El Principio de Eisenhower
4. El taller de capacitación
4.1. Tipos de eventos de capacitación
The group 11 noble metals of Cu, Ag and Au are three systems of varying complexity, which is seen by analysing the sp-band width. Cu shows a close comparison to the free electron band width (Tab. 4.1), whilst Ag and Au become increasingly more relativistic. The effects of the larger nucleus in these increasing complex systems are reected by the size of the d-band splitting in the band diagrams (Figs. 4.22 - 4.24). These noble metals have the same valence electron conguration (d10s1) yet still have vastly different SMDs
due to the difference in complexity of the systems. As such these targets will provide a good test of both the EMS and ARPES experimental techniques in comparison to each other, and also for the comparison of these experimental results to theoretical calculations. EMS is a bulk sensitive process which measures the strongest intensity from bands that are denser in momentum space (sp-bands), due to the limited momentum range in which it is measured over. ARPES is more of a surface sensitive process which measures the strongest intensity from bands that are denser in positional space (d-bands). Typically ARPES measured band structures are used in comparison to theoretical calculations, but with the more sp-band and bulk sensitive EMS technique, both ARPES and EMS could be used in conjunction to measure more accurate band structures. These two different experimental techniques measure relatively similar band positions (Tab. 4.3) and band di- agrams (Figs. 4.22 - 4.24). There are slight discrepancies in some of the d-band positions in which EMS measures through out of plane diffraction effects (Fig. 4.16), and hence is a weak signal, in which case the ARPES results are expected to be more accurate. Al- ternatively some slight differences in the sp-band positions are expected to be measured more accurately with the EMS experiment, due to the increased sp-band sensitivity.
Comparison between the combined EMS and ARPES experiments and the LDA cal- culations in this chapter has shown some consistent failures on the part of the LDA theory. The sp-band width and sp-band position is consistently overestimated by theory which is attributed to a problem in the cancellation of the self-Coulomb and self-exchange cor- relation effects [103, 111, 115]. The same self energy effects are attributed to the LDA theories overestimation of the d-band dispersion. These assumptions are veried by the observed improvement (Tab. 4.2) of an LDA theory with a SIC that accommodates for the self energy effects. The LDA theory also consistently underestimates the position of the d-bands which is attributed to the LDA theory overestimating the effect of metallic screening from the nucleus [103]. Despite the LDA theory having consistent problems, the positive sign is that the LDA theory was consistently able to estimate the band struc- tures of all these systems of varying complexity. The errors associated with the LDA theory were of a similar order for all the bands in all the samples, indicating that the LDA
Disordered Semiconductors and Alloys
Results for the disordered states of silicon (Si) and germanium (Ge) will be presented in order to examine the differences between their amorphous and polycrystalline elec- tronic structure, a comparison which only EMS can provide. Experimental investigations into the complete valence electronic structure of these two states can yield information that has not previously been measured.The second half of this chapter will examine alloys of nickel (Ni) and copper (Cu) in varying concentrations. A close examination of the change in the electronic structure of the NiCu alloys, as they vary in composition, should obtain information about the nature of the valence electrons.
5.1 Semiconductors in Disordered States
EMS measures the real momentum of the bound electron (q) rather than the crystal lattice reduced momentum (k) which is measured in photonic techniques such as ARPES. This gives EMS the ability to measure the electronic structure of disordered states as well as single crystal states which have already been presented (see chapter 4). Samples can be prepared in amorphous, polycrystalline or single-crystal forms; each is expected to have
a different electronic structure resulting from differences in the degree of short and long range order. Single crystal samples have both short and long range order in the atomic lat- tice. A polycrystalline sample consists of many small randomly orientated single crystals separated by grain boundaries. Typically amorphous samples have very limited short or- der and no long range order, which makes them extremely difcult to model with theory. The amorphous state of a semiconductor however is not typical, amorphous semiconduc- tors exist in a special state referred to as a continuous random network (CRN) [128]. In the CRN state each atom has a co-ordination number of 4, but the orientation of the 4 nearest neighbour atoms is still somewhat randomized creating a range of bond angles and bond lengths [129] that vary by as much as 2 % and 10 % respectively [130, 131]. An ideal amorphous semiconductor exists in a perfect CRN state, in reality there is a slight deviation from this picture, with the introduction of dangling bonds, and multi-member rings that create slight variations in electronic density through out the sample [132].
The polycrystalline form of Si and Ge can be approximated theoretically by a spher- ical average of all possible single crystal directions. A spherical average of theoretical calculations from a 16 by 16 mesh of polar and azimuthal angles has been shown to be the required mesh size for convergence [133]. For amorphous semiconductors it is the CRN that has raised much theoretical interest [134, 135, 136, 137, 138]. In a realistic semiconductor amorphous state there is expected to be a reasonable concentration of dan- gling bonds [132] which should have an effect on the electronic structure. The questions arise; what effects do these dangling bonds have? And with partial short range order in the amorphous state, how different are the electronic structures of the amorphous and polycrystalline state semiconductors?