Tamm surface levels

The existence of other deep surface levels, for example Tamm levels (discussed in the preceding section), on the surface of zinc oxide is placed in doubt by an experiment of Bevan and Anderson (32) on sintered zinc oxide. They observed that the activation energy of the conduction electrons (of the order of an electron volt when the sample is subjected to high oxygen pressure) decreases to a few hundredths of an electron volt if the measurements are taken at low pressure (less than 10 mm.) and high temperature (the order of 600°C). Surface traps other than those asso-... 

No "Jilt has so far been assumed that the semiconductor-electrolyte interphase does not contain either ions adsorbed specifically from the electrolyte or electrons corresponding to an additional system of electron levels. These surface states of electrons are formed either through adsorption (the Shockley levels) or through defects in the crystal lattice of the semiconductor (the Tamm levels). In this case—analogously as for specific adsorption on metal electrodes—three capacitors in series cannot be used to characterize the semiconductor-electrolyte interphase system and Eq. (4.5.6) must include a term describing the potential difference for surface states. 

The existence of surface states is a consequence of the atomic structure of solids. In an infinite and uniform periodic potential, Bloch functions exist, which explains the band structures of different solids (Kittel, 1986). On solid surfaces, surface states exist at energy levels in the gap of the energy band (Tamm, 1932 Shockley, 1939 Heine, 1963). 

In the original paper of Tamm (1932), the concept of surface state is demonstrated with a Kronig-Penney potential (Kittel, 1986) with a boundary, as shown in Fig. 4.5. By solving the Schrodinger equation, exphcit expressions for the surface states and their energy levels can be obtained. In... 

Fig. 4.5. Surface states. By solving the Schrodinger equation for a cut-off Kronig-Penney potential, it is found that in the energy gaps of the corresponding Kronig-Penney solid, there are surface states that decay exponentially into the vacuum and into the solid (Tamm, 1932). The explicit wavefiinction of a Tamm state with P = 15 and a = 3Aat = 5eV below the vacuum level is shown. The shaded areas represent allowed energy bands in the bulk.

TAMM LEVELS. Surface states the extra electron energy levels found at ctystal surfaces,... 

As mentioned earlier, the existence of surface shifted core levels has been questioned.6 Calculated results for TiC(lOO) using the full potential linearized augmented plane wave method (FLAPW) predicted6 no surface core level shift in the C Is level but a surface shift of about +0.05 eV for the Tis levels. The absence of a shift in the C Is level was attributed to a similar electrostatic potential for the surface and bulk atoms in TiC. The same result was predicted for TiN because its ionicity is close to that of TiC. This cast doubts on earlier interpretations of the surface states observed on the (100) surface of TiN and ZrN which were thought to be Tamm states (see references given in Reference 4), i.e. states pulled out of the bulk band by a shift in the surface layer potential. High resolution core level studies could possibly resolve this issue, since the presence of surface shifted C Is and N Is levels could imply an overall electrostatic shift in the surface potential, as suggested for the formation of the surface states. 

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