Impurity scattering mobility

The proportionality factor is the electron mobility, xn, which has units of square centimeters per volt per second. The mobility is determined by electron-scattering mechanisms in the crystal. The two predominant mechanisms are lattice scattering and impurity scattering. Because the amplitude of lattice vibrations increases with temperature, lattice scattering becomes the dominant mechanism at high temperatures, and therefore, the mobility decreases with increasing temperature. 

Theory predicts that the mobility decreases as T 3/2 because of lattice scattering (8). But because electrons have higher velocities at high temperatures, they are less effectively scattered by impurities at high temperatures. Consequently, impurity scattering becomes less important with increasing temperature. Theoretical models predict that the mobility increases as T3/2/nj, in which nx is the total impurity concentration (8). The mobility is related to the electron diffusivity, Dn, through the Einstein relation... 

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... 

Neutral shallow-impurity scattering is often discussed in papers about transport in TCO films at room temperature [87,88]. The mobility due to neutral impurity scattering was first derived by Erginsoy [89] who scaled the electron scattering at hydrogen atoms to that in a semiconductor by using its dielectric constant and carrier effective mass, which leads to ... 

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]). 

FIGURE 1 Calculated electron drift mobilities at 300 K in GalnN and AlInN as a function of composition, in the limit of negligible ionised impurity scattering, after [8],... 

Figure 3. Resistivity p (a) and Hall mobility p (b) as a function of the carrier concentration n. Data from various laboratories T ZnO single crystals, ( , ) magnetron sputtering impurity doped, magnetron sputtering without impurity doping. The dashed line is the result of a theoretical estimate for impurity scattering.

The carrier mobility is determined mainly by impurity scattering at the low temperatures of extrinsic photoconductor operation. Furthermore, in the relatively uncompensated Si of most interest for detectors, scattering by the neutral majority dopant atoms will dominate. It can be shown that the neutral impurity scattering mobility is given in Si by [4.65]... 

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