UNIFIED STUDY OF THE CLASSICAL HALL EFFECT

Abstract

Germanium (Ge) samples with different doping types, acceptors (p-type) and donors (n-type), were studied to investigate charge carrier behavior. Carrier concentrations were found to be 1.16×10^21 m^(-3) for the p-type sample and 7.337×10^20 m^(-3) for the n-type sample. These experiments were conducted for the standard Hall effect (Hall voltage versus low magnetic field (B) values) as well as conductivity and Hall voltage versus temperature for different B-fields. The measurements versus temperature at zero-field allow us to obtain band gap ( Eg). While we investigate the conductivities for n-type and p-type doped samples, we also study the conductivity of an undoped Ge sample from which we obtained an energy gap of Eg=0.651eV which compares well with the known value of 0.67eV at room temperature. While it is commonly known that the classical Hall voltage is linear with B-fields, not so common is the behavior of the classical Hall voltage with temperature, especially for both n-type and p-type samples. Thus, we derive a general Hall voltage formula for semiconductors that unifies the understanding of both n-type and p-type carriers. Our experimental results are analyzed with the unified theory using MATLAB. An example MATLAB program is also included to perform calculations with our unified Hall voltage expression