Direct gap materials

This important selection rnle indicates that interband transitions mnst preserve the wave vector. Transitions that preserve the wave vector (snch as those marked by vertical arrows in Figure 4.8(a)) are called direct transitions, and they are easily observed in materials where the top point in the valence band has the same wave vector as the bottom point in the conduction band. These materials are called direct-gap materials. 

For some direct-gap materials, the quantum electronic selection rules lead to = 0. However, this is only strictly true at / = 0. For 0, it can be assumed, in a first order approximation, that the matrix element involving the top valence and the bottom conduction states is proportional to k that is, Pif k. Within the simplified model of parabolic bands (see Appendix Al), it is obtained that Tuo = Tuog + flp., and therefore Pif k co — cog). Thns, according to Equations (4.31) and (4.32), the absorption coefficient for these transitions (called forbidden direct transitions) has the following spectral dependence ... 

It should be noted that the frequency dependence is different to those expected for direct-gap materials, given by Equations (4.33) and (4.34). This provides a convenient way of determining the direct or indirect nature of a band gap in a particular material by simply analyzing the fundamental absorption edge. Table 4.3 summarizes the frequency dependence expected for the fundamental absorption edge of direct- and indirect-gap materials. 

Alg, Zn i, 0 crystallizes in the wurtzite or in the rocksalt structure, depending on the Mg mole fraction x. The alloys remain direct-gap materials over the whole composition range. The wurtzite-structure part reflects a valence-band structure, which is similar to ZnO. For the rocksalt-structure part the... 

No optical emission has been reported for AgF. Agl, which is a direct gap material, exhibits substantial excitonic emission from both low temperature crystal forms. The excitonic recombination shows up as a series of sharp lines on the high energy side of a broader emission band peaking at about 445 nm. This broader band exhibits donor-acceptor characteristics in that it shifts to longer wavelengths after pulsed excitation ( + 6nm after 15 ns) [70], This would suggest that in this direct gap material, a substantial fraction of the electrons and holes are trapped at donors and acceptors at liquid helium temperatures. 

This zone folding effectively creates a direct gap SLS material from bulk materials which have indirect band gaps. As depicted in Figure 6, the absorption coefficients for these materials are enhanced over that for indirect materials. However, this absorption is less than that for direct gap materials due to the spatial separation of the electrons and holes within the SLS (5,20,28). 

The success of piezospectroscopy experiments in the above materials strongly suggests the application to other indirect gap binary semiconductors such as AlSb, AlAs, etc. as well as indirect alloy materials such as GaAlAs, GaAsP, etc. In addition, information about intervalley EP and HP scattering matrix elements could also be obtained from ultra high pressure experiments (such as in a diamond anvil cell) where a direct gap material, such as GaAs, can be made indirect. 

On the other hand, SCs are divided into two types, depending on the kind of band gap direct-gap materials and indirect-gap materials (Fig. 8). Direct-gap materials... 

Indirect-gap materials are the materials for which the top of the VB and the bottom of the CB are not the same value of k (e.g.. Si, Ge, GaP). In the case of an indirect-gap SC, the transition of an electron between the VB and CB involves a substantial change in the momentum of the electron. Therefore, silicon, for instance, in the bulk form is not a luminescent light emitter, in contrast to direct-gap materials, which are mostly efficient emitters [68]. This difference between direct and indirect band structures is very important for LEDs, SC lasers, and PV cells. 

First consider the kind of universal cell structure which would satisfy our requirements. To conserve material, the photovoltaic-ally active semiconductors must be direct gap materials. If the solar cells are to be of the p/n homojunction type, excessive surface recombination losses, which are usually encountered at the light receiving surface, must be eliminated if high efficiencies are to be attained. One way to eliminate surface recombination losses is to use the direct gap semiconductor as the light absorbing, photovoltaically active part of a p/n heterojunction in which the other is a semiconductor whose band gap is so large that it cannot absorb any significant fraction of photons from the solar spectrum A heterojunction device of this type is illustrated in Fig. 6 [15]. ... 

The direct and indirect behaviors mentioned above are sufficiently important that they deserve special mention. The critical aspects of the energy band structures of these two types of semiconductor are shown schematically in Figure 2.8. The minimum energy of the conduction band in indirect materials is at a different momentum than that of the maximum energy of the valence band. Electrons in the conduction band rapidly relax to the minimum band energy. Holes equally rapidly move to the maximum energy of the valence band. Therefore, electrons and holes do not normally have the same momentum in an indirect semiconductor while in a direct-gap material these momenta are equal. This has consequences for the minority carrier lifetimes and optical properties of semiconductors. 

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