Effective mass theory

Ando, T., Nakanishi, T. and Igami, M. (1999) Effective-mass theory of carbon nanotubes with vacancy, J. Phys. Soc. Japan 68(12), 3994-4008. 

The Coulomb interaction between the electron and the donor core is, of course, present in an amorphous semiconductor and binds an electron in much the same way, so the shallow donor state is preserved. The effective mass theory for dopants cannot be applied directly to amorphous semiconductors, because it is formulated in terms of the momentum-space wavefunctions of the crystal. It is not immediately obvious that the effective mass has any meaning in an amorphous... 

Should a system contain donor and acceptormoieties, an exciton like behavior can be observed when the charges recombine. Again, effective mass theory can present us with the energy of the observed transition, as shown in equation (5) ... 

Banin U., Lee J. C., GnzeUan A. A., Kadavanich A. V., Alivisatos A. P., Jaskolski W., Bryant G., Efros A. L. and Rosen M. (1998), Size-dependent electronic level structure of InAs nanocrystal quantum dots test of multiband effective mass theory , J. Chem. Phys. 109, 2306-2309. 

The eigenvalues of Hamiltonian (5.4) where a simple Coulomb potential is used are independent of the chemical nature of the donor. This situation corresponds to experiment for the odd-parity levels, but not for the even-parity ones and especially for the Is ground state. There have been many attempts to use impurity-dependent potentials in Hamiltonian (5.4) in a generalized effective mass theory to provide realistic ground-state energies (see [47]). 

Chapter 1 of the present volume provides the basic concepts related to the properties and characterization of the centres known as shallow dopants, the paradigm of the H-like centres. This is followed by a short history of semiconductors, which is intimately connected with these centres, and by a section outlining their electrical and spectroscopic activities. Because of the diversity in the notations, I have included in this chapter a short section on the different notations used to denote the centres and their optical transitions. An overview of the origin of the presence of H-related centres in crystals and guidelines on their structural properties is given in Chap. 2. To define the conditions under which the spectroscopic properties of impurities can be studied, Chap. 3 presents a summary of the bulk optical properties of semiconductors crystals. Chapter 4 describes the spectroscopic techniques and methods used to study the optical absorption of impurity and defect centres and the methods used to produce controlled perturbations of this absorption, which provide information on the structure of the impurity centres, and eventually on some properties of the host crystal. Chapter 5 is a presentation of the effective-mass theory of impurity centres, which is the basis for a quantitative interpretation... 

Simple approach based on the effective mass theory has been developed and successfully applied to simulate electronic properties of monocrystalline and grained nanocrystalline films accounting for the confinement effect and interactions between the grains. Quantum confinement was found to influence band gap values only for the films with the thickness less than 5 nm. The highest gap varied from 0.63 to 0.91 eV depending on the film thickness as well as on the lateral size of the grains. Inclusion of the grains inside the film induces a eonsiderable increase of the gap as compared to the monocrystalline film of the same effective thickness. 

The electronic properties of monocrystalline and grained nanocrystalline CrSi2 films were estimated within the Effective Mass Theory. Inclusion of the grains inside the film increases the energy gap up to 60% compared to the monocrystalline film of the same effective thickness. 

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