Abstract
Electroluminescence (EL) characterization of InGaN/GaN light-emitting diodes (LEDs), coupled with numerical device models of different sophistication, is routinely adopted not only to establish correlations between device efficiency and structural features, but also to make inferences about the loss mechanisms responsible for LED efficiency droop at high driving currents. The limits of this investigative approach are discussed here in a case study based on a comprehensive set of current- and temperature-dependent EL data from blue LEDs with low and high densities of threading dislocations (TDs). First, the effects limiting the applicability of simpler (closed-form and/or one-dimensional) classes of models are addressed, like lateral current crowding, vertical carrier distribution nonuniformity, and interband transition broadening. Then, the major sources of uncertainty affecting state-of-the-art numerical device simulation are reviewed and discussed, including (i) the approximations in the transport description through the multi-quantum-well active region, (ii) the alternative valence band parametrizations proposed to calculate the spontaneous emission rate, (iii) the difficulties in defining the Auger coefficients due to inadequacies in the microscopic quantum well description and the possible presence of extra, non-Auger high-current-density recombination mechanisms and/or Auger-induced leakage. In the case of the present LED structures, the application of three-dimensional numerical-simulation-based analysis to the EL data leads to an explanation of efficiency droop in terms of TD-related and Auger-like nonradiative losses, with a C coefficient in the 10−30 cm6/s range at room temperature, close to the larger theoretical calculations reported so far. However, a study of the combined effects of structural and model uncertainties suggests that the C values thus determined could be overestimated by about an order of magnitude. This preliminary attempt at uncertainty quantification confirms, beyond the present case, the need for an improved description of carrier transport and microscopic radiative and nonradiative recombination mechanisms in device-level LED numerical models.
Highlights
The ongoing debate on efficiency droop in GaN-based light-emitting diodes (LEDs)[1,2,3,4,5,6] attests the present limitations of both characterization techniques and numerical models of III-nitride active optoelectronic devices
The inadequacies of the standard drift-diffusion (DD) simulation framework when used to describe carrier transport across a LED active region[7,8] have elicited the inclusion of semiempirical corrections for mechanisms such as tunneling,[9,10] carrier overflow,[11,12] ballistic overshoot,13–15 “nonlocal” transport between quantum wells (QWs),[16] and Auger-induced leakage.[17]. The effects of those mechanisms are often hard to discriminate experimentally, which results in a problematic validation of the corresponding models. These intrinsic difficulties are compounded by at least three factors: a. the enduring lack of reliable first-principles models for nonradiative and radiative recombination mechanisms and other critical physical parameters in realistic InGaN QWs, b. the inconsistencies in the definitions of some optical and transport parameters when used in experimental and in simulation contexts (e.g., “bulk” Auger coefficients vs. Auger rates in two-dimensional systems22), c. the large sensitivity of several key parameters to technological/structural details often unaccessible to an accurate experimental determination, to which one could add the bias towards simpler, single-mechanism explanations against more comprehensive descriptions.[23,24,25]
The results of this study, leading to an explanation of efficiency droop in terms of Auger-like nonradiative losses characterized by a C coefficient in the 10−30 cm6/s range at room temperature, are critically discussed in Section V, where the uncertainties and limitations of the modeling framework are shown to correspond to a possible C overestimation by about an order of magnitude and, more generally, underscore the problematic identification between the Auger-like C coefficient considered by DD analysis and the actual Auger rates
Summary
The ongoing debate on efficiency droop in GaN-based light-emitting diodes (LEDs)[1,2,3,4,5,6] attests the present limitations of both characterization techniques and numerical models of III-nitride active optoelectronic devices. The inadequacies of the standard drift-diffusion (DD) simulation framework when used to describe carrier transport across a LED active region[7,8] have elicited the inclusion of semiempirical corrections for mechanisms such as tunneling,[9,10] carrier overflow,[11,12] ballistic overshoot,13–15 “nonlocal” transport between quantum wells (QWs),[16] and Auger-induced leakage.[17] the effects of those mechanisms are often hard to discriminate experimentally, which results in a problematic validation of the corresponding models.
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