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\section{Resonant Tunneling Diode}  As previously stated, an RTD is a tunneling device that makes use of resonances in the tunneling probability for diode control. This resonance arises from the interaction of the potential barriers, which can be thought of as a double potential barrier with adjustable positions relative to each other. When an electron tunnels through one barrier, it will be temporarily bound between the two barriers until it can tunnel out\cite{Mizuta_1995}. The relative positional adjustment of the barriers, which in actuality is the result of applying a bias to the device, results in adjustability of the amount of time the electron is bound. At a certain bias, the tunneling probability spikes and the electron sees virtually no barriers; this is the resonance condition, which can be seen in figure 1a. Using tunneling probability, current can be calculated and has been shown to exhibit unique properties that include a negative differential resistance region, which can be seen in figure 1b\cite{Kluksdahl_1989}. 2.  These properties have made RTD's very useful for switching devices as well as a platform for studying the wave nature of electrons. Using the WKB approximation\cite{Bohm_2012}, one can determine an analytical expression for the transmission probability. For double barrier systems, the WKB method is known to lack accuracy, but the relative simplicity of this method makes it useful for coarse analysis. Using the WKB approximation, a general expression for the transmission coefficient of a double barrier system can be found\cite{Ferry_1994}\textsuperscript{,}\cite{Chowdhury_2015}.  \begin{equation}