The mechanism responsible for the efficiency droop in AlGaInP-based vertically structured red light-emitting diodes (LEDs) is investigated using dynamic measurement techniques. Short electrical pulses (similar to 100 ps) are pumped into this device and the output optical pulses probed using high-speed photoreceiver circuits. From this, the internal carrier dynamic inside the device can be investigated by use of the measured electrical-to-optical (E-O) impulse responses. Results show that the E-O responses measured under different bias currents are all invariant from room temperature to similar to 100 degrees C. This is contrary to most results reported for AlGaInP-based red LEDs, which usually exhibit a shortening in the response time and degradation in output power with the increase of ambient temperature. According to the extracted fall-time constants of the E-O impulse responses, the origin of the efficiency droop in our vertical LED structure, which has good heat-sinking, is not due to thermally induced carrier leakage, but rather should be attributed to defect recombination and the saturation of defect/spontaneous recombination processes under low and high bias current, respectively.