A rectangular bar of germanium is to be characterised for its charge-transport properties at room temperature.
a. (i) Derive an expression that links the mobility of charge carriers in a conductor to its resistivity, carrier density, and the elementary charge.
b. (ii) The resistivity of the germanium sample at 300 K is 4.5×10−2Ωm and the free-electron density is 2.0×1025m−3. Calculate the mobility of electrons in the sample.
c. (iii) On heating the sample to 320 K, the resistivity increases by 2.0% while the carrier density remains unchanged. Determine the percentage change in the mobility over this temperature rise.