  We study small-ball probabilities for the stochastic heat equation with
multiplicative noise in the moderate-deviations regime. We prove the existence
of a small-ball constant and related it to other known quantities in the
literature. These small-ball estimates are known to imply Chung-type laws of
the iterated logarithm (LIL) at typical spatial points; these points can be
thought of as "points of flat growth". For this result in a similar context in
SPDEs see, for example, the recent work of Chen \cite{Ch2023}. We establish the
existence of a new family of exceptional spatial points where the Chung-type
LIL fails.
