Effective mass of charge carrier

Until now there are no experiments with specific single-wall carbon nanotubes to evaluate the effective masses of charge carriers. So we compare the band stmcture obtained in the TB approximation with that obtained in our model. 

One important aspect of the impurity-related states is the effective mass of charge carriers (extra electrons or holes) due to band-structure effects, these can have an effective mass which is smaller or larger than the electron mass, described as light or heavy electrons or holes. We recall from our earlier discussion of the behavior of electrons in a periodic potential (chapter 3) that an electron in a crystal has an inverse effective mass which is a tensor, written as [(/n) ]o . The inverse effective mass depends on matrix elements of the momentum operator at the point of the BZ where it is calculated. At a given point in the BZ we can always identify the principal axes which make the inverse effective mass a diagonal tensor, i.e. [(m) ]a = as discussed in chapter 3. The energy of electronic... 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

In relation to this problem is the fact that as the top of a band is approached the effective mass of a carrier changes and the range of allowed k values is small. Thus, the mobility of a carrier either in a narrow band conductor or at the top of an almost filled band must inevitably be small (9). In these cases it is probably not correct to assume the mass of the carrier and an electron to be the same. Under some circumstances the transfer of charge in a narrow band semiconductor is better described as an activated hopping process. 

Field emission is characterized by its temperature independence. Here meff is the effective mass of the carrier in the dielectric. The essential assumption of the Schottky model is that a carrier can gain sufficient thermal energy to cross the barrier that results from superposition of the external field and image charge potential. Neither tunnelling nor inelastic carrier scattering is taken into account. The following current characteristic is predicted for the Schottky junction ... 

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 ... 

Ion Scattering Spectroscopy mass, molar mass effective mass of electron concentration of ions or charge carriers concentration of acceptors concentration of donors coordination number of shell j complex refraction index photo ionization cross-section electric charge gas constant... 

As described above, the electrons in a semiconductor can be described classically with an effective mass, which is usually less than the free electron mass. When no gradients in temperature, potential, concentration, and so on are present, the conduction electrons will move in random directions in the crystal. The average time that an electron travels between scattering events is the mean free time, Tm. Carrier scattering can arise from the collisions with the crystal lattice, impurities, or other electrons. However, during this random walk, the thermal motion is completely random, and these scattering processes will therefore produce no net motion of charge carriers on a macroscopic scale. 

The proportionality constant between the applied electric field and the resulting drift velocity is called the charge carrier mobility, jx. For electrons, = q r /ml ), for holes, ftp = 7(Trn/mj ). It should be noted that, owing to differences in the effective masses of electrons and holes, their mobilities within a semiconductor may be markedly different. The electrical conductivity, a, of a semiconductor is related to the free carrier concentrations by ... 

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