Application of the Hall Effect in a Semi-conductor to the Measurement of Power in an Electromagnetic Field

Abstract

IT is well known that if, in a piece of semi-conductor such as germanium or silicon, a magnetic field is set up along the z-axis, as defined by a Cartesian coordinate system, with current flow at right angles along the y-axis, then an electromotive force appears, due to the Hall effect¹ along the x-axis. This electromotive force at any instant is given by: where B is instantaneous flux density in gauss; I _c is instantaneous current in amperes ; R is Hall coefficient in volt. cm. per ampere gauss (for ‘n’ type germanium R has a value of about 8 × 10⁻⁵) ; and t is thickness in cm. along the z-axis of the sample of material exhibiting the Hall effect. The particular virtue of a semi-conductor like germanium or silicon for this purpose is that it possesses a comparatively large Hall coefficient and allows a substantial penetration of the field into the material even at ultra-high frequencies.