Shockley type surface states

The 2D electron gas of the Shockley-type surface states plays also an important role in the substrate mediated interaction between adsorbed atoms. 

The required 2D nearly free electron gas is realized in Shockley type surface states of close-packed surfaces of noble metals. These states are located in narrow band gaps in the center of the first Brillouin zone of the (lll)-projected bulk band structure. The fact that their occupied bands are entirely in bulk band gaps separates the electrons in the 2D surface state from those in the underlying bulk. Only at structural defects, such as steps or adsorbates, is there an overlap of the wave functions, opening a finite transmission between the 2D and the 3D system. The fact that the surface state band is narrow implies extremely small Fermi wave vectors and consequently the Friedel oscillations of the surface state have a significantly larger wave length than those of bulk states. 

Thus, we wiU not be able to describe Shockley-type surface states as they require a band gap due to hybridization of different types of orbitals. Rather, in this section we focus on the question when and to what extent an altered potential in the vicinity of the outermost atom can result in the formation of a surface state, that is an electronic state, with an energy outside the bulk band region and a wave function decaying exponentially towards the interior of the sohd. 

T= 18.5 K. Obviously, the oscillation period does not depend on the adatom type, but depends on the substrate, more precisely on the Fermi wavelength of the Shockley surface state. (From Ref [51].)... 

Since surface states with free-electron-like dispersion (Shockley type) have a low occupancy per surface unit cell and a low DOS at Ey, they are in general not considered to dominate the energetics of the surface, although - as discussed in Section 5.4.3 - situations exist where they can afiect the properties of the surface. On the contrary, metallic surface states derived from weakly dispersing bands (Tamm states) may have a high DOS at Ey and thus may influence the surface phase diagram considerably. As mentioned already in the case of quasi-2D states, transition metal surfaces are interesting in this respect, the question... 

Surface states are usually classified as Shockley [178] and Tamm states [179], and we now briefly discuss these two types of surface state in turn. However, we caution in advance that while useful, the distinction is somewhat arbitrary since both types of state describe the same physical phenomenon of a wave function that is localized at the surface and decays exponentially into the bulk (also see Chapter 1). 

The surface electronic states are typically probed with PES and I-PES (photoemission measures occupied states inverse photoemission, unoccupied states) described in Section 7.3.1, or for more accuracy with two-photon photoemission (2PPE), which is particularly suitable for analyzing the image potential states. In the 2PPE technique, a first laser hght pulse (pump) excites an electron from its initial state below the Fermi level Ep into an unoccupied intermediate state (of Shockley or image potential type). A second pulse (probe) lifts the electron to the final state above the vacuum level E c. so it can be detected as a photoelectron. One of the possible data acquisition modes is to record energy-resolved spectra at a particular delay between pump and probe pulses [51]. 

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