RTD Charge Development

The difference between a simulation based on a semi-classical (SC) and quantum mechanical (QM) charge distribution is discussed in this page in the example of a very asymmetric RTD. The figure on the left shows four panels:

Top Left: Charge densities (doping profile (turquoise), SC (green) and QM charge (black)).Top Right: Current-voltage characteristic: SC charge (brown) and QM charge (black).Bottom left: Band profile with Fermi energy and resonances: SC (pink) and QM charge (brown).Bottom right: Traces of the 2 central resonance energies: SC (green - ground state, turquoise - excited state) and QM charge (black - ground state, brown - excited state).

The collector barrier is significantly thicker and taller than the emitter barrier in this particular example. This implies that the influx of carriers through the emitter barrier is significantly larger than the outflux through the collector barrier. Therefore charge will accumulate in the central device region. The semi-classical charge model assumes zero free charge in the central device region, since a Fermi level is not well defined (with some fudging on can define a Fermi-level, but the charge distribution would still be wrong). It can therefore not capture the charge accumulation in the central device region

The Hartree self-consistent charge model does include the non-uniform charge distribution in the central device due to the carrier injection from the emitter. While the resonance in the semi-classical model drop almost linearly (lower right panel) with the applied bias, the quantum mechanical charge based potential pushed the resonances up in energy, resisting further negatively charging the central device region. The resonances seem to bob on top of the Fermi surface defined in the emitter, A larger energy (voltage) must be applied to pull the resonances down in energy. The peak RTD current is therefore shifted to higher voltages. As the voltage is increased further, the resonances empty out their charge dramatically and the resonances fall back onto the curve of the semiclassical resonance traces.

The lower left panel shows the significant potential difference in the voltage rtange between 0.2 and 0.35 Volts due to the charge accumulation in the central device region.

The consequences of charge accumulation in the central device region have been compared to experimental data.