Roughness of heterointerfaces and averaging effects by excitons: Interpretation of cathodoluminescence images

Cathodoluminescence (CL) in a scanning electron microscope is often used to probe the heterointerface roughness of quantum wells. The CL intensity patterns are then interpreted as a direct mapping of the interface structure. We argue that generally the correlation length of the interface roughness is smaller than the lateral resolution of the CL mode and that it is the latter that determines the patterns of the images. A theoretical formulation based on a statistical interpretation of the CL images is proposed as a promising route to extract the characteristic size of interface roughness structures from the modulation depth, i.e., the contrast, of the images. CL data recorded from two GaAs/Alₓ{Ga}_{1{{-}}x}$As quantum wells with completely different interface roughness confirm the validity of our model.