Phenomenological theory of the Hall effect in insulators

It is shown that in noncubic solids the "Hall mobilities" derived from Hall voltage and Hall current measurements are not identical. Their relation together with a consistency test for the measured "Hall mobilities" are obtained for orthorhombic symmetry. The observed quantities in Hall effect measurements on insulators are influenced by the presence of a space charge in the solid. The electromagnetic field equations are solved inside a cuboid of an orthorhombic solid by a Green function method. The results are used to relate the observed Hall voltage in the four-point-probe technique and the observed Hall current in the split-back-electrode technique to the fundamental parameters governing the Hall effect, for space-charge-limited currents under various trapping conditions. The corresponding relation for Ohmic conduction is also given. The advantages of using the Hall current method for insulators rather than the Hall voltage method are stressed.