Optical transitions in semiconductors

Optical transitions in semiconductors can also involve localized states in the band-gap. These become particularly important for semiconductors in nanocrystalline form (see below). Sub-band-gap transitions can be probed with photons of energy below the threshold defined by Eg. 

Lasing on Intraband Optical Transitions in Semiconductor Nanocrystals... 

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

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...

The conservation of momentum selection rules does not apply to optical transitions in amorphous semiconductors. Consequently, the distinction is lost between a direct and an indirect band gap, the latter being those transitions which are forbidden by momentum conservation. Instead transitions occur between states which overlap in real space. This distinction is most obvious in silicon which has an indirect band gap in its crystalline phase but not in the amorphous phase. 

Fast nonradiative relaxation of intraband transitions in semiconductor nanoeiystals with the relaxation times shorter than 1 picosecond is obviously the major obstacle of lasing on these optical transitions. Although, at present time mechanism of the nonradiative relaxation is not clear, it has been recently demonstrated experimentally that fast nonradiative relaxation of intraband transitions is mainly determined by their strong... 

Since many-body optical transitions in zero-dimensional objects was demonstrated experimentally, it is important to assess this phenomenon from the perspective of the well established field of many-body luminescence. This is accomplished in the present chapter. Below we review the many-body luminescence in various systems studied to date experimentally and theoretically. We then demonstrate that many-body luminescence from highly excited zero-dimensional objects has unique features due to large number of discrete lines. This discreteness unravels the many-body correlations that are otherwise masked in the continuous spectrum of luminescence from infinite systems. We describe in detail the emergence of such correlations for a particular nanostructure geometry - semiconductor nanorings - using the Luttinger liquid approach for quasi-one-dimensional finite-size systems. 

Shakeup represents a fundamental many-body effect that takes place in optical transitions in many-electron systems. In such systems, an absorption or emission of light is accompanied by electronic excitations in the final state of the transition. The most notable shakeup effect is the Anderson orthogonality catastrophe [5] in the electron gas when the initial and final states of the transition have very small overlap due to the readjustment of the Fermi sea electrons in order to screen the Coulomb potential of pho-toexcited core hole. Shakeup is especially efficient when the optical hole is immobilized, and therefore it was widely studied in conjunction with the Fermi edge singularity (FES) in metals [6-8] and doped semiconductor quantum wells [9-15]. Comprehensive reviews of FES and related issues can be found in Refs. [16,17]. 

W. Kautek, H. Gerischer, and H. Tributsch, The role of carrier diffusion and indirect optical transitions in the photoelectrochemical behavior of layer type J-band semiconductors, J. Electrochem. Soc. 127 (1980) 2471-2478. 

We shall now discuss a model we shall use for the description of optical transitions in amorphous semiconductors. The basic difference compared to crystals is the non-conservation of the k-vector. This is due to the change of the character of the wave-functions, some of which become localized over a certain volume V(E) rather than extended over the whole volume of the sample as in crystals. When the wavefunctions are localized, the transition probabilities between states localized at different sites are reduced by a factor depending on the overlap of the wavefunctions of the initial and final states. The effects of conelation were considered by Stem (1971), Dow and Hopfield (1971) and Sak (1972). We shall neglect the correlation and consider only transitions between states of which one is localized and the other extended, or of which both are weakly localized so that the over-... 

Optical transitions In a semiconductor are strongly Influenced by the distribution of carriers In the conduction and valence bands. For direct transitions away from exclton resonances the absorption coefficient d can be expressed as... 

Figure 3.2 Optical transitions in a direct bandgap semiconductor on the energy versus momentum (which also represents energy versus density of states though the functional forms deviate) diagram, which is pumped beyond transparency. The transitions 1= 1, 2, 3,...

PL is generally most usefril in semiconductors if their band gap is direct, i.e., if the extrema of the conduction and valence bands have the same crystal momentum, and optical transitions are momentum-allowed. Especially at low temperatures. 

Various polymorphs have been reported for SnS with band gap widths in the range 1.0-1.5 eV, depending on the preparation method. The a-SnS (herzenbergite) is the most frequently occurring phase and is a p-type semiconductor with a direct optical transition at 1.3 eV and a high absorption coefficient (> 10" cm ). The orthorhombic S-SnS phase possesses a direct gap between 1.05 and 1.09 eV. 

In this paper we will describe and discuss the metal-to-metal charge-transfer transitions as observed in optical spectroscopy. Their spectroscopic properties are of large importance with regard to photoredox processes [1-4], However, these transitions are also responsible for the color of many inorganic compounds and minerals [5, 6], for different types of processes in semiconductors [7], and for the presence or absence of certain luminescence processes [8]. 

Let us now return to MMCT effects in semiconductors. In this class of compounds MMCT may be followed by charge separation, i.e. the excited MMCT state may be stabilized. This is the case if the M species involved act as traps. A beautiful example is the color change of SrTiOj Fe,Mo upon irradiation [111]. In the dark, iron and molybdenum are present as Fe(III) and Mo(VI). The material is eolorless. After irradiation with 400 nm radiation Fe(IV) and Mo(V) are created. These ions have optical absorption in the visible. The Mo(VI) species plays the role of a deep electron trap. The thermal decay time of the color at room temperature is several minutes. Note that the MMCT transition Fe(III) + Mo(VI) -> Fe(IV) -I- Mo(V) belongs to the type which was treated above. In the semiconductor the iron and molybdenum species are far apart and the conduction band takes the role of electron transporter. A similar phenomenon has been reported for ZnS Eu, Cr [112]. There is a photoinduced charge separation Eu(II) -I- Cr(II) -> Eu(III) - - Cr(I) via the conduction band (see Fig. 18). 

One important feature of compound semiconductors is that their bands span a much wider range that of elemental silicon and can therefore cover a wider range of the electromagnetic spectrum, in particular the visible region. Compound semiconductors are also more often direct, i.e., there is conservation of the wave vector for optical transitions, leading to allowed... 

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