Elaboration of Mobility Dependent on Temperature in Doped Semiconductors with Proposed Playground Model

A playground model is proposed to elaborate on the dependence of carrier mobility on temperature in doped semiconductors. In the proposed model, carriers are subject to coulomb scattering of ionized impurities and move clockwise in a circular motion. When the carrier moves to the position underlying the ionized impurity, it moves away from the ionized impurity along a straight line. When it moves to the position underlying the neighboring ionized impurity, the carrier is captured by the ionized impurity, and its motion trail converts from the linear motion to the clockwise uniform circular motion. Thus, the playground model is constructed, and the carrier is constrained by two neighboring ionized impurities which are far apart. The carrier’s motion period is composed of both the coulomb scattering time in the circular motion and the non-coulomb interaction time in two straight lines. When the temperature increases, the velocity of the carrier increases, and it moves toward the direction far away from the ionized impurities because the Coulomb force is not increased. In this progress, the velocity of the carrier reduces because the carrier does work against the Coulomb forces. Finally, the carrier moves in a larger circle with decreased velocity. Thus, the Coulomb scattering time increases in the high temperature, and non-Coulomb interaction time also increases due to the reduced velocity. According the calculation formula of the mobility in microscale, the conclusion that the mobility in doped semiconductors increases with the increased temperature is easily drawn due to the increased free movement time. Up to now, we think that the proposed playground model provides a useful manner to elaborate on the dependence of carrier mobility on temperature in doped semiconductors, and the concept is clearly defined, and the calculation process is simple, logical, and easily accepted by the beginners.