  A guiding principle in self-assembly is that, for high production yield,
nucleation of structures must be significantly slower than their growth.
However, details of the mechanism that impedes nucleation are broadly
considered irrelevant. Here, we analyze self-assembly into finite-sized target
structures employing mathematical modeling. We investigate two key scenarios to
delay nucleation: (i) by introducing a slow activation step for the assembling
constituents and, (ii) by decreasing the dimerization rate. These scenarios
have widely different characteristics. While the dimerization scenario exhibits
robust behavior, the activation scenario is highly sensitive to demographic
fluctuations. These demographic fluctuations ultimately disfavor growth
compared to nucleation and can suppress yield completely. The occurrence of
this stochastic yield catastrophe does not depend on model details but is
generic as soon as number fluctuations between constituents are taken into
account. On a broader perspective, our results reveal that stochasticity is an
important limiting factor for self-assembly and that the specific
implementation of the nucleation process plays a significant role in
determining the yield.
