Defects can significantly modify the electro-optical characteristics of InGaN light-emitting diodes (LEDs); however, modeling the impact of defects on the electrical characteristics of LEDs is not straightforward. In this paper, we present an extensive investigation and modeling of the impact of defects on the electrical characteristics of InGaN-based LEDs, as a function of the thickness of the quantum well (QW). First, we demonstrate that the density of defects in the active region of III-N LEDs scales with increasing thickness of the InGaN QW. Since device layers with high indium content tend to incorporate more defects, we ascribed this experimental evidence to the increased volume of defects-rich InGaN associated to thicker InGaN layers. Second, we demonstrate that the current-voltage characteristics of the devices are significantly influenced by the presence of defects, especially in the sub turn-on region. Specifically, we show that the electrical characteristics can be effectively modeled in a wide current range (from pA to mA), by considering the existence of trap-assisted tunneling processes. A good correspondence is obtained between the experimental and simulated electrical characteristics (I-V), by using-in the simulation-the actual defect concentrations/activation energies extracted from steady-state photocapacitance, instead of generic fitting parameters.