Diamond E(kv/cm) 107cm.(Source: R.J. Trew, J. B Yan, and LM. Mack, Proc. IEEE, voL. 79, no 5,P 602, May 1991.@ 1991 IEEE)aS applications. Since T: o Eg the transition to the intrinsic region can be delayed by using widegap semiconductors. Both silicon carbide(several types of SiC with different lattice structures are available with Eg=2.2-2.86 ev) and diamond (Eg=5.5 ev) have been used to fabricate diodes and transistors operating in the 300-700.C temperature range. Transport Properties In a semiconductor the motion of an electron is affected by frequent collisions with phonons(quanta of lattice vibrations), impurities, and crystal imperfections. In weak uniform electric fields, 2, the carrier drift velocity, Va is determined by the balance of the electric and collision forces m*valt=-ga (22.7) where t is the momentum relaxation time. Consequently va=--, 6, where um gt/m is the electron mobility. For an n-type semiconductor with uniform electron density, n, the current density j,=-gnva and we obtain Ohms law in =08 with the conductivity o= qnu The momentum relaxation time can be approximately expressed as l/t=1/ta+1/tn+l/t+1/t+1/t+l/t。+ (228) where ta tna tas tnpoTpo Tpe are the relaxation times due to ionized impurity, neutral impurity, acoustic phonon nonpolar optical, polar optical, and piezoelectric scattering, respectively. In the presence of concentration gradients, electron current density is given by the drift-diffusion equation jn=q叫ng+qD2V (22.9) where the diffusion coefficient D, is related to mobility by the Einstein relation D,=(kgTlq)u, A similar equation can be written for holes and the total current density is j=jn+je The right-hand side of (22.9)may contain additional terms corresponding to temperature gradient and compositional nonunifor mity of the material [Wolfe et al, 1989] In sufficiently strong electric fields the drift velocity is no longer proportional to the electric field. Typical relocity-field dependencies for several semiconductors are shown in Fig. 22.5. In GaAs va 8)dependence is not monotonic,which results in negative differential conductivity. Physically, this effect is related to the transfer of electrons from the conduction band to a secondary valley(see Fig. 22.3) The limiting value v, of the drift velocity in a strong electric field is known as the saturation velocity and is usually within the 10-3.10 cm/s range. As semiconductor device dimensions are scaled down to the submi crometer range, v, becomes an important parameter that determines the upper limits of device performance e 2000 by CRC Press LLC© 2000 by CRC Press LLC applications. Since Ti } Eg the transition to the intrinsic region can be delayed by using widegap semiconductors. Both silicon carbide (several types of SiC with different lattice structures are available with Eg = 2.2–2.86 eV) and diamond (Eg = 5.5 eV) have been used to fabricate diodes and transistors operating in the 300–700°C temperature range. Transport Properties In a semiconductor the motion of an electron is affected by frequent collisions with phonons (quanta of lattice vibrations), impurities, and crystal imperfections. In weak uniform electric fields, %, the carrier drift velocity, vd, is determined by the balance of the electric and collision forces: mn *vd /t = –q% (22.7) where t is the momentum relaxation time. Consequently vd = –mn%, where mn= qt/m* n is the electron mobility. For an n-type semiconductor with uniform electron density, n, the current density jn= –qnvd and we obtain Ohm’s law jn = s% with the conductivity s = qnmn. The momentum relaxation time can be approximately expressed as 1/t = 1/tii + 1/tni + 1/tac + 1/tnpo + 1/tpo + 1/tpe + . . . (22.8) where tii, tni, tac, tnpo, tpo, tpe are the relaxation times due to ionized impurity, neutral impurity, acoustic phonon, nonpolar optical, polar optical, and piezoelectric scattering, respectively. In the presence of concentration gradients, electron current density is given by the drift-diffusion equation jn = qnmn% + qDn—n (22.9) where the diffusion coefficient Dn is related to mobility by the Einstein relation Dn = (kBT/q)mn. A similar equation can be written for holes and the total current density is j = jn + jp. The right-hand side of (22.9) may contain additional terms corresponding to temperature gradient and compositional nonunifor￾mity of the material [Wolfe et al., 1989]. In sufficiently strong electric fields the drift velocity is no longer proportional to the electric field. Typical velocity–field dependencies for several semiconductors are shown in Fig. 22.5. In GaAs vd(%) dependence is not monotonic, which results in negative differential conductivity. Physically, this effect is related to the transfer of electrons from the conduction band to a secondary valley (see Fig. 22.3). The limiting value vs of the drift velocity in a strong electric field is known as the saturation velocity and is usually within the 107 –3·107 cm/s range. As semiconductor device dimensions are scaled down to the submi￾crometer range, vs becomes an important parameter that determines the upper limits of device performance. FIGURE 22.5 Electron (a) and hole (b) drift velocity versus electric field dependence for several semiconductors at Nd = 1017 cm–3. (Source: R.J. Trew, J.-B. Yan, and L.M. Mack, Proc. IEEE, vol. 79, no. 5, p. 602, May 1991. © 1991 IEEE.)