Modeling and measurement of the differential resistance and ideality factors in heterostructure light emitting diodes and laser diodes

In this work, experimental measurements and modeling have been conducted to investigate the nonlinear behavior of the differential resistance and ideality factors in semiconductor heterostructure light emitting diodes (LEDs) and laser diodes (LDs). The modeling consists of both analytical models that experimentalist can easily apply, and numerical models to account for physical mechanisms that can not be solved in closed form. Good agreement is found between the experimental results and the modeling. The limitation of using simple diode equations with constant series/shunt resistance and ideality factors are outlined, and a methodology for including the majority carrier injection and the minority carrier leakage in the model leads to relatively straightforward explanations for complex phenomena such as the reversal of the kink polarity in the differential resistance at laser threshold observed in some laser diodes.;Variable derivative ideality factors which can be measured from different orders of derivatives from the current-voltage characteristics are defined and proposed as important parameters to indicate dominant recombination path(s) and bias level in the active region of LEDs and LDs. The ideality factor associated with a single recombination pathway with power-law dependency of current on the carrier concentration in an intrinsic and quasi-neutral active region is found to have a fixed value inversely proportional to the power factor at low bias conditions. The ideality factor is no longer a constant at high injection levels due to carrier degeneracy. When multiple recombination mechanisms exist at the same time in the same active region, changes in the ideality factors can be observed when the additional recombination paths become significant.;The process of majority carrier injection from the device terminals to the active region creates additional nonlinearity in the differential resistance and the ideality factors. A semianalytical model, in which the interaction between the confining layer and the active region is implied in the thermionic emission boundary conditions at heterointerfaces, is proposed to investigate the effects from majority carrier injection. Instead of being the sum of values directly from the active region and from the heterointerfaces, analysis shows that the differential resistance and ideality factors at the device terminals are partially from the active region and the remainder from the heterointerface. The model was extended to a simple laser model with the inclusion of junction quasi-Fermi level splitting saturation in the active region upon threshold. The model predicts: (1) reduced or even zero kink height in both the differential resistance and the ideality factors at threshold, and; (2) decreasing differential resistance and increasing ideality factor after threshold at the device terminals due to majority carrier injection.;The effects from minority carrier overflow on laser diode differential resistance are investigated through a simplified one dimensional self-consistent numerical model. Simulations showed: (1) that the majority carrier injection could be responsible for the decrease and the disappearance of the differential resistance and the ideality factor kinks at threshold (due to less interaction between the active region and the confining layers as in the semi-analytical model), and; (2) the minority carrier overflow could create kinks with reverse polarity.;Measurements on various LEDs and LDs at different temperatures showed good agreement with the proposed models. The analytical and numerical models correlated many experimentally observed features with specific physical mechanisms. This work has made possible the modeling of semiconductor optoelectronic devices with relatively simple parameters and methods, and experimentalists can use this approach to understand and characterize complex device phenomena.