Introduction

Resonant Tunneling Diodes (RTDs) are two terminal electronic devices in which the transport is achieved by the electrons tunneling through a resonant state in a double potential barrier setup. This is one of the first devices to take advantage of the quantum mechanical electron-wave property (Chang 1974). Since the improvement in crystal growth and nano-fabrication methods, RTDs has been of great interest both as a theoretical study of quantum transport physics (Kluksdahl 1989) and functional quantum devices in the laboratories. The specific property of interest is the region of negative resistance (or conductance) it shows under certain conditions, which is not an intuitive classical result. This can be seen in the figure \ref{fig:graph}, where there are regions where the conductance goes negative at certain applied voltages for a GaAs/GaAlAs double barrier RTD.

Here the electron transport through resonant tunneling diodes are analyzed using path integrals. The negative differential resistance (NDR) is studied by comparing the results of path integrals with traditional WKB approximation method, and is quantitatively shown to lend a better understanding to the origin of the NDR.

\label{fig:graph} Current and conductance characteristics of a double-barrier structure of GaAs between two Ga$$_{0.3}$$Al$$_{0.7}$$As, as shown in the energy diagram. Both the thicknesses and the calculated quasistationary states of the structure are indicated in the diagram. Arrows in the curves indicate the observed voltages of singularities corresponding to these resonant states \cite{Chang1974}.