ENERGY 1-xPx 085155 23 INDIRECT MINIMUM ENERGY X=0.85 GaP GREEN GaAsP RED CONDUCTION BAND N TRAPPING LEVEL CON DUCTION BAND 一 ZnO TRAPPING LEVEL GREEN RED VALENCE BAND VALENCE BAND MOMENTUM FIGURE 83.3 (a) Plot of momentum versus bandgap energy, and(b)corresponding semiconductor parameters for va compounds of the GaAs/GaP system;(c) plot of momentum versus bandgap energy for indirect GaP materials showing special trapping levels. (Source: S Gage et al, Optoelectronics/Fiber-Optics Applications ManuaL, 2nd ed, New York: Hewlett Packard/McGraw-Hill, 1981, PP. 13-4. With permission. (where c is the velocity of light) is very small, and conservation of momentum can be readily accommodated by small deviations from the vertical transition shown in Fig. 83. 2(a). For the indirect case illustrated in Fig 83. 2(b), the energy change AE defines the photon energy and momentum, again according to Eqs. (83. 1) and(83. 2), but conservation of momentum additionally requires that the much greater electron momentum on the order of h/2a be accounted for. For lattice dimensions, a, on the order of 10-10 m and wavelengths, h, on the order of 10-m, it is clearly not possible for both conservation criteria to be met without the participation of a third body, i.e., a phonon. The two consequences of this result are that the indirect transition is inefficient (in that it must transfer momentum and hence thermal energy to the lattice)and less likely to occur than the direct transition(because of the requirement for all three particles to simultaneously meet the energy and momentum conditions). Indirect bandgaps therefore lead to long diffusion lengths and recombination times which produce good transistors but poor LEDs The most common direct-bandgap semiconductor is GaAs, but the photon wavelength calculated for E Ep=1.43 ev as listed in Fig. 83.3(b)is in the infrared. Such a material may be ideal for communications and sory optoelectronic applications but is unsuitable for display purposes. The bandgap may be adjusted, ver, by the substitution of phosphorus for arsenic in the lattice as shown in Fig. 83. 3(a). The color range sted corresponds to the range of LEd colors commonly available: red, yellow, and green. The direct and indirect bandgaps, Ep and Ep of GaAsk-Px vary with x as ED=1.441+1.091x+0.210x2 (83.3) E1=1.977+0.144x+0.211x2 (834) [ Wang, 1989], enabling one to design the material to produce the required LEd color. e 2000 by CRC Press LLC© 2000 by CRC Press LLC (where c is the velocity of light) is very small, and conservation of momentum can be readily accommodated by small deviations from the vertical transition shown in Fig. 83.2(a). For the indirect case illustrated in Fig. 83.2(b), the energy change DE defines the photon energy and momentum, again according to Eqs. (83.1) and (83.2), but conservation of momentum additionally requires that the much greater electron momentum on the order of h/2a be accounted for. For lattice dimensions, a, on the order of 10–10 m and wavelengths, l, on the order of 10–6 m, it is clearly not possible for both conservation criteria to be met without the participation of a third body, i.e., a phonon. The two consequences of this result are that the indirect transition is inefficient (in that it must transfer momentum and hence thermal energy to the lattice) and less likely to occur than the direct transition (because of the requirement for all three particles to simultaneously meet the energy and momentum conditions). Indirect bandgaps therefore lead to long diffusion lengths and recombination times, which produce good transistors but poor LEDs. The most common direct-bandgap semiconductor is GaAs, but the photon wavelength calculated for Eg = ED = 1.43 eV as listed in Fig. 83.3(b) is in the infrared. Such a material may be ideal for communications and sensory optoelectronic applications but is unsuitable for display purposes. The bandgap may be adjusted, however, by the substitution of phosphorus for arsenic in the lattice as shown in Fig. 83.3(a). The color range listed corresponds to the range of LED colors commonly available: red, yellow, and green. The direct and indirect bandgaps, ED and EI , of GaAs1–xPx vary with x as ED = 1.441 + 1.091x + 0.210x2 (83.3) and EI = 1.977 + 0.144x + 0.211x2 (83.4) [Wang, 1989], enabling one to design the material to produce the required LED color. FIGURE 83.3 (a) Plot of momentum versus bandgap energy, and (b) corresponding semiconductor parameters for various compounds of the GaAs/GaP system; (c) plot of momentum versus bandgap energy for indirect GaP materials showing special trapping levels. (Source: S. Gage et al., Optoelectronics/Fiber-Optics Applications Manual, 2nd ed., New York: Hewlett￾Packard/McGraw-Hill, 1981, pp. 1.3–4. With permission.)