Nonparabolic band

A more exact treatment of the electronic states of NCs reqnires nonparabolic bands that can be conpled to each other, a treatment of the energy dependence of the effective masses, consideration of both the nonsphericity of the NCs and the leakage of the wavefnnction ont of the confines of the NC, and inclnsion of electron-hole exchange." Althongh these are important refinements, the remarkable thing is the fact that many essential features of NC spectroscopy can be captnred by models as simple as the effective-mass parabolic band and Brus strong confinement descriptions. 

It should be noted that spectroscopic data obtained over a wide range of a values show that Vi is not quite linear when plotted against 1/a, and the observed curvature is greater than that due to the coulombic term shown explicitly in Eq. (9). Such curvature is due to nonparabolic band contours and to a breakdown of the effective mass approximation. As a result, the filnig values obtained with Eqs. (7) and (9), and to a lesser extent the Epoi value, will depend on the range of a values used in the fits. 

MST, please join us in the MagLab tonight at MIT for a Scotch-filled evening of ion implantation, the Raman Spectrum, and polarons in a nonparabolic band. 

Although most of the studies focus on the size dependence of the band gap (the energy difference between the conduction and valence band), the size dependence of the valence band energy alone has been measured by photoemission spectroscopy [42], It was shown that inter-valence-band mixing and nonparabolic band dispersion (i.e., the breakdown of effective mass approximation) have to be considered to explain the data [43]. 

In the case of a nonparabolic band described by the Kane model (Kane 1957) for the elastic scattering mechanism of electrons by acoustic vibrations, the Lorentz... 

Figure 5 (curves 2 and 3) shows the dependences Ll klef =f(p ) calculated using eq. (15) for a number of parameters j8. A nonparabolic band appreciably changes the L value except for the case of strong degeneration. 

Values are not reported because of the nonparabolic nature of the valence band. 

Fig. 15. Calculated effective densities of states for 40-nm bismuth nanowires (solid curve) and bulk bismuth (dashed curve). The zero energy refers to the band edge of bulk bismuth. The nonparabolic effects of the electron carriers are considered in these calculations.

The first experimental realization of intersubband lasers without inversion exploited the nonparabolicity of the conduction subbands and local population inversion near k=0 even though the lowest subband may have larger global occupation [25]. Later on, valence-band-based designs have been proposed [26-28], Intervalence band emitters based on Si-Ge structures have been... 

Stable, cubic phase, PbS nanoparticles were prepared in a polymeric matrix by exchanging Pb + ions in an ethylene - 15% methacrylic acid copolymer followed by reaction with H2S [91]. The size of the PbS nanoparticles was dependent on the initial concentration of Pb + ions with diameters ranging from 13 to 125 A. The smallest particles (13 A) are reported to be molecular in nature and exhibit discrete absorption bands in their optical spectra. Two theoretical models, which take into account the effect of nonparabolicity, were proposed in order to explain the observed size-dependent optical shifts for PbS nanocrystallites. The authors reported that the effective mass approximation fails for PbS nanocrystallites. 

Nomura S. and Kobayashi T. (1991), Nonparabolicity of the conduction-band in CdSe and CdS cSei c semiconductor microcrystallites . Solid State Comm. 78, 677-680. 

The results are presented of an investigation of the optical infrared transmission and reflection spectra of the alloy 0.7 InSb-0.3 InAs, doped with tellurium to obtain different electron densities (n). The optical width of the forbidden band (AE) and the optical effective mass of the electrons (mn) were determined from the spectra and their dependence on n studied. It was established that the conduction bands of InSb-InAs solid solutions are nonparabolic. Attempts were made by extrapolation to obtain an estimate of the limiting values of AE and mg in the region of low values of n, and an estimate of the matrix element P was made. It is concluded that there is general agreement between the structure of the energy bands of the semiconductor alloys considered and the Kane model. 

The results indicate that the conduction band of the alloys studied is nonparabolic. 

These integrals are tabulated in Smirnov and Tamarchenko (1977). Here 5 = fco2h, z = elk()T, f is the Fermi function and e is the effective width of the forbidden band of interaction, which is near to the real forbidden band width, Cg, for a number of narrow-band semiconductors, /i is also determined from a by equations taking account of the band nonparabolicity. For r= —0.5... 

Indium Arsenide (InAs). Indium arsenide resembles InSb in its band structure, having only a slightly larger energy gap and a smaller spin-orbit splitting of the top of the valence band. The conduction band minimum (Fg) is situated in the center of the Brillouin zone. Near the minimum, E(k) is isotropic but nonparabolic. The valence band shows the usual structure common to all zinc blende-type III-V compounds (Fig. 4.1-116). 

The lowest conduction band has its minimum at the Fi point in the center of the BrUlouin zone. Within an energy range of a few tenths of an electron volt above its bottom, the band is isotropic but highly nonparabolic. The nonparabolicity is revealed by the strong dependence of the optical electron mass on the electron concentration. The lowest conduction band is separated from the higher bands by a small gap. The valence band consists of several branches, with maxima at L3 and E. 

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