Bulk density of states

Of direct interest for photoemission of supported catalysts is that similar increases in the width of d-bands have been observed by Mason in UPS spectra of small metal particles deposited on amorphous carbon and silica substrates [48]. Theoretical calculations by Baetzold et al. [49] indicate that the bulk density of states is reached if Ag particles contain about 150 atoms, which corresponds to a hemispherical particle 2 nm in diameter. Concomitant with the appearance of narrowed d-bands in small particles is the occurrence of an increase in core level binding energies of up to 1 eV. The effect is mainly an initial and only partly a final state effect [48], although many authors have invoked final state - core hole screening effects as the only reason for the increased binding energy. 

The detection and measurement through photoemission spectroscopy of the single particle excitation associated with surface valence electron states is made difficult by the accompanying spectrum of the bulk material. When there is a gap in the bulk density of states at e, as in insulators and semiconductors, there is the possibility of observing surface states which lie in the gap. UPS has been used to observe such states in Si (60). It is practicable also to search for these states in metals at energies where the densities of bulk valence states are low or relatively structureless. Some suitable candidates for investigation should be the transition metals Ti, Zr, Hf, Cr, Mo, and W, which have low q(e) in the vicinity... 

Fig. 17. Local density of surface states (solid line) for the Kahn et al. [166] model of the 110 surface of GaAs. Electronic states localized on the first two layers of Ga and As atoms are shown. The broken line is the bulk density of states, shown for comparison. Only strongly localized surface states are shown. The densities of states have been Gaussian broadened (after Chadi [194]).

Because the X-ray photons may eject electrons from a depth of over 10 atomic layers, mainly the bulk density of states is obtained in this way. The electron density of states for surface atoms should be different from that in the bulk because the bonding environment for surface atoms is different in their number of nearest neighbors, relaxation or reconstruction, and anisotropy of bonding that could give rise to... 

In the following sections we shall describe the field-effect technique in some detail and present a sample of the experimentally determined densities of states. Some of the issues related to the overall sensitivity and reliability of the FE method to determine a bulk density of states in a-Si H will be examined. We shall also mention some of the recent applications of the FE technique to the study of a great variety of phenomena in a-Si H and related materials. Indeed, in spite of their shortcomings, FE measurements continue to be widely applied in the study of amorphous semiconductors and hence still qualify as one of the primary techniques to determine g(E) in these materials. 

These latter experimental results indicate some of the potential problems that exist in interpreting the FE data to give a bulk density of states in a-Si H. 

The dashed portions of the curve are not considered reliable estimates of the bulk density of states. [From Weisfield et al. (1981).]... 

The capacitance-temperature slope method described above is one manner in which C-Tcurves at different applied bias may be used to independently study the spatial and energy variations of the density of states in a-Si H. This and similar methods, we believe, currently offer the most reliable means of learning about the bulk density of states in undoped a-Si H. 

Fig. 47. First g(E) trial function to be used in the iterative fitting procedure which ultimately gives the bulk density of states for this sample (JH152). The dashed lines indicate how the raw DLTS data in Fig. 46 is used to construct the first trial function (solid line) as described in the text.

The values of the best fit parameters are < o 1-0 e V and x = 300 A. This value for Xn corresponds to a bulk density of states of 7 X 10 cm eV" or, equivalently, to 10 cm" eV states per interface. This density of states is more than sufficient to pin the Fermi level in high-quality a-Si H, where the density of gap states in the upper half of the gap is < 10 cm eV. The fit, shown in Fig. 12, is excellent given the range of samples covered and the expected sensitivity of the band bending at the substrate interface to substrate preparation conditions. 

FIGURE 32 Bulk density of states profile versus for (a) tetrahedral a-C and (b)... 

Galanakis et al. [9] correlated the surface energy of some d-metals to the broken bond in the tight-binding approximation. The is the number of d-electrons. Ws and Wb are the bandwidths for the surface and the bulk density of states, which took in rectangular forms. 

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