Theoretical Semiconductors

FIGURE 8. Energy levels at the intrinsic semiconductor/vacuum interface (no band bending or surface states). 

FIGURE 9. Direct and indirect transitions between parabolic semiconductor bands. 

Indirect transitions involve interactions with one or several phonons, as well as with trace impurities, vacancies, etc. In this instance, P, differs from P/. The momentum is conserved via phonon interactions. A phonon is a quantum lattice vibration consequently, indirect transitions are less probable than the direct ones in high-purity crystals. For direct optical transitions and volume excitation, the photocurrent varies linearly with the frequency of the incident radiation,  

As in the case of metal electrodes, photoemission yield measurements can be expressed in empirical Fowler plots.  

For in situ photoemission at the semiconductor/electrolyte interface, the generally accepted theory is that due to Gurevich and Pleskov. This predicts a photocurrent-energy relation known as the law  

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Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

The study of organic semiconductors and conductors is highly iaterdisciplinary, involving the fields of chemistry, soHd-state physics, engineering, and biology. This article provides a treatment of the theoretical aspects of organic semiconductors as well as an overview of recent advances ia the field and the uses of these materials based on their conductive and optical properties. 

Although there has been theoretical and experimental interest in the effects of ion bombardment on materials since about 1960 (153), the growth in ion implantation technology and appHcations since then is due almost solely to the semiconductor (integrated circuit) industry. The advantages of ion implantation for semiconductor doping were first pointed out in 1955 (154), but these advantages were not widely accepted until about 1970. 

A new chapter in the uses of semiconductors arrived with a theoretical paper by two physicists working at IBM s research laboratory in New York State, L. Esaki (a Japanese immigrant who has since returned to Japan) and R. Tsu (Esaki and Tsu 1970). They predicted that in a fine multilayer structure of two distinct semiconductors (or of a semiconductor and an insulator) tunnelling between quantum wells becomes important and a superlattice with minibands and mini (energy) gaps is formed. Three years later, Esaki and Tsu proved their concept experimentally. Another name used for such a superlattice is confined heterostructure . This concept was to prove so fruitful in the emerging field of optoelectronics (the merging of optics with electronics) that a Nobel Prize followed in due course. The central application of these superlattices eventually turned out to be a tunable laser. 

An important step toward the understanding and theoretical description of microwave conductivity was made between 1989 and 1993, during the doctoral work of G. Schlichthorl, who used silicon wafers in contact with solutions containing different concentrations of ammonium fluoride.9 The analytical formula obtained for potential-dependent, photoin-duced microwave conductivity (PMC) could explain the experimental results. The still puzzling and controversial observation of dammed-up charge carriers in semiconductor surfaces motivated the collaboration with a researcher (L. Elstner) on silicon devices. A sophisticated computation program was used to calculate microwave conductivity from basic transport equations for a Schottky barrier. The experimental curves could be matched and it was confirmed for silicon interfaces that the analytically derived formulas for potential-dependent microwave conductivity were identical with the numerically derived nonsimplified functions within 10%.10... 

The theoretically derived formula (21) relating PMC measurements to the surface concentration of minority carriers and interfacial rate constants contains a proportionality constant, S, the sensitivity factor. This factor depends on both the conductivity distribution in the semiconductor elec-... 

On the basis of our theoretical considerations and preliminary experimental work, it is hoped that fast processes of charge carriers will become directly measurable in functioning photoelectrochemical cells, Typical semiconductor electrodes are not the only systems accessible to potential-dependent microwave transient measurements. This technique may also be applied to the interfacial processes of semimetals (metals with energy gaps) or thin oxide or sulfide layers on ordinary metal electrodes. 

Theoretical Aspects of Semiconductor Electrochemistry Uosaki, K. Kita, H. 18... 

T. Ioannides, and X.E. Verykios, Charge transfer in metal catalysts supported on Doped Ti02 A Theoretical approach based on metal-semiconductor contact theory, J. Catal. 161,560-569 (1996). 

Finally, the investigation of noble metal bonding on semiconductor surfaces provides evidence that at moderate temperatures Cu diffuses easily into the Si surface whereas the penetration barrier for Ag is almost as large as its binding energy. The theoretical results help in the understanding of an important catalytic process in the synthesis of silicone polymers and shed light on the Cu/Si and Ag/Si interface formation. 

Loferski JL (1956) Theoretical considerations governing the choice of the optimum semiconductor for photovoltaic solar energy conversion. J Appl Phys 27 777-784... 

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