Determination of Carrier Density through Hall Measurements and Determination of Transition Temperature (\(Tc\)) in a High-Tc Superconductor



The Hall Effect is an important part of finding out about charge transport in a material.In this experiment, we aim to determine the charge density in Ge n-type, Ge p-type semiconductor samples, and in a Ag (silver) sample. We will also be determining the transition temperature (\(Tc\)) of the high-Tc superconductor \(Bi_2 Sr_2 Ca_2 Cu_3 O_{10}\) (aka \(Bi2223\)).


Hall Effect was discovered by Edwin Herbert Hall, an American physicists, in 1879. This phenomenon can be used to determine the sign of the charge carrier in electrical conductors such as semiconductors and superconductors. The fundamental idea of Hall Effect can be illustrated in Figure \ref{fig:HallIllustration}:

\label{fig:HallIllustration} Hall Effect Illustration: The magnetic field is pointing into the page. By convention, the direction of current is defined as the direction of the moving positive charge. Therefore, \(\vec{v}\) is opposite for positive and negative charge carriers for a \(\vec{I}\). And according to right hand rule, the magnetic force \(F_M\) (Equation \ref{eq:righthand}) will be upward for both cases. As charges accumulate at one side of the plate, an electric field \(E\) is created between the sides. The electric force \(F_E\) on the current is opposite to \(F_M\). The Hall voltage is the voltage across the plate when the current does not curve up or down anymore, when \(F_M=F_E\).