Band gap in semiconductors

Flybertsen M S and Louie S G 1985 First-principles theory of quasiparticles Calculation of band gaps in semiconductors and insulators Phys. Rev. Lett. 55 1418... 

Contactless, nondestructive monitoring of band gaps in semiconductors Wide range of temperatures and ambients (air, ultrahigh vacuum) in-situ monitoring of semiconductor growth... 

Band gaps in semiconductors can be investigated by other optical methods, such as photoluminescence, cathodoluminescence, photoluminescence excitation spectroscopy, absorption, spectral ellipsometry, photocurrent spectroscopy, and resonant Raman spectroscopy. Photoluminescence and cathodoluminescence involve an emission process and hence can be used to evaluate only features near the fundamental band gap. The other methods are related to the absorption process or its derivative (resonant Raman scattering). Most of these methods require cryogenic temperatures. 

The properties of the band gap in semiconductors often control the applicability of these materials in practical applications. To give just one example, Si is of great importance as a material for solar cells. The basic phenomenon that allows Si to be used in this way is that a photon can excite an electron in Si from the valence band into the conduction band. The unoccupied state created in the valence band is known as a hole, so this process has created an electron-hole pair. If the electron and hole can be physically separated, then they can create net electrical current. If, on the other hand, the electron and hole recombine before they are separated, no current will flow. One effect that can increase this recombination rate is the presence of metal impurities within a Si solar cell. This effect is illustrated in Fig. 8.4, which compares the DOS of bulk Si with the DOS of a large supercell of Si containing a single Au atom impurity. In the latter supercell, one Si atom in the pure material was replaced with a Au atom,... 

The calculations were performed employing either pure ab initio Hartree-Fock (HF) methods, or hybrid HF-DFT functionals, in particular B3LYP [22]. The hybrid functionals have several advantages. One is that they are commonly applied with great success in computational studies of molecules and clusters, thus making it possible to benefit from the gathered experience from molecular studies. Another is their recently noted ability to accurately model band gaps in semiconductor compounds [57]. 

When temperature is lowered, the band gaps usually increase [15]. There again, a few materials like lead sulphides or some copper halides are exceptions with a band gap increasing with temperature [96]. A quantitative analysis of the temperature dependence of the energy gaps must consider the electron-phonon interaction, which is the predominant contribution, and the thermal expansion effect. The effect of thermal expansion can be understood intuitively on the basis of the decrease of the interatomic distances when the temperature is decreased. A quantitative analysis of the electron-phonon contributions is more difficult, and most calculations have been performed for direct band-gap structures [75], Multi-parameter calculations of the temperature dependence of band gaps in semiconductors can be found in [81],... 

Quasiparticles Calculations of Band Gaps in Semiconductors and Insulators. 

The optical properties of nanomaterials are also different from those of their bulk counterpart due to the effect of surface plasmon resonance. This process appears when the entry free electrons in the conduction band produce an in-phase oscillation, called surface plasmon resonance. In this context, the increase of band gap in semiconductor nanoparticles generates a shift toward shorter wavelengths of the absorption edge. At resonance, light is tightly confined to the surface of the nanostructure until it eventually is absorbed inside the metal or scattered back into photons (Vollath 2008). 

One of the early triumphs of quantum mechanics in the area of solid state materials was the ability to explain why certain materials are metallic conductors while others are insulating or semiconducting. The energy band structure, which can be calculated by ab initio or semiempirical methods, provides access to these electrical properties. As will be shown below, DFT methods are well suited to treat metallic systems whereas there are problems in the accurate prediction of energy band gaps in semiconductors and insulators. Furthermore, certain transition metal oxides and solids containing rare-earth and actinide elements present serious theoretical challenges which have not been completely resolved yet,... 

H. Alawadhi, S. Tsoi, X. Lu, A.K. Ramdas, M. Grimsditch, M. Cardona, R. Lauck, Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors ZnO. Phys. Rev.B 75(20), 205207 (2007)... 

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