Properties of Semiconductors

We have introduced an effective mass in Equation (4.27) and this reflects the fact that the electron and hole are not moving in free space but in a lattice potential. In a lattice it is the group velocity of the associated wavepacket that determines the motion of an electron. In the presence of an applied electric field F the acceleration of the electron is then  

Substituting for dk/dt from Equation (4.29) in Equation (4.28), it follows that  

For free electrons Equations (4.6) and (4.30) give m =m as expected. For the tight-binding model close to k = 0 using Equation (4.22), expanding cos(ka) and neglecting terms beyond (ka)2 gives  

In metals, where the valence bands are only partially filled even in the ground state, the effective concentration of carriers is scarcely affected by temperature. Actually, the conductivity decreases slightly with increasing temperature, because at higher temperatures the lattice vibrations scatter electrons and their mobility goes down. For the same reason mobility also decreases with temperature in the case of silicon, but the conductivity still increases with temperature, because the steep rise of carrier concentration swamps the more gradual decline in mobility. 

Dopants and other impurities and lattice defects will also affect the mobility by acting as scattering centres for electrons and holes. In high purity materials 

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Semiconductors are poor conductors of electricity at low temperatures. Since the valence band is completely occupied, an applied electric field caimot change the total momentum of the valence electrons. This is a reflection of the Pauli principle. This would not be true for an electron that is excited into the conduction band. However, for a band gap of 1 eV or more, few electrons can be themially excited into the conduction band at ambient temperatures. Conversely, the electronic properties of semiconductors at ambient temperatures can be profoundly altered by the... 

Cohen M L and Cheiikowsky J R 1989 Electronic Structure and Optical Properties of Semiconductors 2nd edn (Springer)... 

All teclmologically important properties of semiconductors are detennined by defect-associated energy levels in the gap. The conductivity of pure semiconductors varies as g expf-A CgT), where is the gap. In most semiconductors with practical applications, the size of the gap, E 1-2 eV, makes the thennal excitation of electrons across the gap a relatively unimportant process. The introduction of shallow states into the gap through doping, with either donors or acceptors, allows for large changes in conductivity (figure C2.16.1). The donor and acceptor levels are typically a few meV below the CB and a few tens of meV above the VB, respectively. The depth of these levels usually scales with the size of the gap (see below). 

Semiconductors (qv) are materials with resistivities between those of conductors and those of insulators (between 10 and 10 H-cm). The electrical properties of a semiconductor determine the hmctional performance of the device. Important electrical properties of semiconductors are resistivity and dielectric constant. The resistivity of a semiconductor can be varied by introducing small amounts of material impurities or dopants. Through proper material doping, electron movement can be precisely controlled, producing hmctions such as rectification, switching, detection, and modulation. 

A hst of some impurity semiconductors is given in Table 5. Because impurity atoms introduce new localized energy levels for electrons that are intermediate between the valence and conduction bands, impurities strongly influence the properties of semiconductors. If the new energy levels are unoccupied and He close to the top of the valence band, electrons are easily excited out of the filled band into the new acceptor levels, leaving electron holes... 

Recent texts have assembled impressive information about the production, characterisation and properties of semiconductor devices, including integrated circuits, using not only silicon but also the various compound semiconductors such as GaAs which there is no room to detail here. The reader is referred to excellent treatments by Bachmann (1995), Jackson (1996) and particularly by Mahajan and Sree Harsha (1999). In particular, the considerable complexities of epitaxial growth techniques - a major parepisteme in modern materials science - are set out in Chapter 6 of Bachmann s book and in Chapter 6 of that by Mahajan and Sree Harsha. 

The acoustic microscopy s primary application to date has been for failure analysis in the multibillion-dollar microelectronics industry. The technique is especially sensitive to variations in the elastic properties of semiconductor materials, such as air gaps. SAM enables nondestructive internal inspection of plastic integrated-circuit (IC) packages, and, more recently, it has provided a tool for characterizing packaging processes such as die attachment and encapsulation. Even as ICs continue to shrink, their die size becomes larger because of added functionality in fact, devices measuring as much as 1 cm across are now common. And as die sizes increase, cracks and delaminations become more likely at the various interfaces. 

Semiconductors have a considerably smaller band gap (e.g. silicon 1.17 eV). Their conductivity, which is zero at low temperatures but increases to appreciable values at higher temperatures, depends greatly on the presence of impurities or, if added advertently, dopants. This makes it possible to manipulate the band gap and tune the properties of semiconductors for applications in electronic devices [C. Kit-tel. Introduction to Solid State Physics (1976), Wiley Sons, New York N. Ashcroft and N.D Mermin, Solid State Physics (1976), Saunder College]. 

