Using thermally stimulated current ͑TSC͒ spectroscopy we have identified the presence of several deep traps in low temperature grown ͑LTG͒ nonintentionally doped bulk molecular beam epitaxy ͑MBE͒-GaAs and silicon planar-doped MBE-GaAs samples. The experiments of TSC spectroscopy were carried out on a LTG MBE-GaAs epilayer grown at 300°C and the planar-doped layer with a nominal silicon concentration of 3.4ϫ10 12 cm Ϫ2 . The LTG nonintentionally doped bulk MBE-GaAs sample shows three peaks in the TSC spectra but the planar-doped MBE-GaAs sample shows spectra similar to those of bulk samples grown by the liquid-encapsulated Czochralski and vertical gradient freeze methods. The main achievement is the experimental evidence that the potential well present in the planar-doped sample is effective in detecting the presence of different deep traps previously not seen in LTG bulk MBE-GaAs epilayers due to a shorter carrier lifetime ͑about 10 Ϫ12 s) in the conduction band which occurs due to EL2-like deep traps recombination. This fact is evidenced by a strong hopping conduction in LTG bulk MBE-GaAs samples at temperatures lower than 300 K, but not in planar-doped MBE-GaAs samples because the two-dimensional electron gas has a higher mobility than lateral LTG bulk MBE-GaAs epilayers.