Mixed-cell-height　standard　cells　are　prevailingly　used　in　advanced　technologies　to　achieve　better　design　tradeoffs　among　timing,　power,　and　routability.　As　feature　size　decreases,　the　placement　of　cells　with　multiple　threshold　voltages　may　violate　the　complex　minimum-implant-area　(MIA)　layer　rule　arising　from　the　limitations　of　patterning　technologies.　Existing　works　consider　the　mixed-cell-height　placement　problem　only　during　legalization　or　handle　the　MIA　constraints　during　detailed　placement.　In　this　article,　we　address　the　mixed-cell-height　placement　problem　with　MIA　constraints　in　two　major　stages:　1)　post-global　placement　(Post-GP)　and　2)　MIA-aware　legalization.　In　the　Post-GP　stage,　we　first　present　a　continuous　and　differentiable　cost　function　to　address　the　Vdd/Vss　alignment　constraints　and　add　weighted　pseudonets　to　MIA-violation　cells　dynamically.　Then,　we　propose　a　proximal　optimization　method　based　on　the　given　global　placement　result　to　simultaneously　consider　Vdd/Vss　alignment　constraints,　MIA　constraints,　cell　distribution,　cell　displacement,　and　total　wirelength.　In　the　MIA-aware　legalization　stage,　we　develop　a　graph-based　method　to　cluster　cells　of　specific　threshold　voltages　and　apply　a　strip-packing-based　binary　linear　programming　to　reshape　cells.　Then,　we　propose　a　matching-based　technique　to　resolve　intrarow　MIA　violations　and　reduce　filler　insertion.　Furthermore,　we　formulate　inter-row　MIA-aware　legalization　as　a　quadratic　programming　problem,　which　is　efficiently　solved　by　a　modulus-based　matrix　splitting　iteration　method.　Finally,　MIA-aware　cell　allocation　and　refinement　are　performed　to　further　improve　the　result.　Experimental　results　show　that　without　any　extra　area　overhead,　our　algorithm　still　can　achieve　5.4%　shorter　final　total　wirelength　than　the　state-of-the-art　work.