  We study the electroweak phase transition in three scalar extension models
beyond the Standard Model. Assuming new scalars are decoupled at some heavy
scale, we use the covariant derivative expansion method to derive all of the
dimension-6 effective operators, whose coefficients are highly correlated in a
specific model. We provide bounds to the complete set of dimension-6 operators
by including the electroweak precision test and recent Higgs measurements. We
find that the parameter space of strong first-order phase transitions (induced
by the $|H|^6$ operator) can be probed extensively in $Zh$ production at future
electron-positron colliders.
