5.2 Low Field Transport
First we consider small electric fields. In the low-field regime the velocity is proportional to the electric field.
5.2.1 Mobility
The mobility is defined（scalar terms）as
μ＝v／E （5.2）
By definition，it is a negative number for electrons and positive for holes. 
However，the numerical value is usually given as a positive number for both carrier types. In an intrinsic semiconductor the mobility is determined by scattering with phonons. Further scattering is introduced by impurities，defects or alloy disorder. The conductivity is
σ＝qnμ （5.3）
As a unit，usually cm2/（V·s）is used. While Cu at room temperature has a mobility of 35 cm2/（V·s），semiconductors can have much higher values. In two-dimensional electron gases，the mobility can reach several 107 cm2/（V·s）at low temperature. In bulk semiconductors with small bandgap，a high electron mobility is caused by its small effective mass. Some typical values are given in Tab.5.1.
Tab.5.1 Mobilities ［in cm2/（V·s）］for electrons and holes at room temperature for various semiconductors
5.2.2 Microscopic Scattering Processes
There are two collision or scattering mechanisms that dominate in a semiconductor and affect the carrier mobility：phonon or lattice scattering，and ionized impurity scattering .
The atoms in a semiconductor crystal have a certain amount of thermal energy at temperatures above absolute zero that causes the atoms to randomly vibrate about their lattice position within the crystal. The lattice vibrations cause a disruption in the perfect periodic potential function. A perfect periodic potential in a solid allows electrons to move unimpeded，or with no scattering，through the crystal. But the thermal vibrations cause a disruption of the potential function，resulting in an interaction between the electrons or holes and the vibrating lattice atoms. This lattice scattering is also referred to as phonon scattering.
Lattice scattering is related to the thermal motion of atoms，the rate at which the scattering occurs is a function of temperature. If we denote μL as the mobility that would be observed if only lattice scattering existed，then the scattering theory states that to first order
提示：to first order指“一阶近似”。
Mobility that is due to lattice scattering increases as the temperature decreases. Intuitively，we expect the lattice vibrations to decrease as the temperature decreases，which implies that the probability of a scattering event also decreases，thus increasing mobility.
Fig.5.4 shows the temperature dependence of electron and hole mobilities in silicon. In lightly doped semiconductors，lattice scattering dominates and the carrier mobility decreases with temperature as we have discussed. The temperature dependence of mobility is proportional to T-n. The inserts in the figure show that the parameter n is not equal to 3/2 as the first-order scattering theory predicted. However，mobility does increase as the temperature decreases.
Fig 5.4（a）Electron and（b）hole mobility in silicon versus temperature for various doping concentration.
The second interaction mechanism affecting carrier mobility is called ionized impurity scattering. We have seen that impurity atoms are added to the semiconductor to control or alter its characteristics. These impurities are ionized at room temperature so that a coulomb interaction exists between the electrons or holes and the ionized impurities. This coulomb interaction produces scattering or collisions and also alters the velocity characteristics of the charge carrier. If we denote μI as the mobility that would be observed if only ionized impurity scattering existed，then to first order we have
Fig.5.5 Electron and hole mobilities versus impurity concentrations for germanium，silicon. and gallium arsenide at T=300K.
where NI=N+d+N－a is the total ionized impurity concentration in the semiconductor. If temperature increases，the random thermal velocity of a carrier increases，reducing the time the carrier spends in the vicinity of the ionized impurity center. The less time spent in the vicinity of a coulomb force，the smaller the scattering effect and the larger the expected value of μI . If the number of ionized impurity centers increases，then the probability of a carrier encountering an ionized impurity center increases，implying a smaller value of μI .
Fig.5.5 is a plot of electron and hole mobilities in germanium，silicon，and gallium arsenide at T=300 K as a function of impurity concentration. More accurately，these curves are of mobility versus ionized impurity concentration NI. As the impurity concentration increases，the number of impurity scattering centers increases，thus reducing mobility.