Analysis

According to our calculation above, both n-Ge and Silver have negative carrier densities and p-Ge has positive carrier density. This is a direct result of the signs of \(\frac{V_{H}}{B}\). Since the sign of carrier density of the Silver is consistent with it of n-Ge, we conclude that Silver is n-type. For both n-Ge and p-Ge, the carrier densities are consistent with the absolute theoretical values, which are \(1.2 \cdot 10^{21} \textrm{m}^{-3}\) and \(1.1 \cdot 10^{21} \textrm{m}^{-3}\) respectively. However, although our calculated Silver carrier density has the same order of magnitude as the theoretical value (\(6.6 \cdot 10^{28} \textrm{m}^{-3}\)), they are not consistent with each other. One possibility we can think of is that we only have three data points for each sample as shown in Figure \ref{fig:n}, Figure \ref{fig:p} and Figure \ref{fig:silver}. This is due to the fact that the linear relationship between the magnetic field and the magnet current only falls in the region of \(-2A\) < \(I\) <\(2A\). Due to the time constraint, we are unable to go back and redo the experiment, but this should be something worth noting in the future experiments.