FIGURE 22.2 Band diagrams of metal (a)and semiconductor(b);, electron; o, missing electron(he 11 FIGURE 22.3 Simplified E(k) dependence for Si(a)and GaAs(b) At room temperature E Si)=1.12 eV,E(GaAs)=1. 43 ev, and A=0.31 eV; (1)and(2)indicate direct and indirect band-to-band transitions While considering the contribution j, of the predominantly filled valence band to the current density, it is convenient to concentrate on the few missing electrons. This is achieved as follows: let uk) be the velocity of electron described by the wave function(20.2). Then i=-9∑k)=-∑vk)-∑k) (223) Here we have noted again that a completely filled band does not contribute to the current density. The picture emerging from(22. 3)is that of particles(known as holes) with the charge +q and velocities corresponding to those of missing electrons. The concentration of holes in the valence band is controlled by adding acceptor type impurities(such as boron in silicon), which form local energy levels close to the top of the valence band At room temperature these energy levels are occupied by electrons that come from the valence band and leave e 2000 by CRC Press LLC© 2000 by CRC Press LLC While considering the contribution jp of the predominantly filled valence band to the current density, it is convenient to concentrate on the few missing electrons. This is achieved as follows: let v(k) be the velocity of electron described by the wave function (20.2). Then (22.3) Here we have noted again that a completely filled band does not contribute to the current density. The picture emerging from (22.3) is that of particles (known as holes) with the charge +q and velocities corresponding to those of missing electrons. The concentration of holes in the valence band is controlled by adding acceptor￾type impurities (such as boron in silicon), which form local energy levels close to the top of the valence band. At room temperature these energy levels are occupied by electrons that come from the valence band and leave FIGURE 22.2 Band diagrams of metal (a) and semiconductor (b); ●, electron; C, missing electron (hole). FIGURE 22.3 Simplified E(k) dependence for Si (a) and GaAs (b). At room temperature Eg(Si) = 1.12 eV, Eg(GaAs) = 1.43 eV, and D = 0.31 eV; (1) and (2) indicate direct and indirect band-to-band transitions. jp = -q q v k = - v k - v k q v k È Î Í Í Í ˘ ˚ ˙ ˙ ˙ Â Â ( ) Â ( ) Â ( ) = ( ) empty states filled all states states empty states