An array of sixteen 1 cm^3 CdZnTe semiconductor detectors was operated at the Gran Sasso Underground Laboratory (LNGS) to further investigate the feasibility of double-beta decay searches with such devices. As one of the double-beta decay experiments with the highest granularity the 4 x 4 array accumulated an overall exposure of 18 kg days. The setup and performance of the array is described. Half-life limits for various double-beta decay modes of Cd, Zn and Te isotopes are obtained. No signal has been found, but several limits beyond 10^20 years have been performed. They are an order of magnitude better than those obtained with this technology before and comparable to most other experimental approaches for the isotopes under investigation. An improved limit for the beta^+/EC decay of Te 120 is given.
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