high temperatures... 

T> Tc), the dispersion goes away at long times and the drift mobility becomes an intensive quantity, independent of time and sample thickness. Even in this regime, the drift mobility is smaller than the free-carrier (band) mobility, and it remains time dependent at short times, as discussed by Silver... 

Once again, the range of sensitivity of the experiments to the density of states can be inferred from at the shortest measurement time at the lowest temperature (10" sec at 200°K) and the longest measurement time at the highest temperature (10" sec at 350°K). Using cOq = 10 sec" , we find that the experiment is sensitive to states between 0.16 and 0.5 eV above the valence-band mobility edge. 

The extended-state mobility for holes of 0.5 cm V" sec" is low for a true band mobility, since a mobility of unity corresponds to a mean free path on the order of a lattice constant (see, for example, Mott and Davis, 1978). There are several possible explanations. One possibility is that the transport mechanism in the vicinity of the mobility edge is a hopping process. Another possibility is that since we are actually measuringplqNJNq and not... 

Generally, the aim of doping a semiconductor is to control the electronic properties exclusively by shifting the Fermi energy. In the study of a-Si H, the question arose early as to whether the incorporation of dopants causes side effects as well. The formation of a phosphorus impurity band 0.13 eV below the conduction-band mobility edge E. has been proposed by LeComber et al (1977) from their results of Hall effect experiments. An arsenic impurity level 0.35 eV below E,. and a boron impurity level 0.42 eV above the valence-band mobility edge Ey have been inferred by Jan et al (1979,... 

Figure 35 Electron transport, (a) Quasifree electrons, band mobility (b) trap-controlled band mobility (c) hopping transport.

In solid benzene the electron mobility decreases from 5 cm V s at 173 K to 1.5 cm V s" at the melting point, T p = 278.5 K (Hirth and Stdckmann, 1972). Since the mobility is sufficiently high (>1), it can be interpreted as a band mobility. If the mobility is determined by scattering on acoustic phonons, a power law can be expected for the temperature dependence. 

Note that the mobilities given are band mobilities and apply only to the untrapped fraction of the... 

The DMA is a narrow band mobility filter that needs to be scanned to cover a desired mobility range. It therefore has a duty cycle limitation similar to that of a gated IMS instrument coupled to a steady ion source. For a pulsed ion source such as MALDI,(5 ) however, pulsed IMS would use the available ions more efficiently than the DMA, and the duty cycle would be determined by the repetition rate of the source. For a given mobility, however, the DMA has near unit transmission and is far more efficient than gated IMS with steady ion sources. 

Figure 1.4 Block diagram of a dual band mobile phone (CDMA, PCS) with GPS.

Figure 19 Mobility of carriers in P-rhombohedral boron obtained by different methods and different authors. 1, From space-charge limited currents 2 and 3, (1h 4, field effect 6, thermally activated hopping O, from electrical conductivity and spin density , (Xh. > from electrical conductivity and ESR magnetoresistance , from ESR line width +, band mobility A, hopping mobUity A, from photoconductivity V, from high-field conductivity, I, Hall mobility and photoconductivity. (See Ref. 2 and references therein.)...

Figure 8.7 Conduction mechanisms illustrated schematically for an electron. Similar processes exist for holes. Normal band mobility requires thermal exeitation from a trap state into the band.

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