Effects of Temperature and Doping on Mobility
Effects of Temperature and Doping on Mobility:
- The two basic types of scattering mechanisms that influence electron and hole mobility are lattice scattering and impurity scattering.
- In lattice scattering a carrier moving through the crystal is scattered by a vibration of the lattice, resulting from the temperature.
- The frequency of such scattering events increases as the temperature increases, since the thermal agitation of the lattice becomes greater.
- Therefore, we should expect the mobility to decrease as the sample is heated (Fig. given below).
- On the other hand, scattering from crystal defects such as ionized impurities becomes the dominant mechanism at low temperatures.
- Since the atoms of the cooler lattice are less agitated, lattice scattering is less important; however, the thermal motion of the carriers is also slower.
- Since a slowly moving carrier is likely to be scattered more strongly by an interaction with a charged ion than is a carrier with greater momentum, impurity scattering events cause a decrease in mobility with decreasing temperature.
- Fig. given below indicates, the approximate temperature dependencies are T-3/2 for lattice scattering and T3/2 for impurity scattering.
- Since the scattering probability is inversely proportional to the mean free time and therefore to mobility, the mobilities due to two or more scattering mechanisms add inversely:
As a result, the mechanism causing the lowest mobility value dominates, as shown in Fig. given below.
As the concentration of impurities increases, the effects of impurity scattering are felt at higher temperatures.
For example, the electron mobility μn of intrinsic silicon at 300 K is 1350 cm2/(V-s).
With a donor doping concentration of 1017 cm-3, however, μn is 700 cm2/(V-s).
Thus, the presence of the 1017 ionized donors/cm3 introduces a significant amount of impurity scattering.