Tunneling throught a barrier under transverse magnetic field and I-V characteristic

The case whereby the transmission coefficient through a barrier, sandwiched by semiconductor reservoirs, under bias is provided by a general formula involving the logarith micwave function derivative at the barrier entrance is now extended to include the influence of magnetic field perpendicular to the longitudinal barrier direction. Under the circumstances, theequation governing the logarithmic wave function derivative is appropriately modified via aneffective potential energy which takes account of the magnetic field. Subsequently, the procedurefor obtaining the transmission coefficient is applied to the case involving a smooth double, as wellas quadruple, barrier for which theI-V characteristic is obtained. The results show reduction incurrent with increase in the magnetic field, up to a certain value of bias. Furthermore, increasein temperature exhibits increase in current as well as movement of the current peaks in the I-V curves towards lower bias.