The Einstein Relation in Compound Semiconductors Under Crossed Fields Configuration

The influence of crossed electric and quantizing magnetic fields on the transport properties of semiconductors having various band structures has relatively less investigated as compared with the corresponding magnetic quantization, although, the cross fields are fundamental with respect to the addition of new physics and the related experimental findings. It is well known that in the presence of an electric field (E _o ) along the x-axis and the quantizing magnetic field (B) along the z-axis, the dispersion relations of the conduction electrons in semiconductors become modified and the electron moves in both the z and y directions. The motion along the y-direction is purely due to the presence of E ₀ along the x-axis and in the absence of an electric field, the effective electron mass along the y-axis tends to infinity which indicates the fact that the electron motion along the y-axis is forbidden. The effective electron mass of the isotropic, bulk semiconductors having parabolic energy bands exhibits mass anisotropy in the presence of cross fields and this anisotropy depends on the electron energy, the magnetic quantum number, the electric and the magnetic fields respectively, although, the effective electron mass along the z-axis is a constant quantity.

In 1966, Zawadzki and Lax [1] formulated the electron dispersion law for III V semiconductors in accordance with the two band model of Kane under cross fields configuration which has generated the interest to study this particular topic of semiconductor science in general [2–14].