The electric field in a circular semiconductor plate placed in a magnetic field

Abstract

The current distribution in an isothermic isotropically conducting plate of circular form is investigated theoretically and experimentally, in the absence and in the presence of an external magnetic field that is perpendicular to the plate. The general solution of the Riemann-Hilbert boundary value problem has been obtained under these conditions. The analysis of this solution points to experimental possibilities of determining parameters of a crystal under consideration such as the specific electric conductivity (in the absence and in the presence of an external magnetic field), the mobility of current carriers in it, and others. All the basic results of the calculations undertaken were experimentally verified and quantitatively confirmed in a series of tests carried out on homogeneous monocrystalline n-germanium (with the specific resistivity of 1.1 ohm cm) at room temperature. It is known that investigations into the galvanomagnetic phenomena (longitudinal and transverse magneto-resistance, the usual, planar and longitudinal Hall effects and others) at the present time constitute not only a means of determining the characteristics of the parameters of the crystals in question (concentration of current carriers, their mobility, etc.) [1], but serve also as a proven and simple means of obtaining important information about the zone structure of crystals [2–5]. Such broadening of the circle of problems affecting the sphere of galvanomagnetic investigations already begins not to correspond to the established traditions of carrying out these investigations on test pieces of rectangular shape (as a rule, in the form of parallelepipeds). This lack of correspondence is greater due to a number of completely logical causes, certain requirements as to the geometrical dimensions of such test pieces (the ratio of length to width) [6] can far from always be satisfied. We note in this connection that in the study of galvanomagnetic phenomena in impulsive magnetic fields, for example, the use of test pieces of circular form would simplify the use of working volumes of small diameter. This, in the final analysis, is equivalent to broadening the scale of magnetic fields that can be used. The replacement of a rectangular plate by a circular disc enables us also to simplify a measurement of the parameters of semiconductor crystals which usually are obtained in circular form. Below we present theoretical and experimental investigations into the problem of measuring the galvanomagnetic effects in conducting crystals having a circular form.