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Simple algorithms, which are based on the principle of factorisation of an integer, are proposed to generate the polynomial zeros of degree 2 of the 3-j and 6-j coefficients.

We examined the epitaxial growth of ZnO films on a sapphire (0001) substrate by an atmospheric pressure atomic layer epitaxy technique using ZnCl 2 and O 2 sources. The films were deposited epitaxially in a substrate temperature range of 450-550°C with a constant growth rate of 0.26 nm/cycle. It is noteworthy that the rate corresponds to just a half-length of the c axis of hexagonal ZnO, indicating that the alternate deposition of ZnCl 2 and O 2 on the substrate is governed by a self-limiting mechanism. This was also confirmed by the facts that the film thickness was dependent only on the growth cycles and that the surface was quite smooth. A strong photoluminescence band edge emission of 3.36 eV was observed at 20 K.