We present the implementation of an efficient terahertz (THz) photoconductive antenna (PCA) emitter design that utilizes high mobility carriers in the two-dimensional electron gas (2DEG) of a modulation-doped heterostructure (MDH). The PCA design is fabricated with recessed metal electrodes in direct contact with the 2DEG region of the MDH. We compare the performance of the MDH PCA having recessed contacts with a PCA fabricated on bulk semi-insulating GaAs, on low temperature-grown GaAs, and a MDH PCA with the contacts fabricated on the surface. By recessing the contacts, the applied bias can effectively accelerate the high-mobility carriers within the 2DEG, which increases the THz power emission by at least an order of magnitude compared to those with conventional structures. The dynamic range (62 dB) and bandwidth characteristics (3.2 THz) in the power spectrum are shown to be comparable with the reference samples. Drude-Lorentz simulations corroborate the results that the higher-mobility carriers in the MDH, increase the THz emission. The saturation characteristics were also measured via optical fluence dependence, revealing a lower saturation value compared to the reference samples. The high THz conversion efficiency of the MDH-PCA with recessed contacts at low optical power makes it an attractive candidate for THz-time domain spectroscopy systems powered by low power fiber lasers.