Indirect bandgap transition

Recent developments in solid state solutions of AlN/SiC/InN/GaN open up the possibility of a new generation of heterostructure devices based on SiC. Single crystal epitaxial layers of AlN/SiC/InN have been recently demonstrated by Dmitriev [4]. A whole range of solid state solutions has been grown. Recently Dmitriev et al [5] reported on an (AlNx-SiC,.x)-(AlNySiC,.y) p-n junction. Solid state solutions of AlN-SiC [6,7] are also expected to lead to direct gap ternary materials for UV and deep blue optoelectronics, including the development of visible lasers. The direct to indirect bandgap transition is predicted to occur at between 70 and 80 % of AIN in SiC. 

S-band hydrogen-terminated surface From near-infiared to blue 400-1,300 A few ns to 150 ps Yes Quantum confinement in Si nanocrystals indirect bandgap transitions blueshift upon size reduction (Cullis et al. 1997 Bisi et al. 2000 Wolkin et al. 1999)... 

Schematic of direct and indirect bandgap transition. The vertical transitions are allowed direct transitions. The indirect transition from the fc = 0 to the minimum of the conduction band requires the photon to combine with a phonon in order to conserve momentum.

The n parameter equals 1 for direct bandgap semiconductors or 4 for indirect bandgap semiconductors in the case of allowed fundamental transitions [22], Other values of n, 2 or 3, are valid only for forbidden transitions. The proper transformation allows estimation of the bandgap energy, Eg, for both types of crystalline semiconductors. Figure 7.7 presents the procedure of Eg evaluation. 

Fig. 1.7 Optical transitions in semiconductors with an indirect bandgap...

An electron hole pair is created in a semiconductor when a photon of sufficient energy is absorbed, resulting in excitation of an electron from the valence band to the conduction band [115]. In the context of semiconductor photoelectrochemistry, it is useful to distinguish between direct and indirect optical transitions. If the top of the valence band and the bottom of the conduction band are both situated at = 0 (A being the electron wave vector), one-step optical processes between delocalised states in the valence and conduction band can occur. The absorption coefficient for direct absorption of photons of energy hv, in a semiconductor with bandgap Eg is given by... 

The calculated values of the principal energy gaps reported are tabulated in TABLE 3 as well as those obtained from the optical measurements [3]. Herman et al [11] assigned the minimum indirect bandgap as the r6v-K2c transition. The value of this indirect T-K gap in the... 

Fig. 2.5 Optical transitions in semiconductors with a direct and an indirect bandgap. The indirect transition requires assistance of a phonon with energy hm...

Here, is a constant and m depends on the nature of the optical transition m = Vi for a direct bandgap, and ni = 2 for an indirect gap. From (2.6), extrapolation of a plot of (ahv) vs. hv plot gives the indirect bandgap, while a plot of (ahv) vs. hv yields the direct bandgap of the material. Such a plot is called a Tauc plot [7] and is often encoimtered in the photoelectrochemistry and photocatalysis literature. 

For direct and indirect bandgap optical transition, the ((cn) can be traditionally simplified as [25, 26]... 

In an indirect bandgap material such as Si and Ge, a transition at the bandgap energy must be accompanied by a phonon to supply the needed momentum to reach the conduction band at its lowest point, as illustrated in Figure 20.5. Such transitions are possible but are not as likely as the direct transitions possible in a direct bandgap material. This difference is reflected in the absorbance at the band edge as seen in Section 20.6. 

Photons may induce direct or vertical transitions from any occupied band to a higher energy band that is not completely full. Such transitions are called interband transitions and contribute to the absorption spectra. So even in an indirect bandgap material, valence electrons can be promoted vertically to the conduction band by adsorbing photons of sufficient energy. Once in the conduction band, the hot electrons become thermalized through collisions and will eventually move to the lowest point in the band. 

In a direct bandgap system such as GaAs, an electron may also make a transition from the conduction band directly to the valence band by giving off a photon with energy Eg. However, such a transition is not likely in an indirect bandgap system because the minimum in the conduction band, where the electrons are likely to reside, does not occur at fc = 0 (at E). In this case the transition, called a nonradiative transition, must involve a phonon and the energy Eg eventually goes into lattice vibrations or heat. Thus either... 

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