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Connecting Theory and Practice in Optoelectronics
Roughly four years ago researchers at the École Polytechnique and UCSB reported that III-Nitride (III-N) LEDs exhibit hot carrier effects in a strong correlation with the efficiency droop. These new measurements added fuel to the already actively ongoing discussion in the III-N LED device simulation community about the development of more accurate simulation models than the presently used quasi-equilibrium models. In particular, the measurements and subsequent works suggested that hot electrons and holes created in the process of Auger recombination might even affect the operating voltage of LEDs. However, full LED device simulations have so far lacked detailed models of hot carrier effects and primarily relied on drift and diffusion currents of carriers within the Fermi-Dirac distribution.
To better understand the role of hot carriers in LEDs, we recently developed a full Monte Carlo (MC) model of electron and hole dynamics in III-N multi-quantum well (MQW) LEDs (published in Advanced Electronic Materials). In our model, we simulate the trajectories of a large number of electrons and holes in full MQW LED devices, represented as (super)particles with a certain position and k vector. The free flights and scattering processes of these particles are simulated in time and space using random numbers and scattering probabilities, taking into account the self-consistent electrostatic potential profile, all the major intraband scattering processes, and radiative and nonradiative electron-hole recombination processes. Both the electric fields and the recombination rates are calculated self-consistently using the time-dependent MC carrier densities. As such, the carrier distributions are not required to follow Fermi-Dirac statistics, but the spatial steady-state non-equilibrium carrier distributions are instead obtained as a final result from the MC simulations.
Having carried out the MC simulations, we compared the results to standard drift-diffusion (DD) simulations to investigate the contribution of hot carriers in the device characteristics. As described in more detail in our article, we were able to make several interesting observations. First of all and slightly in contrast to what we expected, the MC simulations did not predict notably larger currents than the DD simulations, unless the bias voltage of the LED was very large (see the featured image with the current-voltage characteristics simulated for MQW LEDs consisting of different numbers of InGaN QWs with (a) small and (b) large Indium compositions). At large bias voltages, however, the current in MC became notably larger than in DD on the one hand due to the more efficient carrier spreading and the resulting more uniform recombination within the quantum wells (QWs), and on the other hand due to the hot-electron mediated unipolar electron overflow. In contrast, the hot carriers created in Auger recombination processes were not a major source of leakage current, and this was due to the relatively small amount of Auger-generated hot carriers with respect to all carriers and due to the fast hot carrier relaxation especially by optical phonons and carrier-carrier scattering. However, despite the relatively small direct effect on the device performance, a clear Auger-excited electron population in the high-energy sidevalley could be observed all the way to the p-contact. Also quite interestingly, the MC simulations reproduced qualitatively the transport losses, which are typically seen in DD simulations as quasi-Fermi level drops between the QWs and as elevated bias voltages.
In summary, based on our results we believe that hot carrier effects play a major role in the device-level characteristics of typical LEDs only when the conduction band edge on the n-side rises well above the conduction band edge on the p-side. On the other hand, based on the presence of hot carriers close to the active region, hot carrier effects may be more prominent in truly nanoscale LED structures where the doped layers might be only tens of nanometers thick. In any case, detailed multivalley carrier transport models such as the described MC model, potentially complemented by more precise accounts of quantum effects in the active region, are needed to gain detailed knowledge of the electron and hole distributions in the LED and to analyze for example electron emission spectroscopy measurements. In terms of more realistic device characteristics, we believe that the very recent works accounting for material fluctuations and tunneling effects will enable obtaining even more quantitative understanding of the underlying phenomena.