Field-Effect Electroluminescence
4.9 First Principles Calculation of Tunnel Currents
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Figure 4.22. Semiclassical self-consistent electrostatic simulation of afeledin equilibrium at a gate bias of +6 V.
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Figure 4.23. Semiclassical self-consistent electrostatic simulation of thefeledin equilibrium at a gate bias of −6 V.
A comparison of the rise times for electroluminescence in figure 4.3 (∼0.25 μs and
∼2.5 μs) to the injection time for the first charges (∼10–100 μs) suggests that tunneling is dramatically enhanced by the presence of the complementary charge in the nanocrystal array. This trend is reproduced by our model for the tunneling currents, which shows that the electron and hole currents vary strongly as a function of the total charge stored in the nanocrystal layer. For example, the electron injection is enhanced by a factor of ∼10 by the presence of holes with an areal density of 2.4×1012cm−2 in the nanocrystal ensemble.
Hole tunneling is enhanced by a factor of ∼10 by the presence of electrons with an areal density of 1.6×1012cm−2in the nanocrystals (figure 4.24). On the other hand, like charges injected into the nanocrystal array partially shield the electric field due to the gate bias, resulting in a dramatic decrease of channel carrier densities as well as tunneling currents.
The phenomenon of Coulomb field inhibited tunneling is especially evident for the injection of electrons. At an applied +6 V gate potential, the strong inversion layer in the channel disappears when the areal density of electrons in nanocrystals exceeds ∼3.5× 1012 cm−2. In this case, the electron tunneling current is greatly reduced.
The calculated tunneling current densities in figure 4.24 are far too small to correspond to our observations. The tunneling rates increase if the assumed tunnel oxide thickness is
Figure 4.24. Calculated tunneling currents from the channel into the nanocrystal layer demonstrate the Coulomb field enhancement and inhibition of the charge injection. The calculated current magnitudes are far too small to explain field-effect electroluminescence.
reduced. Additionally, the effective mass of holes in SiO2 is not well known and might be adjusted in the tunneling calculation to improve the match to the experimental charging time constants.
We also calculated the injection currents using the semianalytical direct tunneling model of Cordan [171]. These simulations solve Schr¨odinger’s equation in the channel and in a representative single nanocrystal and look for aligned energy levels that could support direct tunneling. In simulations of structures with 2 nm and 3 nm tunnel oxide thicknesses, the typical tunneling times for charge injection into either neutral or singly charged nanocrystals are orders of magnitude too slow to correspond to our experiment.
Taken together, these simulations suggest that injection may not be dominated by tun- neling processes. In view of the damage that ion implantation may cause to the tunnel oxide, it is possible that charge injection could also occur via the Poole-Frenkel mechanism or some other defect mediated process [172]. The particular mechanism for carrier injection in thefeleddoes not substantially change the sequential carrier injection model.
An alternative explanation can be formulated that relies only on electron transport across both the tunnel oxide and the control oxide of the device.
In this alternative model, the silicon nanocrystal ensemble is assumed to be located in roughly the center of the gate oxide, so that charge transport can occur across both the tunnel and control oxide layers. We believe based on our fabrication process that the control oxide is actually thicker than the tunnel oxide. When the gate bias is switched to +6 V, hot electrons are injected into the silicon nanocrystal ensemble from the polysilicon gate contact, causing exciton formation through impact ionization. The gate oxide acquires a net negative charge over a 10–100μs time scale due to nanocrystal or oxide defect charging. This stored charge eventually inhibits the further injection of electrons from the gate and the device stops emitting light. When the gate bias is switched to −6 V, the previously stored charge is flushed to the gate contact and electrons are injected into the nanocrystal ensemble from the inverted channel. A pulse of electroluminescence is observed while impact ionization occurs. Eventually, negative charge builds up in the gate oxide or on the nanocrystals that are closer to the channel than to the gate and the injection of electrons stops.
We are able to explain the pulsed emission characteristics of ourfeledusing this model.
The asymmetry of the pulses could be attributed to a difference in the thickness of the tunnel and control oxide barriers. The stored electrons that cause the pulsed output might require a large reversed gate bias to flush from the oxide, possibly explaining the small electroluminescence intensity for cycling the gate bias between 0 V and ±6 V in contrast to symmetrical gate bias modulation between −6 V and +6 V (see figure 4.4).
We do not prefer this description for our devices because it does not seem to satisfac- torily explain our observation of electroluminescence for gate bias modulation at 2.5 VRMS. We believe impact ionization is unlikely to occur under such low voltage conditions. How- ever, there are reports in the literature that posit impact ionization by electrons that have sub-bandgap energy in silicon [173, 174]. It is also known that charge transport in very thin SiO2 films can be nearly adiabatic [74]. The process might even be enhanced in silicon
nanocrystals due to carrier confinement, given the reciprocal relationship between impact ionization and Auger recombination. In any case, it appears that this alternative explana- tion can not be dismissed based on the evidence of our experiments and that further work will be required to resolve the issue.