As for the size dependence of nonlinear optical properties of semiconductor nanomaterials, detailed investigations are required from both the theoretical and experimental points of view. 

Semiconductor nanoparticles have been intensively studied because of their properties of quantum size effects [54]. A number of synthetic techniques have been reported and their characteristics have been studied by various spectroscopic methods [55, 56]. However, magnetic field effects (MFEs) on the photoelectrochemical properties of semiconductor nanocrystals had not until now been reported. 

High-Temperature Crystallization The size-tunable optical and electronic properties of semiconductor nanocrystals are attractive for a variety of optoelectronic applications. In solution-phase crystallization, precursors undergo chemical reaction to form nuclei, and particle growth is arrested with capping ligands that... 

The role of electronic theory of chemisorption in developing ideas on effects of adsorption on electrical and physical properties of semiconductor adsorbents. 

The necessity of the use of electronic notions to resolve several diemical and physical problems stemming hrom the studies of heterogeneous processes was realized by Pisarjevsky already in early twenties [1]. Several non-trivial ideas concerning the effect of adsorption on electrophysical properties of semiconductor adsorbents were formulated in classical studies of Yoffe [2], Roginsky [3] and others. These theoretical ideas were further developed by Volkenshtein and his colleagues (see book [4] and the reference list therein) as well as in studies by Hauffe [5, 6] and some other authors [7, 8]. 

Above we have considered the possibility of existence of various types of polycrystalline semiconductor adsorbents differing in the character of contact of specific microcrystals. Let us consider the effect of this difference on adsorption and electrophysical properties of adsorbents in more detail and, which is more important, address the item of the mechanisms of the change of electrophysical properties of semiconductor caused by its interaction with gaseous phiise. 

If the above comparison of the properties of metal atoms with those of hydrogen deposited on the surface of a solid body (semiconductor) is correct, the effect of their adsorption on electric properties of semiconductor oxide films will be similar to features accompanying adsorption of hydrogen atoms. The atoms of hydrogen are very mobile and, in contrast to metal atoms, are capable of surface recombination resulting in formation of saturated molecules with strong covalent bond. 

Above reasoning can be confirmed by a number of experimental results which showed that although with some peculiarities irrelevant to the properties of semiconductor sensors the correlation between the amount of the atoms in the flux incident on the target, or their surface concentration, and the variation (increase, if we are dealing with semiconductor of n-type) of the target conductivity takes place [28]. Based on the relations cited in Chapter 1, one can estimate concentrations (i. e., flow intensities) of these particles in vacuum or in gaseous medium if these values are quite small, using the values of conductivity variation of the semiconductor film. 

Semiconductors. In Sections 2.4.1, 4.5 and 5.10.4 basic physical and electrochemical properties of semiconductors are discussed so that the present paragraph only deals with practically important electrode materials. The most common semiconductors are Si, Ge, CdS, and GaAs. They can be doped to p- or n-state, and used as electrodes for various electrochemical and photoelectrochemical studies. Germanium has also found application as an infrared transparent electrode for the in situ infrared spectroelectrochemistry, where it is used either pure or coated with thin transparent films of Au or C (Section 5.5.6). The common disadvantage of Ge and other semiconductors mentioned is their relatively high chemical reactivity, which causes the practical electrodes to be almost always covered with an oxide (hydrated oxide) film. 

Basic properties of semiconductors and phenomena occurring at the semiconductor/electrolyte interface in the dark have already been discussed in Sections 2.4.1 and 4.5.1. The crucial effect after immersing the semiconductor electrode into an electrolyte solution is the equilibration of electrochemical potentials of electrons in both phases. In order to quantify the dark- and photoeffects at the semiconductor/electrolyte interface, a common reference level of electron energies in both phases has to be defined. 

Gaponenko S.V. Optical Properties of Semiconductor Nanocrystals, Cambridge University Press, Cambridge, UK, 1998. 

Charles H. Henry, Spectral Properties of Semiconductor Lasers... 

The unique electronic properties of semiconductor devices arise at the regions where p-typc and ra-typc materials ate in close proximity, as in p-n junctions. Typical impurity levels ate about 0.0001 at %, and their inclusion and distribution need to be very strictly controlled during preparation. Without these deliberately introduced point defects, semiconductor devices of the type now commonly available would not be possible. 

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