5.3 Coherent Tunneling

In this description the electron does not experience any phase-coherence breaking events throughout the structure, it is based on the Schrödinger equation. We refer to this model as ``global coherent tunneling picture''. It neglects any scattering processes. Note that transport in the absence of scattering is referred to as ballistic transport. Ballistic transport through a device can be assumed when the device length is short compared with the mean free path of the electron.

When no voltage is applied electrons are injected from the left and the right, and due to the symmetry of the device, no current results, as should be the case in equilibrium. With a positive bias applied to the right contact relative to the left, the Fermi energy on the left is pulled through the resonant level $E_0$. As the Fermi energy passes through the resonant energy, a large current flows due to the increased transmission from left to right. It reaches a local maximum, called peak current. With higher bias, the current ceases to flow, when $E_0$ falls below the conduction-band edge. The result is a marked decrease of the current with increasing voltage, giving rise to a region of negative differential resistance, see Figure 5.2.

Figure 5.2: Influence of phonon scattering on the I/V characteristics of an RTD

The minimum current following the peak current as the voltage increases is denoted valley current. The nonzero valley current is mainly due to thermionic emission over the barriers, and it has a large temperature dependence. Another small but conceivable contribution is due to tunneling of electrons through higher quantized levels. At larger bias the current increases again as particles acquire enough kinetic energy.