Mixed-cell-height　standard　cells　are　prevailingly　used　in　advanced　technologies　to　achieve　better　design　trade-offs　among　timing,　power,　and　routability.　As　feature　size　decreases,　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　paper,　we　address　the　mixed-cell-height　placement　problem　with　MIA　constraints　into　two　major　stages:　post　global　placement　and　MIA-aware　legalization.　In　the　post　global　placement　stage,　we　first　present　a　continuous　and　differentiable　cost　function　to　address　the　Vdd/Vss　alignment　constraints,　and　add　weighted　pseudo　nets　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　intra-row　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　8.5%　shorter　final　total　wirelength　than　the　state-of-the-art　work.