Material carrier mobility is a function of temperature. Generally, it exhibits a temperature

dependence of $T^{\frac{3}{2}}$ at low temperatures and $T^{-\frac{3}{2}}$ at high temperatures, as shown below.

Please explain the rationale behind the temperature exponents $\frac{3}{2}$ and $-\frac{3}{2}$ in the low and high

temperature regimes.