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The electroweak phase transition can be made first order by extending theStandard Model (SM) Higgs sector with extra scalars. The same new physics canexplain the matter-antimatter asymmetry of the universe by supplying an extrasource of CP violation and sphaleron processes. In this paper we study theexistence of a strong first order electroweak phase transition (SFOEWPT) in thetype-I and type-II two Higgs doublet models (2HDM). We focus on how the SFOEWPTrequirement constraints the spectrum of non-SM Higgs. Through a parameter spacescan, we find that SFOEWPT suggests upper limits on the masses of heavy Higgs$m_{A/H/H^\pm}$, which is less than 1 TeV. High temperature expansion and Higgsvacuum uplifting is used for an analytical understanding of our results. Wealso study the probe ability on SFOEWPT from Higgs and $Z$-pole precisionmeasurements at the one-loop level at future Higgs & $Z$ factories. Andtogether with theoretical constraints, sizeable loop corrections require $m_A\approx m_{H^\pm} > m_H$ to meet SFOEWPT condition in Type-II 2HDM.

Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories