Effective mass approximation potential

We use the effective mass approximation. The structure potential is approximated b y a c onsequence o f rectangular quantum barriers a nd wells. Their widths and potentials are randomly varied with the uniform distribution. The sequence of the parameters is calculated by a random number generator. Other parameters, e.g. effective masses of the carriers, are assumed equal in different layers. To simplify the transmission coefficient calculations, we approximate the electric field potential by a step function. The transmission coefficient is calculated using the transfer matrix method [9]. The 1-V curves of the MQW stmctures along the x-axis (growth direction) a re derived from the calculated transmission spectra... 

Two quantities - Bohr radius (ug) and binding (ground state) energy -characterize excitons in a semiconductor [3]. The dielectric constant e) of the semiconductor stabilizes these two quantities through equations (1) and (2) derived in a hydrogenic model with the coidomb potential normalized by e, within the framework of the effective mass approximation. 

Very delocalized excitons are treated in the Waimier effective mass approximation. The hole and the electron interact by the coulombic attraction, modified by an appropriate dielectric constant k. The effects of the periodic crystalline potential show up only in a reduced mass 11 (which may be anisotropic) containing the effective masses of the hole and the electron. Excitonic states are then hydrogen-like, with binding energies E (with respect to the conduction-band... 

To consider the influence of pressure on the CTT and IT and on the luminescence and luminescence kinetics of Ln and Ln ions, a more convenient description called the ITE [67] [68] can be used that allows precise specification of the IT and CCT states. In this description, a perturbation approach is applied where the potential created by the Ln ion is the perturbation of the ideal crystal potential. A similar approach was successfully used in the 1950s to describe the shallow donor and acceptor states in semiconductors [196] it is called the effective mass approximation (EMA). 

Here, u is the displacement of the /ith molecule from its equilibrium position and M the reduced mass of each molecular site. Second, the electron is described within the frame of the tight-binding approximation, where it is assumed that the effect of the potential at a given site of the one-dimensional chain is limited to its nearest neighbors. In that case, the energy dispersion of the electron is given by... 

A disadvantage of this technique is that isotopic labeling can cause unwanted perturbations to the competition between pathways through kinetic isotope effects. Whereas the Born-Oppenheimer potential energy surfaces are not affected by isotopic substitution, rotational and vibrational levels become more closely spaced with substitution of heavier isotopes. Consequently, the rate of reaction in competing pathways will be modified somewhat compared to the unlabeled reaction. This effect scales approximately as the square root of the ratio of the isotopic masses, and will be most pronounced for deuterium or... 

A description of nuclear matter as an ideal mixture of protons and neutrons, possibly in (5 equilibrium with electrons and neutrinos, is not sufficient to give a realistic description of dense matter. The account of the interaction between the nucleons can be performed in different ways. For instance we have effective nucleon-nucleon interactions, which reproduce empirical two-nucleon data, e.g. the PARIS and the BONN potential. On the other hand we have effective interactions like the Skyrme interaction, which are able to reproduce nuclear data within the mean-field approximation. The most advanced description is given by the Walecka model, which is based on a relativistic Lagrangian and models the nucleon-nucleon interactions by coupling to effective meson fields. Within the relativistic mean-field approximation, quasi-particles are introduced, which can be parameterized by a self-energy shift and an effective mass. 

Here /ie and are effective masses of electron and hole, respectively. Near to bottom of conductivity band and near to top of valent band where dependence E from k is close to parabolic, electron and hole move under action of a field as particles with effective masses fie — h2l(d2Ec(k)ldk1) and jUh = —h2l( E (k)ldk ) [6]. In particular, in above-considered onedimensional polymer semiconductor /ie — /ih — h2AEQj2PiP2d2 [6]. As a first approximation, it is possible to present nanocrystal as a sphere with radius R, which can be considered as a potential well with infinite walls [6], The value of AE in such nanocrystal is determined by the transition energy between quantum levels of electron and hole, with the account Coulomb interaction between these nanoparticles. 

Here im is the effective mass of the i th vibration and Pi is the momentum conjugate to the corresponding normal vibrational coordinate Qi. The first two terms transform the electronic levels into potential energy manifolds in the coordinates of the octahedral normal modes Qi with vibrational frequencies m,- = yZ T/I/", and the complete wave functions in the Born-Oppenheimer approximation can be written as a product of the electronic and vibrational parts. The third term describes the distortions produced by the vibrations and can be interpreted in terms of a force Fi, which acts along the vibrational mode Qi associated with the electronic state E ... 

For a relatively shallow lattice potential (Ut> < 15 Erec), it is possible to derive the approximate formulae for Vhop and the single-atom effective mass rrieff from the quantum-pendulum Schrodinger equation ... 

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