Role of the junction voltage on the overflow current in light-emitting diodes

Quantum-well (QW)-based light emitters, such as light-emitting diodes (LEDs) and lasers, of various semiconductor materials experience a reduction in their efficiency when operating at higher temperatures, a phenomenon referred to as ``thermal droop.'' Among the various claims on the origins of thermal droop, an increased overflow current with increasing temperatures is a common contender. Since overflow of carriers can only occur when the junction voltage ${V}_{\mathrm{Junction}}$ approaches the built-in voltage ${V}_{\mathrm{BI}}$ of any diodes, we develop a simple method relating the difference between ${V}_{\mathrm{Junction}}$ and ${V}_{\mathrm{BI}}$ to approximate the upper limit of overflow occurring in QW-based light-emitting diodes. The measured difference between ${V}_{\mathrm{Junction}}$ and ${V}_{\mathrm{BI}}$ of state-of-the-art commercial blue and green $\mathrm{In}\mathrm{Ga}\mathrm{N}$-based LEDs at temperatures up to \ensuremath{\sim}450 K suggests negligible overflow. To further experimentally verify the absence of overflow, we perform temperature-dependent electron emission spectroscopy on the same commercial blue and green LEDs and find no evidence of thermally enhanced overflow carriers up to \ensuremath{\sim}450 K. In agreement with our claims that ${V}_{\mathrm{Junction}}$ must approach ${V}_{\mathrm{BI}}$ for overflow to occur, two-dimensional temperature-dependent electrical simulations of violet, blue, and green LEDs including alloy disorder and V-defects demonstrate that overflow can be significant in violet LEDs, where the small band offset between the $\mathrm{In}\mathrm{Ga}\mathrm{N}$ QW and $\mathrm{Ga}\mathrm{N}$ cladding layers due to the larger QW bandgap requires larger ${V}_{\mathrm{Junction}}$ to reach standard operating current densities, thereby approaching ${V}_{\mathrm{BI}}$. By contrast, simulations indicate that overflow is negligible in blue and green LEDs, whose smaller QW bandgaps result in smaller quasi-Fermi levels difference to reach significant carrier injection, resulting in a ${V}_{\mathrm{Junction}}$ much smaller than ${V}_{\mathrm{BI}}$ up to large operating current densities. Considering that overflow is negligible in blue and longer-wavelength LEDs, and our observations of the large thermal droop occurring at low current densities, where Shockley-Read-Hall (SRH) recombination dominates, we conclude that thermally enhanced SRH processes are the most significant contributor to thermal droop. Finally, we also simulate the carrier densities in the different QWs of a multiple-QW LED and observe a reduction in the total carrier density at a given operating current density, which results in a decrease in the total Auger-Meitner current of the LED from just the thermally enhanced carrier redistribution among QWs without taking any possible additional temperature dependence of their recombination coefficients. Taking all this into account, minimizing thermal droop effects in LEDs can be achieved by a reduction in defect density, using wider band gap p-n junction-defining cladding layers, and operating at higher currents.