Valence band, characteristic function

Blom et al. [85] stated that the l/V characteristics in LEDs based on ITO/di-alkoxy-PPVs/Ca are determined by the bulk conductivity and not by the charge carrier injection, which is attributed to the low barrier heights at the interface ITO/PPV and PPV/Ca. They observed that the current flow in so called hole-only devices [80], where the work function of electrodes are close to the valence band of the polymer, with 1TO and Au as the electrodes, depends quadratically on the voltage in a logl/logV plot and can be described with following equation, which is characteristic for a space-charge-limitcd current (SCL) flow (s. Fig. 9-26) ... 

Fig. 16 (a) Schematic band diagram of Alq3 in between two ferromagnetic electrodes, (b) Valence band spectra for an increasing Alqa layer on AI2O3, where the characteristic occupied molecular orbitals are seen in the 3-nm film. Calculation of (c) junction resistance and TMR for two-step tunneling as a function of dj. (d) 1// as a function of d. Taken from [59] with permission... 

DFT calculations, as discussed in Section 6.3.1, yield a similar picture. Furthermore, modification of the valence band envelope as a function of hv was characteristic for all Ml and reference catalysts. Therefore it should be stressed that although we adopt the formalism of oxidation states it is essentially always only a formal oxidation state, which is just a chemical tool but does not represent any serious physical meaning, since the electron occupations are considerably different. 

Quantitative spectra with optimized resolution are recorded in the FAT mode with optimized pass energies. Figure 6 exemplifies the drastic effects of the analyzer convolution function on a photoemission spectriun for a valence band UPS experiment on graphite. The spectra characterize the very same surface and are both recorded with Hel radiation. The characteristic differences of the two operation modes of the hemispherical analyzer (LH EA 200) can be clearly seen as well as the different suitability of the relevant spectra for qualitative and quantitative analysis. In XPS data, the same differences occur for the two modes of operation. The intrinsically more symmetric line profile of core level lines tends, however, to obscure the effects of the analyzer in narrow scan spectra. 

These n values we call the rth band. So we can collect all terms which result from the w-dimensional problem in a sensible way into bands. We call the function (33) the characteristic function of the band. When the characteristic function is known and when the Hiickel numbers for the molecule are known, one can deduce the energy values in a way which is schematically described in Fig. 5. According to (32) the characteristic functions themselves are independent of the special molecule. They are general. The band for r = 1 we call the valence band. Hiickel s pure 2p theory gives as characteristic function of the valence band... 

From (37) one gets the characteristic function of the valence band if one takes the negative sign. 

Figure 7 shows the four curves which one gets for the characteristic function of the valence band if one inserts the values —1, —2, —3, and —4 ev for the parameter H is easily seen that there are only small differences between the four curves. The general type is always the same. And even this type is quite different from the characteristic function which resulted from the Hiickel theory. 

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