Localized impurity states

This transition has been emphasized by Mott for the case of localized impurity states in a semiconductor, forming a metallic band at some concentration of impurities (i.e. at some average distance between the impurities). It is referred to very often as the Mott (or Mott-Hubbard) transition. 

Materials that are formally insulating such as WO3 may become semiconducting by appropriate doping for example, Na WO3 where x < 0.3. Upon further doping, what had been W(V) localized impurity states coalesce into a band and the bronze phase becomes metalhc for x > 0.3. 

In most covalent NCS it is found that AE, the thermal activation energy of the conductivity is about half the magnitude of the optical energy gap. This means that Ep is not far from the center of the mobility gap. Does this mean that these materials are intrinsic In the case of crystalline semiconductors the word intrinsic is used to mean that the conduction properties are not affected by the presence of localized impurity states. The position of Ep is then determined by the equality... 

The matrix element for an electronic transition from a state e) in the redox electrolyte via a localized impurity state r) in the film to a state m) in the metal is according to second-order perturbation theory ... 

In the second method, going beyond Bom, we examined the density of states within the coherent potential approximation (CPA) which takes into account multiple scattering processes. One might think that on this level impurity states are introduced in the gap. However, we find [16] that the existence of such localized impurity states strongly depends on the relative strength of site vs. bond impurity. Only states in the gap due to disorder can be found if the site amplitude f/s is stronger than the bond amplitude Ufc. Since CPA is an effective medium theory this result might be questionable in one dimension. 

If the cross-coupling is strong enough this may include a transition to a lower electronic level, such as an excited triplet state, a lower energy indirect conduction band, or a localized impurity level. A common occurrence in insulators and semiconductors is the formation of a bound state between an electron and a hole (called... 

When normal sites in a crystal structure are replaced by impurity atoms, or vacancies, or interstitial atoms, the local electronic structure is disturbed and local electronic states are introduced. Now when a dislocation kink moves into such a site, its energy changes, not by a minute amount but by some significant amount. The resistance to further motion is best described as an increase in the local viscosity coefficient, remembering that plastic deformation is time dependent. A viscosity coefficient, q relates a rate d8/dt with a stress, x ... 

The band gap Eg of semiconductors is typically of the order of 0.5 - 2 eV (e.g., 1.12 eV for Si, and 0.67 eV for Ge at room temperature), and consequently the conductivity of intrinsic semiconductors is low. It can be greatly enhanced by doping, which is the controlled introduction of suitable impurities. There are two types of dopants Donors have localized electronic states with energies immediately below the conduction band, and can donate their electrons to the conduction band in... 

Another type of structure may result from localized resonance states formed by either traps or impurities in the film39 (see Fig. 6B). In this case, the electrons are localized at the trap and due to the high charge concentration strong electron-vibration interactions exist that result in inelastic processes in the film. While these traps are observed clearly in LEET,39 in the LEPS experiments they are manifest by reduction in the transmission probability and sometimes by charging effects, but cannot be observed as modulation on the amplitude of the spectra. 

A complicating matter disregarded in the discussion concerns surface states . At a semiconductor surface, because of the discontinuity, the atomic arrangement is quite different from that in the interior of the crystal. In consequence the electrons on the surface atoms occupy localized energy states quite different from those in the interior. As an added complication impurity atoms carrying their own localized energy states will e adsorbed on the semiconductor surface. 

In fact, this is confirmed by analysing the propotion of the atomic orbitals in the impurity-state MOs by Mulliken s method (25). The results for the models (2) and (3) are shown in Table I. We can see from the result that the MOs in the model (2) are more Cr-3fi like ones, and the 0-2p component is smaller than that of the model (3). This indicates that the impurity-state orbitals in the model (2) are relatively localized on the chromium ion, therefore, the electron-electron repulsive interaction in the model (2) is much larger than that of the model (3). In the model (3), we can expect that the additional contribution of S - ispd orbitals causes further extensions of MOs, resulting in the reduction of the Coulomb repulsion energy. 

In solid-state laser materials, such as ruby (chromium doped alumina, AljOjiCr " ) (1) and emerald (chromium doped beryl, Be,Al,(Si03)5 Cr ) (2), transitions between multiplets of impurity states are utilized. These states mainly consist of 3d orbitals of the impurity chromium ions. For the analysis of these multiplet structures, the semi-empirical ligand-field theory (LFT) has been frequently used (3). However, this theory can be applied only to the high symmetry systems such as O, (or T ). Therefore, the effect of low symmetry is always ignored in the analysis based on the LFT, although most of the practical solid-state laser materials actually possess more or less distorted local structures. For example, in ruby and emerald, the impurity chromium ions are substituted for the aluminum ions in the host crystals and the site symmetry of the aluminum ions are C, in alumina and D, in beryl. Therefore, it is important to clarify the effect of low symmetry on the multiplet structure, in order to understand the electronic structure of ruby and emerald. 

Fig. 9. Structures of vibrational spectra in impure crystals, (a) represents impurities whose electronic states (e, e, ...) are uncoupled from the vibrations of the crystal. The phonon-spectra are superimposed on the eletron-ic levels (shaded area). Resonance (cor) or localised (coi) levels may appear, (b) If the impurity states are coupled to local vibrations, vibronic levels (v, v, .. .) appear whose spacings are generally much closer than for the electronic levels in (a). The superimposed phonon structures will fill in the energy range...

Soviet scientists have been particularly interested in impurity effects in ID metals. It was shown (INV 8) that impurities in a half-filled band give a singular enhancement in the density of states at the Fermi surface. This may be another manifestation of the well known impurity localization of states in ID. This latter implies (INV 13) that at T=0, o(to)-K) as u>-K). With increasing temperature, phonons allow a hopping type transport from one localized site to another, with increasing conductivity. At still higher temperatures, phonons scatter the electrons with a corresponding decrease in a(co). The theory developed fits quantitatively with experiments on TCNQ salts with structural disorder. 

The two-level model of hopping conductivity allows calculating from the set of experimental data the fundamental microscopical parameters of hopping conductivity - the electron localization radius and the concentration of localization centers corresponding to the intrinsic and impurity states [3]. 

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