Gap, band

There are difficulties in making such cells practical. High-band-gap semiconductors do not respond to visible light, while low-band-gap ones are prone to photocorrosion [182, 185]. In addition, both photochemical and entropy or thermodynamic factors limit the ideal efficiency with which sunlight can be converted to electrical energy [186]. 

Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

Irradiation of a semiconductor with light of quantum energy greater than the band gap can lead to electron-hole separation. This can affect adsorption and lead to photocatalyzed or photoassisted reactions [187]. See Section XVIII-9F for some specifics. 

Figure Al.3.8. Schematic energy bands illustrating an insulator (large band gap), a semiconductor (small band gap), a metal (no gap) and a semimetal. In a semimetal, one band is almost filled and another band is almost empty.

Semiconductors are poor conductors of electricity at low temperatures. Since the valence band is completely occupied, an applied electric field caimot change the total momentum of the valence electrons. This is a reflection of the Pauli principle. This would not be true for an electron that is excited into the conduction band. However, for a band gap of 1 eV or more, few electrons can be themially excited into the conduction band at ambient temperatures. Conversely, the electronic properties of semiconductors at ambient temperatures can be profoundly altered by the... 

Several factors detennine how efficient impurity atoms will be in altering the electronic properties of a semiconductor. For example, the size of the band gap, the shape of the energy bands near the gap and the ability of the valence electrons to screen the impurity atom are all important. The process of adding controlled impurity atoms to semiconductors is called doping. The ability to produce well defined doping levels in semiconductors is one reason for the revolutionary developments in the construction of solid-state electronic devices. 

It is possible to identify particular spectral features in the modulated reflectivity spectra to band structure features. For example, in a direct band gap the joint density of states must resemble that of critical point. One of the first applications of the empirical pseudopotential method was to calculate reflectivity spectra for a given energy band. Differences between the calculated and measured reflectivity spectra could be assigned to errors in the energy band... 

Even in semiconductors, where it might appear that the exciton binding energies would be of interest only for low temperaPire regimes, excitonic effects can strongly alter tlie line shape of excitations away from the band gap. 

Figure B3.2.5. The imaginary part of the dieleetrie fiinetion of GaAs, aeeording to tire AFC ELAPW-/c p method (solid eiirve) [195] and the experiment (dashed enrve) [196], To eorreet for the band gap underestimated by the loeal density approximation, the eonduetion bands have been shifted so that tlie 2 peaks agree in theory and experiment.

Flybertsen M S and Louie S G 1985 First-principles theory of quasiparticles Calculation of band gaps in semiconductors and insulators Phys. Rev. Lett. 55 1418... 

Saito A Y, Shinohara FI, Kato M, Nagashima FI, Ohkohohi M and Ando Y 1992 Eleotrio oonduotivity and band gap of solid Cgg under high pressure Chem. Rhys. Lett. 186 236... 

Germanium is very similar to Si, but its band gap is too small for many practical applications. Large crystals of ultra-high-purity Ge have been grown for use as gamma-ray detectors. In such crystals, the net concentration of... 

Figure C2.17.10. Optical absorjDtion spectra of nanocrystalline CdSe. The spectra of several different samples in the visible and near-UV are measured at low temperature, to minimize the effects of line broadening from lattice vibrations. In these samples, grown as described in [84], the lowest exciton state shifts dramatically to higher energy with decreasing particle size. Higher-lying exciton states are also visible in several of these spectra. For reference, the band gap of bulk CdSe is 1.85 eV.

Here, E and s are the band gap energy and the dielectric constant of the bulk semiconductor, and p is the reduced 0 mass of the exciton system, 1/p = + 1/fffi,. The second tenn, proportional to /R, arises from a simple... 

Fig. 3.19 The effect of a weak external potential is to lift degeneracy and create band gaps as illustrated for a 2D hexagonal lattice (compare with Figure 3.18).

Boron of 99.9999% purity has been produced and is available commercially. Elemental boron has an energy band gap of 1.50 to 1.56 eV, which is higher than that of either silicon or germanium. 

In some cases, researchers only need to know the band gap for a crystal. Once a complete band structure has been computed, it is, of course, simple to find the... 

Simply doing electronic structure computations at the M, K, X, and T points in the Brillouin zone is not necessarily sufficient to yield a band gap. This is because the minimum and maximum energies reached by any given energy band sometimes fall between these points. Such limited calculations are sometimes done when the computational method is very CPU-intensive. For example, this type of spot check might be done at a high level of theory to determine whether complete calculations are necessary at that level. 

Some researchers use molecule computations to estimate the band gap from the HOMO-LUMO energy separation. This energy separation becomes smaller as the molecule grows larger. Thus, it is possible to perform quantum mechanical calculations on several molecules of increasing size and then extrapolate the energy gap to predict a band gap for the inhnite system. This can be useful for polymers, which are often not crystalline. One-dimensional band structures are... 

Extended Hiickel gives a qualitative view of the valence orbitals. The formulation of extended Hiickel is such that it is only applicable to the valence orbitals. The method reproduces the correct symmetry properties for the valence orbitals. Energetics, such as band gaps, are sometimes reasonable and other times reproduce trends better than absolute values. Extended Hiickel tends to be more useful for examining orbital symmetry and energy than for predicting molecular geometries. It is the method of choice for many band structure calculations due to the very computation-intensive nature of those calculations. 

As described in the chapter on band structures, these calculations reproduce the electronic structure of inhnite solids. This is important for a number of types of studies, such as modeling compounds for use in solar cells, in which it is important to know whether the band gap is a direct or indirect gap. Band structure calculations are ideal for modeling an inhnite regular crystal, but not for modeling surface chemistry or defect sites. 

Figure 9.8(a) shows how the conduction band C and the empty valence band V are not separated in a conductor whereas Figure 9.8(c) shows that they are well separated in an insulator. The situation in a semiconductor, shown in Figure 9.8(b), is that the band gap, between the conduction and valence bands, is sufficiently small that promotion of electrons into the conduction band is possible by heating the material. For a semiconductor the Fermi energy E, such that at T= 0 K all levels with E < are filled, lies between the bands as shown. 

Semiconductors may also be made from a maferial which is normally an insulator by infroducing an impurify, a process known as doping. Figure 9.9 shows fwo ways in which an impurify may promote semiconducting properties. In Figure 9.9(a) fhe dopanf has one more valence election per atom fhan fhe hosf and confribufes a band of filled impurify levels 1 close to fhe conduction band of fhe hosf. This characterizes an n-fype semiconductor. An example is silicon (KL3s 3p ) doped wifh phosphoms (KL3s 3p ), which reduces fhe band gap to abouf 0.05 eY Since kT af room femperafure is abouf 0.025 eY the phosphoms... 

Alternatively, as in Figure 9.9(b), a dopant with one valence electron fewer than the host contributes an impurity band 1 which is empty but more accessible to electrons from the valence band. An example of such a p-type semiconductor is silicon doped with aluminium KL3s 3p ) in which the band gap is about 0.08 eY... 

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