Energy bands semiconductors

On a somewhat larger scale, there has been considerable activity in the area of nanocrystals, quantum dots, and systems in the tens of nanometers scale. Interesting questions have arisen regarding electronic properties such as the semiconductor energy band gap dependence on nanocrystal size and the nature of the electronic states in these small systems. Application [31] of the approaches described here, with the appropriate boundary conditions [32] to assure that electron confinement effects are properly addressed, have been successful. Questions regarding excitations, such as exdtons and vibrational properties, are among the many that will require considerable scrutiny. It is likely that there will be important input from quantum chemistry as well as condensed matter physics. 

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. 

Fig. 3.6 A schematic representation of semiconductor energy band levels and energy distribution of the electrolyte redox system.

Entry number Oxide semiconductor Energy band gap, eV Comments Reference (s)... 

To facilitate a self-contained description, we will start with well-established aspects related to the semiconductor energy band model and the electrostatics at semiconductor electrolyte interfaces in the dark . We shall then examine the processes of light absorption, electron-hole generation and charge separation at these interfaces. Finally, the steady-state and dynamic (i.e., transient or periodic) aspects of charge transfer will be considered. Nanocrystalline semiconductor films and size quantization are briefly discussed, as are issues related to electron transfer across chemically modified semiconductor electrolyte interfaces. 

Complications arise when there are surface states that mediate charge exchange at the interface. When their density is high [37], they act as a buffer in that in the extreme case, carriers in the semiconductor energy bands are completely excluded from the equilibration process. 

Fig. 6.9 Space-charge region at a semiconductor surface, here represented for the case of an n-type semiconductor. Energy band profiles and electron concentration n(x). Ec, Ev, Ef respectively stand for conduction band energy, valence band...

In Eq. (11), Vfb is the so-called flat band potential, that is the applied potential (V) at which the semiconductor energy bands are flat , leading up to the solution junction. Several points with respect to the applicability of Eq. (11) must be noted. 

At the flat band potential, there is no potential drop across the semiconductor and, hence, the semiconductor energy bands are flat from the bulk up to the semiconductor surface (see Fig. lb). Moreover, because el is approximately constant, the energy bands are fixed at the semiconductor surface. Hence, the position of the band edges at the surface may be calculated once the flat band potential is known. 

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