  We study the Electroweak phase transition with the Standard Model effective
field theory at finite temperature and finite density. Utilizing the
dimensional reduction approach, we construct the tree dimensional thermal
effective field theory at finite density and investigate the phase transition
dynamics. We evaluate how the results depend on the renormalization scale and
the chemical potential. Our results show that, with the tree dimensional
thermal effective potential at 2-loop level, we can effectively reduce the
theoretical uncertainty in the calculations of the phase transition parameters
due to the renormalization scale dependence, and the new physics scale is
restricted to be $\Lambda\lesssim (770-800)$ GeV by the baryon number washout
avoidance condition. Meanwhile, the presence of the chemical potential would
affect the phase transition parameter and make the constraints from the baryon
number washout avoidance condition more strict, especially for weaker
first-order phase transition scenarios at higher new physics scales.
