Momentum matrix elements

A6.4 Luttinger and Bir-Pikus parameters of GaN and AIN A6.5 Electron and hole effective masses of GaN and AIN A6.6 Deformation potentials of GaN and AIN A6.7 Momentum matrix elements of GaN A6.8 Subband structures of GaN/AlGaN quantum wells A6.9 Optical gain of bulk GaN and GaN/AlGaN quantum wells... 

In the analyses of conventional zincblende (ZB) semiconductors, we frequently assume a parabolic band for the conduction bands, and the 6 x 6 Luttinger-Kohn Hamiltonians are used to describe the upper valence bands [1,2], In treating the valence bands together with the conduction bands on an equal footing, as when estimating the momentum matrix elements, we often make use of the 8 x 8 Kane Hamiltonian [3], However, the form of the Hamiltonians reflects the crystal symmetry, and Kane Hamiltonians are constructed under the condition of cubic symmetry. For wurtzite (WZ) materials, therefore, we must consider hexagonal symmetry in the effective Hamiltonian. Let us consider the 8 x 8 k.p Hamiltonian for WZ structure [4,5],... 

Note that the momentum matrix elements, P ( and P , are different from each other in WZ structure due to the anisotropy between the directions parallel and perpendicular to the c-axis. P2 and P2i can be analytically derived from the WZ 8x8 Hamiltonian as follows ... 

A6.7 Momentum matrix elements of GaN B MOMENTUM MATRIX ELEMENTS... 

Kageshima and Shiraishi directly calculated the momentum matrix elements from the wave functions at the T point, with the ultrasoft pseudo-potential method including a core-repair term [14], Their result shows that the momentum matrix elements of ZB and WZ GaN are almost the same and about 40% smaller than that of ZB GaAs. This trend is consistent with the result of Suzuki et al although the absolute values are about 30% smaller. Experimentally, the momentum matrix element was indirectly deduced from a fit to photoluminescence (PL) spectra and optical absorption by Im et al [15], Fanciulli et al measured the g-value by electron spin resonance (ESR) and indirectly determined it with the k.p model [16], The agreement between theoretical and experimental results is fairly good. 

Recipes for Evaluation of Molecule-Fixed Angular Momentum Matrix Elements... 

In these formulae, P (k) is the momentum matrix element between states in bands n,n at wave-vector k, e is a unit vector in the direction of the electric field vector of the incident electromagnetic radiation, En,n(k) s En. (k) - En (k) is the transition energy fico, m is the effective mass of the electron and the other symbols have their ususal meanings. The integral in eqn. (4) is now explicitly over that surface in /2-space at which Em. = fico. 

In this context it is noted that Kildal [2] proposed the energy spectrum of the conduction electrons in non-linear optical materials under the assumptions of isotropic momentum matrix element and isotropic spin-orbit splitting, respectively, although the anisotropies of the aforementioned band parameters are the significant physical features of this compound. Besides, III-V optoelectronic compounds find extensive application in distributed feedback lasers and infrared photodetectors. In what follows, we study the photoemission in quantum confined CdGeAs2 on the basis of a newly formulated electron... 

R E) is the position matrix dipole element and is related to the momentum matrix element by... 

Having the DOS and before resorting to the Kubo-Greenwood equation (7) one can calculate o/ q(w) and in turn a( ) simply from the convolution of the DOS in the valence and the conduction bands after making some simplifying assumptions for the matrix element Px,ij The usual convenient assumption is that this momentum matrix element on the average is constant. Another assumption that Cody others have proposed is that the dipole matrix... 

Due to the electron-phonon interactions, which contribute to the emission process by phonon-assisted transitions, the above expression may be modified to take into account the vibrational states. In that case, the dipole momentum matrix elements include both electronic... 

For an oblate top, the unique axis is denoted by c. By replacement of A by C and a by c, the energy expression and angular momentum matrix elements for an oblate top may be obtained. In particular, for the energy. 

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