Factors contributing to Schottky barrier lowering in ideal Al/GaAs Schottky diodes are discussed both theoretically and experimentally. The diodes used in this study were grown by molecular beam epitaxy with in situ Al deposition. Two different GaAs surface reconstructions (As-stabilized and Ga-rich) were used. The Schottky barrier heights of these diodes were measured by both the current-voltage (I-V), phi-B(IV) and capacitance-voltage (C-V), phi-B(CV), methods, with phi-B(CV) larger by 47 +/- 10 meV in all the diodes. The barrier lowering effects observed in the I-V measurements are consistent with the measured ideality factor of 1.03 +/- 0.01. The experimental results coincide closely with theoretical values when the barrier lowering effects due to quantum mechanical tunneling calculated by the transfer matrix technique and image force are included. These two barrier lowering effects result in the observed larger than unity ideality factor. Simulations show that barrier lowering due to image force is reduced when tunneling occurs. The use of the effective mass approximation as opposed to the k.p method in obtaining the complex wave-vectors of the electrons does not lead to any significant change in the results. In view of these findings, the MBE grown diodes reported here are the closest to ideal ever reported in the literature.