In this paper, using a fully-coupled, three-dimensional electro-thermal device simulator, we study the mechanism of efficiency degradation at high current operation in planar GaN-based light emitting diodes (LED). In particular, the improvement of the efficiency degradation using thicker conductive GaN substrates has been demonstrated. First, it is found that local Joule heating inside thin conductive GaN substrates degrades internal quantum efficiency (IQE) and increases the series resistance. Then, we introduced thicker conductive GaN substrates and simulated distributions of the current density and temperature inside the substrate. It is found that the maximum current density inside the GaN substrate decreases by about six times for a 100-µm-thick substrate compared to that for a 5-µm-thick substrate. Therefore, the maximum junction temperature decreases, and then IQE and the driving voltage are improved. The present study proves that thick GaN substrates are effective to improve the properties of planar LEDs at high current operation.