As seen in figure 1a and 1b, at a certain electron energy and applied bias resonant conditions are met and the transmission probability spikes in value. Changing the voltage in figure 1a and the electron energy in figure 1b has the effect of shifting the region in which resonance occurs. In this respect, RTD’s are tunable to the required application. It is assumed that this transmission probability expression is applicable to all materials, including those that are topologically non-trivial.

For a given barrier height and effective mass, the transmission probability can be used in equation 3 to solve for current. \[J_d = \frac{qg_sg_v}{\hbar(2\pi)^d}\int d^dk* v_g(k)T(k)[f_L(k)-f_R(k)]\] For conventional RTD’s, the low energy band structure can be represented by a parabolic band with a effective mass. When barrier height and effective mass are chosen appropriately, this scheme can represent conventional RTD’s with parabolic band structures, such as GaAs RTD’s. The general form of the I-V curve for a RTD can be reproduced using equation 3. As seen in figure 2, once past the resonant region, the current goes through a negative differential resistance region. This region makes RTD’s unique and desirable devices.