Electronic structure of semiconductors

The difference between metals and semiconductors is, fundamentally, electronic in origin. In a metal, overlap of atomic or ionic orbitals on neighbouring sites leads to a continuum of levels that are only partially occupied by electrons. There are, therefore, energy levels immediately above the topmost occupied level that are empty and easily accessible thermally and the ability of electrons to move freely into these levels gives rise to the characteristic properties associated with a metal, such as conductivity, reflectivity etc. 

In the case of a semiconductor, overlap of the orbitals on each centre gives 

this picture is reasonably adequate but, as the temperature is raised, some thermal excitation of the electrons can occur from the valence band to the conduction band. Statistical calculations, beyond the scope of this article [2], lead to the conclusion that the number density of electrons at energy E in the CB, n(E), is given by 

The reference energy EF is called the Fermi energy and corresponds to the chemical potential of the electrons in the solid, and the factor 2 in eqn. (1) takes account of the fact that each level may be occupied by two electrons of opposite spins. 

Excitation of the electron from the VB leaves behind a vacancy or hole . Electrons in the VB can move to fill these holes leaving, in turn, further holes conceptually, it is easier to consider the holes moving in a sea of immobile electrons and we may develop expressions for the number density of these holes in close analogy to the formulae above for the electrons. Thus, the number density of holes in the VB at energy E, p(E ), is given by 

Many naturally occurring substances, in particular the oxide films that form spontaneously on some metals, are semiconductors. Also, electrochemical reactions are used in the production of semiconductor chips, and recently semiconductors have been used in the construction of electrochemical photocells. So there are good technological reasons to study the interface between a semiconductor and an electrolyte. Our main interest, however, lies in more fundamental questions How does the electronic structure of the electrode influence the properties of the electrochemical interface, and how does it affect electrochemical reactions What new processes can occur at semiconductors that are not known from metals  

We begin by recapitulating a few facts about semiconductors. Electronic states in a perfect semiconductor are delocalized just as in metals, and there are bands of allowed electronic energies. According to a well-known theorem [1], bands that are either completely filled1 

Electrons will move in an external fields only if they gain energy in doing so. This is not possible in a completely filled band 

The last approximation is valid if Ec — Ep kT (i.e., if the band edge is at least a few kT above the Fermi level), and the Fermi-Dirac distribution /(e) can be replaced by the Boltzmann distribution. Similarly, the concentration of holes in the valence band is  

The band gap Eg of semiconductors is typically of the order of 0.5 - 2 eV (e.g., 1.12 eV for Si, and 0.67 eV for Ge at room temperature), and consequently the conductivity of intrinsic semiconductors is low. It can be greatly enhanced by doping, which is the controlled introduction of suitable impurities. There are two types of dopants Donors have localized electronic states with energies immediately below the conduction band, and can donate their electrons to the conduction band in 

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Electrochemical reactions at semiconductor electrodes have a number of special features relative to reactions at metal electrodes these arise from the electronic structure found in the bulk and at the surface of semiconductors. The electronic structure of metals is mainly a function only of their chemical nature. That of semiconductors is also a function of other factors acceptor- or donor-type impurities present in bulk, the character of surface states (which in turn is determined largely by surface pretreatment), the action of light, and so on. Therefore, the electronic structure of semiconductors having a particular chemical composition can vary widely. This is part of the explanation for the appreciable scatter of experimental data obtained by different workers. For reproducible results one must clearly define all factors that may influence the state of the semiconductor. 

Lieske, N. P. (1984). The electronic structure of semiconductor surfaces. J. Phys. Chem. Solids 45, 821-870. 

The electronic structure of semiconductors is usually comprised of a filled valence band and an empty conduction band which are energetically separated by an inter-band gap, Es. All of the reactions described above involve the initial absorption of photons by the semiconductor and, for ultra-band gap photon energies, the subsequent generation of electron-hole pairs within the material lattice (ec B> J vb). as shown in Fig. 9.1a and equation (9.1). The entire process is thought to occur in <1 fs [96]. 

The electronic structure of semiconductors is characterized by a gap between electronic states populated by valence band (VB) electrons and empty states in the conduction band (CB), as shown in Fig. 2. The former can be promoted to the CB upon excitation with photons carrying energy in excess of Eg, the band-gap energy. This energy is calculated as the difference between the energies at the bottom of the CB and the top of the VB. Such a process yields CB electrons (e ) and VB holes (byB), which initiate redox reactions at the particulate/solution interface. For these reactions to occur the highest... 

