Scattering ionized impurity

For lattice acoustic-mode deformation potential scattering, s =, giving r = /8 = 1.18. For ionized-impurity scattering, s = —f, giving rn0 = 315 /512 = 1.93. For a mixture of independent scattering processes we must... 

Consider a mixture of acoustic-mode (rL) and ionized-impurity (r,) scattering. For tL t, we would expect r 0 = 1.18 and for r, tl, rn0 = 1.93. But for intermediate mixtures, r 0 goes through a minimum value, dropping to about 1.05 at 15% ionized-impurity scattering (Nam, 1980). For this special case (sL = i, s, = — f), the integrals can be evaluated in terms of tabulated functions (Bube, 1974). For optical-mode scattering the relaxation-time approach is not valid, at least below the Debye temperature, but rn may still be obtained by such theoretical methods as a variational calculation (Ehrenreich, 1960 Nag, 1980) or an iterative solution of the Boltzmann equation (Rode, 1970), and typically varies between 1.0 and 1.4 as a function of temperature (Stillman et al., 1970 Debney and Jay, 1980). 

The maxima of the mobilities around 50-100 K are caused by the onset of ionized impurity scattering. The highest measured mobility at about 80 K is... 

Fig. 2.5. Temperature-dependent mobility of ZnO single crystals measured with the current flowing parallel (a) or perpendicular (b) to the c-axis of the crystals. The theoretical mobilities for the different scattering processes (optical, acoustical, and piezoelectric as well as ionized impurity scattering) as calculated by Wagner and Helbig [34,35] are shown as differently dashed lines. The calculated combined mobility curves (solid lines) fit the experimental data quite well for temperatures above about 20-50 K. The carrier concentrations at 300 K were about Ad — Na = 2.25 x 1016 cm 3 and Na = 2.75 x 1016 cm 3 (compensation ratio Aa/Ad = 0.55)...

Fig. 2.8. (a) Hall mobility as a function of the temperature for an undoped epitaxial ZnO layer and (b) Hall mobility of Ga-doped ZnO layers as a function of the carrier concentration. The ZnO films were grown epitaxially on lattice-matched ScAlMg04 (SCAM) by Makino et al. [64], In (a) the calculated mobilities for acoustical, polar-optical, piezoelectric, and ionized impurity scattering are shown, together with the total theoretical mobility. In (b) the solid curve is the fit curve (2.24) from Fig. 2.6, while the dashed line is the theoretical curve, calculated by Makino et al. [64]. The dotted line was calculated for transport across depletion regions at grain barriers (see Sect. 2.2.3), also present in epitaxial films [106]... 

As mentioned in the preceding section the mobility of degenerately-doped zinc oxide (as well as of other TCO materials and semiconductors) is limited by ionized impurity scattering in homogeneously-doped materials. Since about 30 years it is well known that the mobility can be increased by the so-called modulation doping method, introduced by Dingle et al. [179] for GaAs/C.ai, Af As superlattice structures (for a review see [180]). 

Fig. t(..1-95 GaAs. Temperature variation of Hall mobility at 5 kG for three n-GaAs samples. In the temperature range from 300 K to 77 K, the electron mobility of sample a is dominated by polar optical scattering. Samples b and c show increased effects of ionized-impurity scattering [1.88]... 

Fig.tr.1-123 InN. Electron mobility vs. temperature for three samples with RT carrier concentrations of 5.3 X IQi (1), 7.5 X 10 6 (2), and 1.8x 10 cm (3). Left broken line, calculated ionized-impurity-scattering mobility right broken line, empirical high-temperature mobility jjL (X T ) for sample 1. Solid lines, total mobdity calculated for each sample [1.109]... 

Ion intercalated crystalline W oxide films can be treated as strongly doped semiconductors. The inserted electrons make the material infrared reflecting, and the imavoidable ion-electron scattering hmits the metallic properties. Drade theory can be used for qualitative work, but is unable to give quantitative predictions. Instead, the Gerlach theory for ionized impurity scattering is of much value. Screening of the ions can be represented by the random phase approximation or an extension thereof This theory has been used before to model the optical properties of ITO in considerable detail. ... 

FIGURE 16.9. Computed spectral reflectance R for a 0.2-pm-thick slab of a material characterized by a theory for heavily doped semiconductors with ionized impurity scattering of the charge carriers. The electron density is denoted n,.. (From Granqvist, C., Handbook of Inorganic Electrochromic Materials, Elsevier Science, 1995. With permission.)... 

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