The flat crystal was connected to the silver substrate by silver paste, with the QW layers parallel to the substrate. The crystal orientation was verified by XRD patterns obtained from Philips Xpert Pro X-ray Siffractometer (Almelo, The Netherlands) using Cu-Kα radiation (fig. S1A). The c-AFM measurement was performed using the Park XE7 system in the contact mode with a Pt-coated tip. To eliminate the concerns on surface contamination by the solution environment on samples, we exfoliated the samples to obtain a fresh top surface for the c-AFM measurement. The whole setup was installed in a mating chamber from Park Systems Corp to minimize the ambient disturbance. The experiment was carried out at room temperature with the gas environment of ambient air (78 volume % nitrogen and 21 volume % oxygen) with a relative humidity of ~30% at 1 atm. During the measurement, a Ag/pero-MQW/Pt diode was constructed. The silver substrate acts as the bottom electrode and the top-conducting tip on a cantilever serves as the mobile top electrode reflecting both the electrically conductive feature and surface topographical character of the sample (optical lever method). The sample bias was applied on the bottom silver electrode with the top tip electrode grounded. Note that the energy difference between the Fermi levels of the sample and the work function of the Pt electrode should be taken into consideration for this microscopic mapping. The light bias was provided by an MK-R 12-V light-emitting diode (CREE, Durham, NC). The illumination intensity was tuned through a computer-controlled program from 0 to 70 mW/cm2, as calibrated separately by a standard silicon solar cell. A ~5-mW infrared (860 nm) beam was used to reflect the tip deflection by the AFM, which was expected to cause negligible influence on the measurement as the absorption edge of the 2D pero-MQWs was far below 860 nm, and the shadow of the overhanging cantilever on the interrogated region could also significantly dilute the infrared photons.

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