The structure of semiconducting solids provides a convenient basis for understanding the important electronic properties of these materials. The important optical and electrical characteristics of semiconducting solids arise from the delocalized electronic properties of these materials. To understand the origin of this electronic delocalization, we must consider the nature of the bonding within semiconductor crystals. The basic model that has been successfully used to describe the electronic structure of semiconductors is derived from the Band Theory of solids. Our treatment of band theory will be qualitative, and the interested reader is encouraged to supplement our discussion with the excellent reviews by... 

Efros AL, Rosen M (2000) The electronic structure of semiconductor nanocrystals. Annual Rev. Mater. 

The structure and composition of a nanocrystalline surface may have a particular importance in terms of chemical and physical properties because of their small size. For instance, nanocrystal growth and manipulation relies heavily on surface chemistry [261]. The thermodynamic phase diagrams of nanocrystals are strongly modified from those of the bulk materials by the surface energies [262]. Moreover, the electronic structure of semiconductor nanocrystals is influenced by the surface states that He within the bandgap but are thought to be affected by the surface reconstruction process [263]. Thus, a picture of the physical properties of nanocrystals is complete only when the structure of the surface is determined. 

The first atomic resolution for metal surfaces came later because of the different surface electronic structure of semiconductors and metals. In the case of semiconductor, the energies... 

Electronic Structure of Semiconductors, Semiconductor-Metal Interfaces... 

In this section we discuss the electronic structure of semiconductors, metals, and semiconductor-metal interfaces as determined by APS. First, we describe the APS studies on Si. Then we take the example of elemental Ti studied by DAPS, AEAPS, and SXAPS. After this, the SXAPS results on intermetallics TySfij (x=0, 0.3, 0.5, 0.7, 1.0) are discussed. These are included to give an idea of the types of information available from APS spectra. The reaction of silicon upon titanium deposition which is used as a metallization material in microelectronics is then discussed. The study also includes the effect of temperature on Ti-Si interface. Finally, the apphcations of APS for band... 

Figure 3 illustrates the band model usually employed in discussions of the electronic structure of semiconductors. Electrons can reside at energy... 

Margaritondo, G. 1988. Electronic structure of semiconductor heterojunctions. Milana Jaca Book. 

Optical properties of nanocrystals have been of interest for centuries (see Sect. 1.1) and have become the subject matter of several books in recent years [50,73-75] and reviews [66-69,713]. The plasmon resonance band has emerged as a probe of events taking place in the proximity of metal nanocrystals. Advances have been made in understanding the electronic structure of semiconductor nanocrystals from the excitonic absorption spectra. 

After band structures of metal, insulator, and semiconductors are described and historical back-grotmd of semiconductor electrochemistry is presented, electronic structure of semiconductor/ electrolyte solution interface is discussed in relation to the unique electrochemical behavior of semiconductor electrode. Finally, effect of illumination as well as the surface modification on the electrochemical behavior of semiconductor electrode are described. Fundamental knowledge of semiconductor electrode presented here should be very important for the future development of photoelectrochemical and photocatalytic energy... 

Control and observation of electrochemical and photoelectrodiemical reactions at semiconductor electrodes are very important in establishing the electrochemical/ photoelectrochemical etching processes and stable photoelectrochemical cells (1,2). To understand the mechanism of the electrochemical and photoelectrochemical reactions, in situ information of morphological and electronic structures of semiconductor electrode surfaces with atomic resolution is essential. Although techniques such as electron microscopy and optical microscopy have been applied to examine the morphology of the surface of solid substrates, the former can be used only for ex situ examination and the latter has poor resolution (3,4),... 

Size-dependent electronic structure of semiconductor nanoparticles... 

The electronic structure of semiconductor surfaces close to the Fermi level is dominated by the dangbng bonds of its surface atoms. While the states originating from strong surface bonds such as dimers or adatom backbonds are almost completely hidden as broad resonances in the valence band, the dangbng bond orbitals from dimers, adatoms, or rest atoms form bands that are partially locabzed in the energy range forbidden for bulk electrons. 

Figure 7.29 The surface states for Si(lOO) in the 2x1 Feconstmction. Circles indicate experimental data and dashed curves show the calculated surface states. The bands indicated represent a range of energies covered by the surface component of the bulk band structure. Bulk band details are conventionally omitted in such diagrams to emphasize the surface states. Because the surface is reconstructed the surface Brillouin zone is rectangular. The results demonstrate why a maximum in the surface-state density of states occurs at an energy of -0.5 eV. After Surface Science 299/300, Himpsel F.J., Electronic structure of semiconductor surfaces and interfaces. , 525-540 (1994) with permission, copyright Elsevier 1994.

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