The present disclosure discloses a method for manufacturing a capacitor, a capacitor array structure and a semiconductor memory. The method for manufacturing a capacitor includes: providing an underlayer; forming a substrate to be etched on the underlayer; enabling a wafer to include a central area and an edge area; forming a first hard mask layer having a first pattern in the central area on the substrate to be etched; using the first hard mask layer as a mask to etch the substrate to be etched, to form capacitor holes; depositing a lower electrode layer; and sequentially forming a capacitor dielectric layer and an upper electrode layer.