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# Introduction and Overview

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.

In this paper, the the negative differential resistance (NDR) will be probed by comparing the traditional WKB approximation method and path integral approach, and will quantitatively show that the latter lends a better understanding to the origin of the phenomenon.

\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 (Chang 1974).

The tunneling effect in these devices can be of two kinds :

• Interband tunneling : Where the electron tunnels from the conduction band on one side to the valence band on the other side.

• Intraband Tunelling : Where the electron tunnels from the conduction band on one side to the conduction band on the other. That is, no interband transport occurs. This paper will examine the intraband tunneling phenomenon in greater detail.

Modern RTDs can be fabricated in many ways (heavily doped p–n junction in Esaki diodes, double barrier, triple barrier, quantum well, or quantum wire), but the most common one is to use a heterostructure in order to create a confined potential well between two barrier materials. III-V compounds are usually used to make such double barrier devices, as well as other multi-barrier devices which work on the same principle.