Direct gap

The occupied bands are called valence bands the empty bands are called conduction bands. The top of tire valence band is usually taken as energy zero. The lowest conduction band has a minimum along the A direction the highest occupied valence band has a maximum at F. Semiconductors which have the highest occupied k -state and lowest empty state at different points are called indirect gap semiconductors. If k = k, the semiconductor is call direct gap semiconductor. Gennanium is also an indirect gap semiconductor whereas GaAs has a direct gap. It is not easy to predict whether a given semiconductor will have a direct gap or not. 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

Calculated plots of energy bands as a function of wavevector k, known as band diagrams, are shown in figure C2.16.5 for Si and GaAs. Semiconductors can be divided into materials witli indirect and direct gaps. In direct-gap... 

Radiative recombination of minority carriers is tlie most likely process in direct gap semiconductors. Since tlie carriers at tlie CB minimum and tlie VB maximum have tlie same momentum, very fast recombination can occur. The radiative recombination lifetimes in direct semiconductors are tlius very short, of tlie order of tlie ns. The presence of deep-level defects opens up a non-radiative recombination patli and furtlier shortens tlie carrier lifetime. 

Figure C2.17.11. Exciton energy as a function of particle size. The Bms fonnula is used to calculate the energy shift of the exciton state as a function of nanocrystal radius, for several different direct-gap semiconductors. These estimates demonstrate the size below which quantum confinement effects become significant.

Fig. 7. Light-emission spectra of various LEDs emission from (—) AIGalnP LEDs results from direct gap recombination, whereas that of (-) GaP...

Fig. 6. Band gap versus lattice constant for Group 13—15 (III—V) semiconductors where (—) denotes direct gap and (-) iadirect. Liaes joining the...

Fig. 2. Electron drift velocities as a function of electric field for A, GaAs and B, Si The gradual saturation of curve B is characteristic of all indirect semiconductors. Curve A is characteristic of direct gap semiconductors and at low electric fields this curve has a steeper slope which reflects the larger electron mobiUty. The peak in curve A is the point at which a substantial fraction of the electrons have gained sufficient energy to populate the indirect L minimum which has a much larger electron-effective mass than the F minimum. Above 30 kV/cm (not shown) the drift velocity in Si exceeds that in...

As an example, PL can be used to precisely measure the alloy composition xof a number of direct-gap III-V semiconductor compounds such as Alj Gai j, Inj Gai jfAs, and GaAsjfPj j(, since the band gap is directly related to x. This is possible in extremely thin layers that would be difficult to measure by other techniques. A calibration curve of composition versus band gap is used for quantification. Cooling the sample to cryogenic temperatures can narrow the peaks and enhance the precision. A precision of 1 meV in bandgap peak position corresponds to a value of 0.001 for xin AljfGai j, which may be usefiil for comparative purposes even if it exceeds the accuracy of the x-versus-bandgap calibration. 

Extensive structural, optical, and electronic studies on the chalcopyrite semiconductors have been stimulated by the promising photovoltaic and photoelectrochem-ical properties of the copper-indium diselenide, CuInSe2, having a direct gap of about 1.0 eV, viz. close to optimal for terrestrial photovoltaics, and a high absorption coefficient which exceeds 10 cm . The physical properties of this and the other compounds of the family can be modulated to some extent by a slight deviation from stoichiometry. Thus, both anion and cation deficiencies may be tolerated, inducing, respectively, n- and p-type conductivities a p-type behavior would associate to either selenium excess or copper deficiency. 

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. 

Direct food additives, 12 29, 34 categories of, 22 30 function of, 22 30 Direct formed polyimides, 20 284 Direct fuel cells, 22 221 Direct-gap semiconductors, 14 837 ... 

Electron-donor end group, 20 504 Electron donors, in Ziegler-Natta polymerization, 26 518-521 Electron effective mass, in direct gap semiconductors, 22 143—144 Electronegativities, Pauling scale of,... 

Electron mobility, in direct gap semiconductors, 22 143-144 Electron paramagnetic resonance (epr), 17 418... 

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. 

EXAMPLE 4.3 Figure 4.9(a) shows the dependence of the absorption coefficient versus the photon energy for indium arsenide, (a) Determine whether or not InAs is a direct-gap semiconductor, (b) Estimate the band-gap energy, (c) If an InAs sample of 1 mm thickness is illuminated by a laser of 1 W at a wavelength of 2 jam, determine the laser power for the beam after it passes through the sample. Only consider the loss of light by optical absorption. 

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. 

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