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Spontaneous pair production for spin-$1/2$ and spin-$0$ particles is exploredin a quantitative manner for a static $\tanh$-Sauter potential step (SS),evaluating the imaginary part of the effective action. We provide finite-valuedper unit-surface results, including the exact sharp-edge Klein paradox (KP)limit, which is the upper bound to pair production. At the vacuum instabilitythreshold the spin-$0$ particle production can surpass that for the spin-$1/2$rate. Presenting the effect of two opposite sign Sauter potential stepscreating a well we show that spin-$0$ pair production, contrary to the case ofspin-$1/2$, requires a smoothly sloped wall.

Particle production at a finite potential step: Transition from Euler-Heisenberg to Klein paradox