FIGURE 22.7 Experimental curves for the Hall resistance Px =8 jx and the resistivity Px =6 jx of a heterostructure as a function of the magnetic field at a fixed carrier density. Source: K. von Klitzing, Rev. Modern Phys., voL 58, no 3, P 525 1986. With permission. TABLE 22.1 Impact lonization Threshold Energy(ev) Energy gap, E electron-initiated 1.18 0.76 1.7 2.6 0.2 Eh, hole-initiated 1710.88142.30.2 where x=qa/Eh, a=0.217(E, /En )-14, A is the carrier mean free path, and Eo is the optical phonon energy (Eopt =0.063 eV for Si at 300%C) An alternative breakdown mechanism is tunneling breakdown, which occurs in highly doped semiconductors when electrons may tunnel from occupied states in the valence band into the empty states of the conduction Optical Properties and Recombination Processes If the energy of an incident photon ho Eg, then the energy conservation law permits a direct band-to-band transition,as indicated in Fig 22. 2(b). Because the photons momentum is negligible compared to that of an electron or hole, the electrons momentum hk does not change in a direct transition. Consequently, direct transitions are possible only in direct-gap semiconductors where the conduction band minimum and the valence band maximum occur at the same k The same is true for the reverse transition where the electron is transferred© 2000 by CRC Press LLC where x = q%l/Eth, a = 0.217 (Eth/Eopt)1.14, l is the carrier mean free path, and Eopt is the optical phonon energy (Eopt = 0.063 eV for Si at 300°C). An alternative breakdown mechanism is tunneling breakdown, which occurs in highly doped semiconductors when electrons may tunnel from occupied states in the valence band into the empty states of the conduction band. Optical Properties and Recombination Processes If the energy of an incident photon \w > Eg, then the energy conservation law permits a direct band-to-band transition, as indicated in Fig. 22.2(b). Because the photon’s momentum is negligible compared to that of an electron or hole, the electron’s momentum \k does not change in a direct transition. Consequently, direct transitions are possible only in direct-gap semiconductors where the conduction band minimum and the valence band maximum occur at the same k. The same is true for the reverse transition, where the electron is transferred FIGURE 22.7 Experimental curves for the Hall resistance rxy = %y /jx and the resistivity rxx = %x /jx of a heterostructure as a function of the magnetic field at a fixed carrier density. (Source: K. von Klitzing, Rev. Modern Phys., vol. 58, no. 3, p. 525, 1986. With permission.) TABLE 22.1 Impact Ionization Threshold Energy (eV) Semiconductor Si Ge GaAs GaP InSb Energy gap, Eg 1.1 0.7 1.4 2.3 0.2 Eth, electron-initiated 1.18 0.76 1.7 2.6 0.2 Eth, hole-initiated 1.71 0.88 1.4 2.3 0.2