The previous lecture indicated that the quantum charge self-consistency changes the I-V curve of an RTD qualitatively compared to the semi-classical (Thomas-Fermi) charge model. This change in the I-V curve really can be related to the charge accumulation inside the RTD and the emitter well. This lecture explores this effect in more detail by targeting an RTD that has a deliberate asymmetric structure. The collector barrier is chosen thicker than the emitter barrier. With this set-up we expect that the tunneling rate into the RTD from the emitter is faster than the tunneling rate from the RTD into the collector. That means that we expect to see a charge accumulation in forward bias such that the charge inside the RTD is larger than the symmetric case considered in the previous section. In the reverse bias direction we expect to see the opposite, carrier exit the central RTD faster than they can tunnel in from the emitter. The central resonance will be empty. These two different charge behaviors result in dramatically different I-V curves in forward and reverse bias. The behavior can be nicely explained by the traces of the resonance energies as well as the sheet charge densities in the central RTD and the emitter. A comparison between the sheet charge densities and the current-voltage curve reveals that the tunneling rates through the RTD must be very strong functions of energy.
- An asymmetric RTD with different emitter and collector barriers shows dramatically different current voltage characteristics in the forward and reverse bias directions.
- The different behavior in the forward and the reverse bias direction is due to charge accumulation and depletion, respectively, in the central RTD in the two different bias directions.
- Valley current is increased in a quantum charge-self-consistent calculation (Hartree) compared to calculation based on potential derived from a semi-classical charge (Thomas-Fermi)
- Hopping matrix elements G are strong function of bias
• need to be cautious about analytical formulas!
Università di Pisa, Pisa, Italy