Impurities electronic states

The coefficients W originate from the matrix elements (over the impurity electronic states) of the electron-lattice potential function 5V = W(rj, Ik ) introduced in (2.5). Concretely for the E e example... 

In photoluminescence one measures physical and chemical properties of materials by using photons to induce excited electronic states in the material system and analyzing the optical emission as these states relax. Typically, light is directed onto the sample for excitation, and the emitted luminescence is collected by a lens and passed through an optical spectrometer onto a photodetector. The spectral distribution and time dependence of the emission are related to electronic transition probabilities within the sample, and can be used to provide qualitative and, sometimes, quantitative information about chemical composition, structure (bonding, disorder, interfaces, quantum wells), impurities, kinetic processes, and energy transfer. 

Photoluminescence is a well-established and widely practiced tool for materials analysis. In the context of surface and microanalysis, PL is applied mostly qualitatively or semiquantitatively to exploit the correlation between the structure and composition of a material system and its electronic states and their lifetimes, and to identify the presence and type of trace chemicals, impurities, and defects. 

The techniques for calculating the electronic states of an impurity in a metal from first principles are well understood and have already been implemented. An approximate method that leads to much simpler calculations has been proposed recently. We investigate this method within the framework of the quadratic Korringa-Kohn-Rostoker formalism, and show that it produces surprisingly good predictions for the charge on the impurity. 

The proposed scenario is mainly based on the molecular approach, which considers conjugated polymer films as an ensemble of short (molecular) segments. The main point in the model is that the nature of the electronic state is molecular, i.e. described by localized wavefunctions and discrete energy levels. In spite of the success of this model, in which disorder plays a fundamental role, the description of the basic intrachain properties remains unsatisfactory. The nature of the lowest excited state in m-LPPP is still elusive. Extrinsic dissociation mechanisms (such as charge transfer at accepting impurities) are not clearly distinguished from intrinsic ones, and the question of intrachain versus interchain charge separation is not yet answered. 

When normal sites in a crystal structure are replaced by impurity atoms, or vacancies, or interstitial atoms, the local electronic structure is disturbed and local electronic states are introduced. Now when a dislocation kink moves into such a site, its energy changes, not by a minute amount but by some significant amount. The resistance to further motion is best described as an increase in the local viscosity coefficient, remembering that plastic deformation is time dependent. A viscosity coefficient, q relates a rate d8/dt with a stress, x ... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

We start out this section with a simple treatment and discussion of the electronic states that are introduced by a hydrogen impurity. 

The electronic states introduced by hydrogen in the band structure of Si are quite different depending upon the location of the impurity in the lattice. For H at the bond center we can, to a first approximation, treat the problem as involving only three states (Schaad, 1974 Fisch and Licciardello, 1978) the semiconductor bonding (b) and antibonding (a) states (which, in turn, are symmetric and antisymmetric combinations of hydrid orbitals on the two atoms) and the hydrogen Is orbital. The cor-... 

Thus far, I have mainly discussed neutral impurities. From the treatment of the electronic states, however, it should be clear that occupation of the defect level with exactly one electron is by no means required. In principle, zero, one, or two electrons can be accommodated. To alter the charge state, electrons are taken from or removed to a reservoir the Fermi level determines the energy of electrons in this reservoir. In a self-consistent calculation, the position of the defect levels in the band structure changes as a function of charge state. For H in Si, it was found that with H fixed at a particular site, the defect level shifted only by 0.1 eV as a function of charge state (Van de Walle et al., 1989). 

The band gap Eg of semiconductors is typically of the order of 0.5 - 2 eV (e.g., 1.12 eV for Si, and 0.67 eV for Ge at room temperature), and consequently the conductivity of intrinsic semiconductors is low. It can be greatly enhanced by doping, which is the controlled introduction of suitable impurities. There are two types of dopants Donors have localized electronic states with energies immediately below the conduction band, and can donate their electrons to the conduction band in... 

Electron states of impurities McClure (1959b) Bums (1970)... 

Our results clearly show that modification of the electronic state of titanium oxide by metal ion implantation is closely associated with the strong and longdistance interaction which arises between the titanium oxide and the metal ions implanted, as shown in Fig. 13, and not by the formation of impurity energy levels within the band gap of the titanium oxides resulting from the formation of impurity oxide clusters which are often observed in the chemical doping of metal ions, as shown in Figs. 6 and 13. 

To describe the effect of the change of the elastic springs on the optical spectrum of an impurity center, we use the adiabatic approximation. In this approximation, phonons are described by different phonon Hamiltonians in different electronic states. The optical spectrum, which corresponds to a transition between different electronic states is determined by the expression /( >) = const X oj1 1 I(oj) [28], where the — sign corresponds to the absorption spectrum and the + sign stands for the emission spectrum,... 

Multicentre vibronic interactions are found in a wide number of systems such as impurity Jahn-Teller centres, molecular clusters and Jahn-Teller crystals [1], In these compounds the localized electrons in orbitally degenerate states interact directly only with active distortions of the local environment of corresponding vibronic centres. The distortions of different centres interact via the common vibrational modes of the system, which thus mediate the indirect interaction between Jahn-Teller centres [2,3]. As a result the corresponding vibronic problem becomes rather involved, with many electronic states mixed by many vibrational modes. 

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