There are two basic types of scattering mechanisms that influence the mobility of electrons and holes: lattice scattering (also called phonon scattering) and impurity scattering. We have already discussed lattice scattering in the class; we know that lattice vibrations cause the mobility to decrease with increasing temperature. However, the mobility of the carriers in a semiconductor is also influenced by the presence of charged impurities. Impurity scattering is caused by crystal defects such as ionized impurities. At lower temperatures, carriers move more slowly, so there is more time for them to interact with charged impurities. As a result, as the temperature decreases, impurity scattering increases and the mobility decreases. This is just the opposite of the effect of lattice scattering. The total mobility then is the sum of the phonon-scattering mobility and the impurity-scattering mobility. Figure 1 shows how the total mobility has a temperature at which it is a maximum. The approximate temperature dependence of mobility due to lattice scattering is T-3/2 , while the temperature dependence of mobility due to impurity scattering is T+3/2 (see Figure 1). In practice, impurity scattering is typically only seen at very low temperatures. In the temperature range we will measure, only the influence of lattice scattering will be expected. Figure1. Approximate temperature dependence of mobility with both lattice and impurity scattering Temperature dependence of carrier concentration (density) The carrier concentration in a semiconductor is also affected by temperature. The intrinsic carrier concentration can be calculated using the electronic density of states (DOS) and Fermi distribution (or approx. by Boltzmann distribution). By using Boltzmann distribution, the intrinsic carrier density is given by: (3) where the exponential temperature dependence dominates ni(T). It can be also proved the following relationship so called Mass Law: (4) Where n(T) and p(T) are electron and hole densities. To determine the total carrier concentration, we must also consider space-charge neutrality condition: and: (5)
There are two basic types of scattering mechanisms that influence the mobility of electrons and holes: lattice scattering (also called phonon scattering) and impurity scattering. We have already discussed lattice scattering in the class; we know that lattice vibrations cause the mobility to decrease with increasing temperature. However, the mobility of the carriers in a semiconductor is also influenced by the presence of charged impurities. Impurity scattering is caused by crystal defects such as ionized impurities. At lower temperatures, carriers move more slowly, so there is more time for them to interact with charged impurities. As a result, as the temperature decreases, impurity scattering increases and the mobility decreases. This is just the opposite of the effect of lattice scattering. The total mobility then is the sum of the phonon-scattering mobility and the impurity-scattering mobility. Figure 1 shows how the total mobility has a temperature at which it is a maximum. The approximate temperature dependence of mobility due to lattice scattering is T-3/2 , while the temperature dependence of mobility due to impurity scattering is T+3/2 (see Figure 1). In practice, impurity scattering is typically only seen at very low temperatures. In the temperature range we will measure, only the influence of lattice scattering will be expected. Figure1. Approximate temperature dependence of mobility with both lattice and impurity scattering Temperature dependence of carrier concentration (density) The carrier concentration in a semiconductor is also affected by temperature. The intrinsic carrier concentration can be calculated using the electronic density of states (DOS) and Fermi distribution (or approx. by Boltzmann distribution). By using Boltzmann distribution, the intrinsic carrier density is given by: (3) where the exponential temperature dependence dominates ni(T). It can be also proved the following relationship so called Mass Law: (4) Where n(T) and p(T) are electron and hole densities. To determine the total carrier concentration, we must also consider space-charge neutrality condition: and: (5)
2011teachingnotebyProf.Shum.docx