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Stacked layers of self-assembled In(Ga)As quantum rings on GaAs grown by solid source molecular beam epitaxy are studied by ex situ atomic force microscopy (AFM), low temperature photoluminescence (PL) and cross-sectional transmission electron microscopy (XTEM). The influence of the strain field and InAs segregation on the surface morphology, optical properties and vertical ordering of three quantum ring layers is analyzed for GaAs spacers between layers from 1.5 to 14 nm. AFM and PL results show that samples with spacers >6  nm have surface morphology and optical properties similar to single layers samples. XTEM results on samples with 3 and 6 nm GaAs spacers show that the rings are preserved after capping with GaAs, and evidence the existence of vertically ordered quantum rings.This work was supported by Spanish MCyT under\udNANOSELF project sTIC2002-04096d, by NANOMAT\udproject of the EC Growth Program sContract No. G5RD-CT-2001-00545d and by the SANDiE Network of excellence sContract No. NMP4-CT-2004-500101d. The authors also thank the Junta de Andalucía sPAI research group TEP-\ud0120d. TEM measurements were carried out in the DMESCCYT. The authors acknowledge P. Offermans and P. Koenraad for fruitful discussions.Peer reviewe

Vertical order in stacked layers of self-assembled In(Ga)As quantum rings on GaAs (001)