  A set of vertices $S$ in a simple isolate-free graph $G$ is a semi-total
dominating set of $G$ if it is a dominating set of $G$ and every vertex of $S$
is within distance 2 or less with another vertex of $S$. The semi-total
domination number of $G$, denoted by $\gamma_{t2}(G)$, is the minimum
cardinality of a semi-total dominating set of $G$. In this paper, we study
semi-total domination of Cartesian products of graphs. Our main result
establishes that for any graphs $G$ and $H$, $\gamma_{t2}(G\,\square\, H)\ge
\frac{1}{3}\gamma_{t2}(G)\gamma_{t2}(H)$.
