The technique of deep level photothermal spectroscopy ͑DLPTS͒ is extended to the low temperature region in order to cover several defect states in semi-insulating GaAs. Measurements are taken at three different modes, temperature-scanned, pulse-rate-scanned, and time-scanned DLPTS. It is demonstrated that each mode provides unique information about the defect configuration, and the combination of the different modes offers a powerful tool for DLPTS studies of physical optoelectronic processes in SI-GaAs. The nonexponentiality/broadening of experimental data is extensively studied using the two prevalent broadening theories: the stretched exponential and the Gaussian distribution of activation energies. A hierarchical carrier emission model has been proposed for the stretched exponential behavior. Simulations indicate that the two broadening theories exhibit roughly similar broadening effects and good fits to the experimental data. The origin of this similarity indicates an ergodic equivalence of random energy distribution and the constrained hierarchical emission process.