Potential Calculations in Hall Plates

Abstract

This chapter describes Hall effect and its mathematical representation. It discusses the Van Der Pauw method for Hall-mobility measurements. The chapter also compares several techniques for potential calculations in Hall plates, such as conformal mapping, finite differences, and boundary-element method. Hall plates are thin semiconducting layers placed in a magnetic field.With suitable contacts, commonly called Hall contacts, a Hall voltage can then be measured. In first approximation, one can state that the Hall voltage is proportional to the applied magnetic field, the externally supplied current and the mobility of the charge carriers. Knowledge of the current and of the Hall voltage yields the product μ H B of the mobility, and the magnetic field B . This essentially indicates two major applications of Hall effect components— namely, if the mobility is known magnetic field strengths can be measured. On the other hand, if the magnetic field is known the mobility can be calculated.