Band theory calculations 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... 

This book systematically summarizes the researches on electrochemistry of sulphide flotation in our group. The various electrochemical measurements, especially electrochemical corrosive method, electrochemical equilibrium calculations, surface analysis and semiconductor energy band theory, practically, molecular orbital theory, have been used in our studies and introduced in this book. The collectorless and collector-induced flotation behavior of sulphide minerals and the mechanism in various flotation systems have been discussed. The electrochemical corrosive mechanism, mechano-electrochemical behavior and the molecular orbital approach of flotation of sulphide minerals will provide much new information to the researchers in this area. The example of electrochemical flotation separation of sulphide ores listed in this book will demonstrate the good future of flotation electrochemistry of sulphide minerals in industrial applications. 

It is well known that the flotation of sulphides is an electrochemical process, and the adsorption of collectors on the surface of mineral results from the electrons transfer between the mineral surface and the oxidation-reduction composition in the pulp. According to the electrochemical principles and the semiconductor energy band theories, we know that this kind of electron transfer process is decided by electronic structure of the mineral surface and oxidation-reduction activity of the reagent. In this chapter, the flotation mechanism and electron transferring mechanism between a mineral and a reagent will be discussed in the light of the quantum chemistry calculation and the density fimction theory (DFT) as tools. 

The PPV spectra of Fig. 16 show all the signatures of exciton absorption and emission, such as in typical molecular crystals. The existence of well-defined structure in the absorption spectrum is not so easily accounted for in a band-to-band absorption model. In semiconductor theory, the main source of structure is in the joint density of states, and none is predicted in one-dimensional band structure calculations (see below). However, CPs have high-energy phonons (molecular vibrations) which are known (see, e.g., RRS spectra) to be coupled to the electron states. The influence of these vibrations has not been included in previous theories of band-to-band transition spectra in the case of such wide bands [176,183]. For excitons, the vibronic structure is washed out in the case of very intense transitions, corresponding to very wide exciton bands, the strong-coupling case [168,170]. Does a similar effect occur for one-electron bands Further theoretical work would be useful. 

A computational design procedure of a thermoelectric power device using Functionally Graded Materials (FGM) is presented. A model of thermoelectric materials is presented for transport properties of heavily doped semiconductors, electron and phonon transport coefficients are calculated using band theory. And, a procedure of an elastic thermal stress analysis is presented on a functionally graded thermoelectric device by two-dimensional finite element technique. First, temperature distributions are calculated by two-dimensional non-linear finite element method based on expressions of thermoelectric phenomenon. Next, using temperature distributions, thermal stress distributions are computed by two-dimensional elastic finite element analysis. 

A completely different viewpoint is adopted in calculations of infinite periodic structures (molecular crystals, semiconductors, large polymers). Band structure approaches that focus on the dynamics of electron-hole pairs are then used. " " Band theories may not describe molecular systems with significant disorder and deviations from periodicity, and because they are formulated in momentum (k) space they do not lend themselves very easily to real-space chemical intuition. The connection between the molecular and the band structure pictures is an important theoretical challenge. ... 

The concentration of electric charge carriers in intrinsic semiconductors are represented by the particle density of electrons, n, and holes, p, both expressed in m They can be calculated from the energy band theory in solids, assuming that the energy difference between the Fermi level and the band edges is larger than the thermal motion kT (0.025 eV at room temperature). Therefore, the statistical distribution of charge carrier follows a classical Boltzmann distribution ... 

Density functional theory calculations. deMon for density functional calculations. Turbomole for Hartree-Fock and MP2 ab initio calculations. ZINDO for extended Hiickel, PPP, CNDO, and INDO semiempirical molecular orbital calculations and prediction of electronic spectra. Plane Wave for band structures of semiconductors. ESOCS for electronic structure of solids. DSolid for density functional theory calculations of periodic solids. Silicon Graphics and IBM workstation versions. 

It is traditional for quantmn theory of molecular systems (molecular quantum chemistry) to describe the properties of a many-atom system on the grounds of interatomic interactions applying the hnear combination of atomic orbitals (LCAO) approximation in the electronic-structure calculations. The basis of the theory of the electronic structure of solids is the periodicity of the crystalline potential and Bloch-type one-electron states, in the majority of cases approximated by a linear combination of plane waves (LCPW). In a quantmn chemistry of solids the LCAO approach is extended to periodic systems and modified in such a way that the periodicity of the potential is correctly taken into account, but the language traditional for chemistry is used when the interatomic interaction is analyzed to explain the properties of the crystalhne sohds. At first, the quantum chemistry of solids was considered simply as the energy-band theory [2] or the theory of the chemical bond in tetrahedral semiconductors [3]. From the beginning of the 1970s the use of powerful computer codes has become a common practice in molecular quantum chemistry to predict many properties of molecules in the first-principles LCAO calculations. In the condensed-matter studies the accurate description of the system at an atomic scale was much less advanced [4]. 

Answer Using simple theory of semiconductors and knowing the F-center concentration one can estimate the position of the Fermi level with respect to the conduction band. I do not determine the Fermi level experimentally, but by calculation from known F-center concentration. I believe that the K2 molecules are contained in small cavities in the crystal. The volume of a cavity containing one K2 molecule should essentially be equal to the combined volumes of two K+ and two Cl" ions, because K2 is formed from two cations and two F centers. Some K2 molecules exist by themselves and others condense into larger cavities as in the formation of a droplet of liquid in a supersaturated vapor. 

With the help of these experimental techniques the study of semiconductors in recent years has been a highly successful marriage of theory and experiment. The trends of the important parameters of band structure from one element or compound to the next were found to follow rules which are remarkably simple when one considers the potpourri of effects and approximations involved in band structure calculations. This led Phillips to construct a much simpler semiempirical picture based on bonds rather than bands—but that is another storytold elsewhere in this volume (Chapter 1). 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

Recent calculations of hyperfine parameters using pseudopotential-density-functional theory, when combined with the ability to generate accurate total-energy surfaces, establish this technique as a powerful tool for the study of defects in semiconductors. One area in which theory is not yet able to make accurate predictions is for positions of defect levels in the band structure. Methods that go beyond the one-particle description are available but presently too computationally demanding. Increasing computer power and/or the development of simplified schemes will hopefully... 

We now look at some results, calculated via the above theory, for a pair of H atoms chemisorbed on several d-band metals (Ti, Cr, Ni, Cu). Corresponding results for III-V and sp-hybrid semiconductor substrates have been given by Schranz and Davison (1998, 2000). 

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