Semiconductors, optical transitions

Direct semiconductors have strongly allowed optical transitions, with relatively short radiative rate constants and thus short-lived excited states, which can be highly emissive following excitation. For indirect semiconductors optical transitions are forbidden, absorption coefiftcients are low, they have relatively long radiative lifetimes and therefore potentially long-lived excited states, and deactivation after excitation is not usually emissive. 

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. 

Fig. 21. Energy level diagram for a semiconductor photoanode sensitized by a dye (D) layer. The black arrow indicates the optical transition on the dye. The semiconductor is on the left-hand side...

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... 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

The situation is utterly different for semiconductors or insulators with a wide enough band gap 6.8,27,28). if the band gap exceeds the energy range of the fluorescence spectrum of the dye, energy transfer is either prevented or at least reduced to a very small rate which is controlled by the number of electronic energy levels within the band gap of the semiconductor or insulator. Such states are usually localized and can be caused by impurities or structural defects and represent optical transitions with a low oscillator strength. With a suitable position of the... 

Energy band gaps for selected semiconductors are summarized in Table I. On the basis of the nature of the transition from the valence band to the conduction band, semiconductors are classified as direct or indirect. In a direct semiconductor, the transition does not require a change in electron momentum, whereas in an indirect semiconductor, a change in momentum is required for the transition to occur. This difference is important for optical devices such as lasers, which require direct-band-gap materials for efficient radiation emission (7, 8). As indicated in Figure 7, Si is an indirect semiconductor, whereas GaAs is a direct semiconductor. 

The transition from LDA to HDA Si was observed in the successive experiment by McMillan et al. [264]. In situ Raman spectra and electronic resistance measurements were performed with optical observation. After compression, the LDA form prepared by solid-state metathesis synthesis [10] was found to be transformed to the HDA form at 14 GPa. The electronic resistance exhibited a sharp decrease at 10-14 GPa (Fig. 15), which is consistent with the early experimental findings by Shimomura et al. [260], Optical micrographs show that HDA Si is highly reflective, whereas LDA Si is dark colored and nonreflective. This finding again supports that the LDA-HDA transition of Si is accompanied by a semiconductor-metal transition. Reverse transitions with large hysteresis were also observed LDA Si began to form from HDA Si at 4-6 GPa after decompression from --20 GPa. 

Hydrogenated amorphous silicon, a new form of a common element, is a semiconductor that has come of age. Its scientific attractions include a continuously adjustable band gap, a usable carrier lifetime and diffusion length, efficient optical transitions, and the capability of employing either n-or p-type dopants. 

V.L. Rupasov, V.I. Klimov, Carrier multiplication in semiconductor nanocrystals via intraband optical transitions involving virtual biexdton states, Phys. Rev. B 76 (2007) 125321. 

NiO 3.47 A p-type semiconductor with indirect gap optical transition. 371, 372... 

YFeOs 2.58 N-type semiconductor with an indirect optical transition. 428... 

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. 

Thermally-induced network vibrations broaden the absorption edge and shift the band gap of semiconductors. The thermal disorder couples to the optical transition through the deformation potential, which describes how the electronic energy varies with the displacement of the atoms. The bond strain in an amorphous material is also a displacement of atoms from their ideal position, and can be described by a similar approach. The description of static disorder in terms of frozen phonons is a helpful concept which goes back 20 years. Amorphous materials, of course, also have the additional disordering of the real phonon vibrations. 

Indirect band gap means that the minimum of the conduction band and the maximum of the valence band are at different positions in the Brillouin zone, i.e., the electrons in the corresponding quantum states have different wave vectors k. Because the momentum of a photon is very small the optical transitions (absorption, emission) of the electrons have to occur with M = 0. GaAs and many other compound semiconductors are efficient optoelectronic materials because of their direct band gap. In silicon, however, such transitions between the top of the valence and bottom of the conduction bands require assistance of a phonon which delivers the momentum needed [2, 3]. 

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