Band gap indirect

Fig. 1. Schematic diagram of semiconductor materials showing band gaps where CB and VB represent the conduction band and valence band, respectively and 0 and 0, mobile charge. The height of the curve represents the probabiUty of finding an electron with a given momentum bound to an N-isoelectronic impurity, (a) Direct band gap the conduction band minimum, F, is located where the electrons have 2ero momentum, ie, k = 0. The couples B—B, D—A, B—D, and B—A represent the various routes for radiative recombination. See text, (b) Indirect band gap the conduction band minimum, X, is located...

Eig. 6. Plot of band gap energy vs lattice parameter for (a) common III—V materials employed for LEDs where (—) corresponds to direct and (—) to indirect band gaps. Both Al Gaj As and (Al Gaaj )q lattice matched to GaAs, whereas In Gaj As P can be matched to InP. (b)... 

Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

Another parameter of relevance to some device appHcations is the absorption characteristics of the films. Because the k quantum is no longer vaUd for amorphous semiconductors, i -Si H exhibits a direct band gap (- 1.70 eV) in contrast to the indirect band gap nature in crystalline Si. Therefore, i -Si H possesses a high absorption coefficient such that to fully absorb the visible portion of the sun s spectmm only 1 p.m is required in comparison with >100 fim for crystalline Si Further improvements in the material are expected to result from a better understanding of the relationship between the processing conditions and the specific chemical reactions taking place in the plasma and at the surfaces which promote film growth. 

For optoelectronics the binary compound semiconductors drawn from Groups 13 and 15 (III and V) of the Periodic Table are essential. These often have direct rather than indirect band gaps, which means that, unlike Si and Ge, the lowest lying absorption levels interact strongly with light. The basic devices of... 

For compositions with 50 and 57% sodium Ep lies within the tail of the partial DOS of the sp-band of tin, but Ep has still not reached the region where the partial DOS of sodium is large. This yields a small DOS (pseudogap) for these cases at the Fermi level. Therefore, one gets an explanation for the minimum of the conductivity (i.e. the maximum of the resistivity) near the equimolar composition, as can be seen in Table 1. (Analogously, for solid equimolar /3-NaSn even a indirect band gap at the Fermi level was reported in literature [16].)... 

Richard J. Stirn, Band Structure and Galvanomagnetic Effects in III-V Compounds with Indirect Band Gaps... 

Figure 4.8 Interband transitions in solids with band-gap energy Eg-, (a) A direct band gap. Two direct transitions are indicated by arrows, (b) An indirect band gap. Two indirect band-gap transitions are indicated by arrows. The transitions at photon energies lower than Eg require absorption of phonons. The transitions at photon energies higher than Eg involve emission of phonons.

In cases in which both the upper edge level of the valence band and the lower edge level of the conduction band are at the same wave vector of electrons (GaAs, etc.), the band gap is called the direct band gap-, while it is called the indirect band gap in cases in which the two band edge levels are at difierent wave vectors (Si, etc.). The band gap is e, = 1.1 eV for silicon and e, = 1.4 eV for gallium arsenide. 

FIGURE 8.8 Sketch of energy bands for (a) a solid with a direct band gap and (b) a solid with an indirect band gap. Note that in this diagram the horizontal axis is k, not the density of states. In this representation, a band is depicted as a line going from 0 to the maximum value of k occurring for that band. 

One consequence of an indirect band gap is that an electron in the bottom level of the conduction band has only a small probability of emitting a photon and returning to the top of the valence band. This is of importance when selecting materials for some of the applications we are going to consider. 

It should be noted that semiconductors with indirect band gaps are used for LEDs, but in these cases, impurity levels play an important role. Thus, GaP is used... 

Silicon is an indirect band gap solid with an available non-radiative pathway from the conduction band to the valence band. In photo voltaic cells, electrons are promoted from the valence band to the conduction band and are then used to do electrical work. The promoted electrons do not return directly to the valence band either by emitting energy or by a non-radiative pathway. In LEDs, the return of the electrons to the valence band by emitting light is important. This return has a low probability because of the indirect band gap and the electrons use the non-radiative pathway instead. Promotion to the conduction band in the solar cell will also be of low probability, but no competing non-radiative route is available. 

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