Semiconductors indirect-band-gap

MoS2-type materials are indirect band-gap semiconductors. The energies of the indirect (momentum forbidden) and direct (momentum allowed) band-gap transitions are given in Table 1. The electronic structure of these materials may be qualitatively understood in terms of the crystal structure. 

Since this calculation of the quantum size effect is demonstrated for direct band gap, this equation must be carefully applied to the indirect band gap semiconductor such as Ti02.9) The effective mass of the conduction band electron reported for rutileTi02 ranges from 3 to 30 with a usual value of 20. For anatase Ti02, on the other hand, the effective electron mass is reported to be l.,0) The smaller effective mass of anatase can be attributed to the higher mobility of the electron, which is 40 times larger than that of rutile.l0)... 

Bulk HfSz is an indirect band gap semiconductor with au indirect band gap energy of 2.1 eV.67 The reflectance spectrum of the nanotubes shows a small blue shift compared with the bulk. The photoluminescence spectrum of the nanotubes shows a band at 676 nm due to trapped states, and the band is blue-shifted with respect to that of bulk HfS2 powder (see Fig. 21a). The Raman spectrum of the HfSz nanotubes is shown in Fig, 21b. It shows a band due to the Aiemode, corresponding to the S atom vibration along the c-axis perpendicular to the basal plane, and another due to the Eg mode due to the movement of the S and Hf atoms in the basal plane.68 The full-width at half maximum (FWHM) of the Alg band is 11 cm 1 in the nanotubes compared to 8 cm 1 for the bulk sample. Such broadening of the Raman band has been noted with MoS2 and WS2 nanotubes.19... 

Hole an electronic vacancy in the valence band of a solid Indirect band gap semiconductors semiconductors in which the lowest energy electronic transition between the valence and conduction bands is formally optically forbidden Intrinsic semiconductor an undoped semiconductor Majority carrier the predominant charge carrier in the bulk of a doped semiconductor... 

The excitation spectra of nc-Si/a-Si02, prepared by plasma-CVD show a significant and systematic blue shift for decreasing crystallite sizes D, which reflects the increase of the band gap. Due to the distribution of crystallite sizes in the samples the evaluation of the spectra cannot follow conventional methods of extrapolation of (/pLE- hv) to zero, as expected for an indirect band gap semiconductor [2]. 

The anisotropy of the electron effective masses at the energy minima of the CB reflects its symmetry. For indirect-band-gap semiconductors, like group-IV crystals (see Table3.4), the CB has equivalent energy minima along the six equivalent < 100 > directions for Cdiam and silicon, and along the four equivalent < 111 > directions for germanium (these directions are the same for the reciprocal and direct lattices). There are as many total donor wave functions ip = (r) k(i) (r) as equivalent CB minima. We first consider... 

It has been mentioned at the end of Sect. 3.3.1 that for hydrostatic pressures > 4 GPa, GaAs turned from a direct-band-gap semiconductor with GB minimum at the T point into an indirect-band-gap semiconductor with an absolute CB minimum at the X point. This has consequences on the absorption spectrum of the shallow donors in this material discrete electronic absorption has been reported in GaAs at 487 (60.4 meV) and 405 cm-1 (50.2 meV) for the Sica and Snc a donors, respectively under hydrostatic pressures of about 6GPa, with a small pressure dependence of their positions (—0.5 and I 0.14 moVGPa 1 for the Si and Sn lines, respectively) [107]. This absorption is shown in Fig. 6.46 for GaAs Sn. 

The creation of an excess ehp requires an energy equal to the semiconductor band gap. When excess electron-hole pairs recombine they release this energy by one of several distinct physical mechanisms. When the energy is given to phonons or lattice vibrations, the recombination mechanism is known as multiphonon recombination or Shockley-Read-Hall (SRH) recombination. SRH recombination dominates in the indirect band gap semiconductors Si, Ge and GaP. 

A detailed band gap analysis involves plotting and fitting the absorption data to the expected trendlines for direct and indirect band gap semiconductors. Ideally, the absorbance A is first normalized to the path length I of the light through the material to produce the absorption coefficient a as per Eq. (5.3). Values of a > 10" cm often obey the following relation presented by Tauc and supported by Davis and Mott [4, 5] ... 

Following the work on luminescent porous Si, a number of studies have been undertaken to render other semiconductors nanoporous. The motivation of such studies was based on the fact that if they can exhibit tunable luminescence in a similar way to nanoporous Si, then common features or differences might reveal the mechanisms involved. Studies concern indirect band gap semiconductors such as those of column IV (Ge, Sii j Gej , SiG) and GaP, as well as direct band gap III-V alloys (GaAs and InP) and II-VI compounds (CdTe, Cd0.95Zn0.05Te, CdTe, and ZnTe). 

Indirect band gap semiconductor A semiconductor in which the conduction band minimum and the valence band maximum do not occur at the same place in momentum space. In these semiconductors, electrons in the conduction band minimum require a change in momentum in order to recombine with ahole at the valence band maximum. The recombination process in this case usually requires a phonon. 

The basic principles involved in the light generation process of semiconductor injection lasers can most easily be described by examining the energy level diagram of a p-n junction made from a direct band gap semiconductor. Indirect band gap semiconductors are not used for... 

A semiconductor is called direct band gap semiconductor if the energy of the top of the VB lies below the minimum energy of the CB without a change in electron momentum, whereas it is called indirect band gap semiconductor if the minimum energy in the CB is shifted by a difference in momentum (see Fig. 6.2). 

Energy vs momentum for (a) direct band gap semiconductor and (b) indirect band gap semiconductor. 

The feasibility of excitation of an electron from the VB to the CB is allowed if the angular momenta of the photon and electron are conserved during excitation. The semiconductor is then called a direct band gap semiconductor. For example, CdS, CdSe, GaAs, InP, etc., are direct band gap semiconductors, whereas Si is an indirect band gap semiconductor. 

---