Electrons envelope function

Cowley 1981) ( is a convolution integral and FT is the Fourier transform). The phase-contrast imaging performance of an HRTEM is controlled by sin x, which contains the basic phase-contrast sinusoidal terms modified by an attenuating envelope function, F 9), which is essentially due to the partial coherence of the electron beam ... 

Presented experimental data reveal that for CdSe/ZnS quantum dots with two ZnS monolayers values follow a monotonous function drastically decaying with the QD core diameter. From the physico-chemical point of view, we conjecture that upon interaction of P with QD surface, the electron wave function may be locally modified (via inductive and/or mesomeric effects [9]) forming a surface local state capable to trap the electron of the photogenerated exciton (Fig. 2A). Thus, we will consider the behaviour of the electron wave function at the interface to the functional pyridyl group of the attached porphyrin. The single-carrier envelope wave functions y/a in a spherical core/shell QD are determined by the Schrodinger equation... 

The energies and wavefunctions of holes and electrons of these "W" and "M" QW cell were calculated by solving the Schrbdinger equation within the envelope function approximation in the framework of a 10-bands k p model including strain effects on the valence and conduction bands and the bandanticrossing (BAG) approach [4]. Further details in modeling are described elsewhere [5,6]. As shown in Fig. 1, an emission at 3.3 pm at RT with a carrier wavefunction overlap as high as 71% and 78% at equilibrium are predicted in... 

In the case of photon absorption, the incident light field drives a polarisation in the material that promotes an electron from the valence band to the conduction band. At the instant of creation of the electron-hole pair, the spatial envelope functions of the electron and hole wavefunctions overlap and have a well-defined phase relationship. This initial state preparation is different from an exciton in that the electron-hole pairs are formed within an electronic continuum of states and are therefore unbounded. In such circumstances, the use of dynamics to describe the state evolution is more appropriate than an eigenstate description with perturbative couplings between states. 

The confinement of electrons or holes in potential wells leads to the creation of discrete energy levels in the wells, compared with the continuum of states in hulk material quantisation also leads to a major change in the density of states. The energy levels can be calculated by solving the Schrodinger equation for the well-known particle in a box problem. Using the effective mass envelope function approximation (Bastard, 1981 and 1982 Altarelli, 1985 Bastard and Brum, 1986), the electron wavefunction % is then... 

Quantum films represent a beautiful physical example of the particle in the box problem. The energy levels of the conduction band electrons in the electron well (MQW) can be easily calculated using the envelope function or the effective mass approximation [6]. The electron wave function is then [29-31]... 

First, we express the operator of the electron-hole interband polarization Pw in terms of the electron and hole creation and annihilation operators in the envelope function approximation, following the standard procedure (18), (39) ... 

Typically the broadening of the Wannier-Mott exciton resonance (several meV) is negligible compared to the width of the absorption spectrum of organics (several hundred meV). Thus, one may consider the excited state in a semiconductor to be discrete with energy Kujd- The excited state Iff) of the semiconductor is an electron-hole pair described by the two-particle envelope function (r r/A assumed to be normalized to unity ... 

We adopt a simplified microscopic quantum-mechanical model of a 2D Wannier-Mott exciton, in which the polarization (eqn C.3) can be taken to vanish for L > Lw/2 and inside the well to be given by the product of the Is-wave function of the relative motion of the electron and hole at the origin, with the lowest subband envelope functions for the electron and hole in the approximation of... 

Figure Bl.17.5. Examples of CTFs for atypical TEM (spherical aberration = 2.7 mm, 120 keV electron energy). In (a) and (b) the idealistic case of no signal decreasing envelope functions [77] are shown, (a) Pure phase contrast object, i.e. no amplitude contrast two different defocus values are shown (Scherzer focus of 120 run underfocus (solid curve), 500 run underfocus (dashed curve)) (b) pure amplitude object (Scherzer focus of 120 run imderfocus) (c) realistic case including envelope functions and a mixed weak...

Since the early studies on the quantum confinement effect in colloidal semiconductor QDs, electronic levels have been assigned according to the spherical symmetry of the electron and hole envelope functions [9, 48]. The simplistic... 

The two lower data sets (II) compare the difference between the first strong excited optical transition and the band gap from PLE (b-a in Figure 5.1), with the separation Avb = 2vb — IvB in the tunneling data (open and full squares, respectively). The excellent correlation observed enables assignment of this first excited transition in the PLE to a 2vb — ISg excitation, as shown schematically in the inset of Figure 5.4a. Strong optical transitions are allowed only between electron and hole states with the same envelope function symmetry. Thus, it is inferred that the envelope function for state 2vb should have s character, and this state can be directly identified as the 2S3/2 valence band level. 

Hyperfine splitting due to interaction with ligand nuclei with 7 > 0 reflects the extent of spin delocalization onto neighboring atoms and can be used to characterize the types and numbers of such nuclei. In cases where these couplings are too small to be resolved in the EPR spectra, electron nuclear double resonance (ENDOR) or electron spin echo envelope modulation (ESEEM) can be used to measure the couplings as discussed in Chapter 2.3. Modern calculational tools are approaching the capabilities required to calculate g and A values from electronic wave functions. However, much of the spectroscopy that has been performed to date has used empirical correlations to interpret g and A values. 

Again Adt) = e°Adt) is an envelope function, with e° the peak amplitude. The matrix representation of a 1 (Q) in the basis of the diabatic electronic states reads... 

---