Abstract
Carrier scattering, originating from deviations from ideal lattice periodicity, acts as a damping process for carrier motion. Both elastic and inelastic scattering involve a large variety of scattering centers. Carriers are scattered by acoustic and optical phonons, at neutral or charged impurities, at interfaces, and at other scattering centers. Most scattering events are elastic, changing only the momentum of a carrier but not its energy. Inelastic scattering involves optical phonons and intervalley scattering; in these processes carriers lose much of their energy to the lattice.
At low electric fields, many elastic scattering events precede an inelastic event. The dominating type of scattering changes with lattice temperature. Usually, ionized-impurity scattering prevails at low temperatures and scattering at phonons at high temperatures. The type of carrier scattering determines the relaxation time and with it the carrier mobility.
K. W. Böer: deceased
Notes
- 1.
These are electric fields F ≪ vrms/μ, where carriers gain only a small fraction of k T between scattering events; this means F ≪ 5×104 V/cm for a typical semiconductor with mn = 0.05 m0 and μ = 1000 cm2/(Vs).
- 2.
- 3.
The deformation potential is defined as the change in bandgap energy per unit strain and is typically on the order of 10 eV. For a listing, see Table 1. It should be noted that deformation potentials are generally tensors with components Ξij, relating the shift of the band edge δEc to the components of the strain tensor eij (see chapter “Elasticity and Phonons”): \( \delta E=\sum \limits_{ij}{\varXi}_{ij}\;{e}_{ij} \); Eq. 9 hence provides only an average in anisotropic media.
- 4.
The experimentally observed exponent of T is −1.67 for Ge (Conwell 1952) and not −1.5. The exponent of T for Si is still larger (≅ 2.4). Inserting actual values for Si (cl = 15.6·1010 N/m2, mn = 0.2 m0, and Ξ = 9.5 eV), one obtains μn = 5900 cm2/Vs, a value that is larger by a factor of ~4 than the measured μn = 1500 cm2/Vs at 300 K.
- 5.
K2 can be expressed as the ratio of the mechanical to the total work in a piezoelectrical material: \( {K}^2=\left({e}_{\mathrm{pz}}^2/{c}_l\right)/\left(\varepsilon\;{\varepsilon}_0+{e}_{\mathrm{pz}}^2/{c}_l\right) \), with epz the piezoelectric constant (which is on the order of 10−5 As/cm2), and cl the longitudinal elastic constant (relating the tension T to the stress S and the electric field F as T = cl S − epz F).
- 6.
Here, \( {F}_{\mathrm{opt}}=1+\frac{2}{\beta}\ln \left(\beta +1\right)+1/\left(\beta +1\right) \), With β = (2|k|LD)2; LD is the Debye length given in Eqs. 94 of chapter “Interaction of Light with Solids” and 49 of chapter “Crystal Interfaces”.
- 7.
- 8.
See Fig. 8b, which shows two equivalent transitions: one requires 2·0.8 π/a = 1.6 π/a in the extended E(k) diagram, but actually one needs only a momentum transfer of 2·0.2 π/a = 0.4 π/a.
- 9.
Umklapp processes were introduced for scattering in metals, in which changes in the magnitude of the momentum after scattering from one to another side of the near-spherical Fermi surface are even smaller.
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Böer, K.W., Pohl, U.W. (2020). Carrier Scattering at Low Electric Fields. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_23-3
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