Traditional solutions to antenna effect, such as jumper insertion and diode insertion performed at post-route stage may produce extra vias and degrade circuit performance. Previous work suggests combining layer assignment, jumper insertion, and diode insertion together to achieve a better design quality with less additional cost. Based on our observations on global and local antenna violations, this paper proposes an antenna-safe single-net layer assignment (AS-SLA), which first enumerates all antenna-safe layer assignment solutions of a net, and then extracts the minimum-cost one for the net. AS-SLA can minimize via count and separators as well. In addition, an antenna avoidance layer assignment flow (AALA) adopting AS-SLA as its kernel not only avoids global antenna violations, but also eliminates local antenna violations. Experimental results reveal that, in 16 benchmarks, AALA can yield ten antenna-violation-free assignments, while the algorithms of other works yield no antenna-violation-free assignment. However, AALA performs about seven times slower than other antenna-aware layer assignment algorithm. Accordingly, two acceleration techniques are proposed to reduce the runtime of AALA by 57.6%.