Methods of forming gate contact structures and cross-coupled contact structures for transistor devices

A method, comprising:

• forming a source/drain region of a first transistor;
• forming a conductive source/drain contact structure contacting the source/drain region;
• forming a gate-to-source/drain (GSD) contact opening in at least one layer of insulating material exposing at least one surface of said conductive source/drain contact structure of said first transistor and a first gate structure, wherein a height of said conductive source/drain contact structure is greater than a height of said first gate structure;
• forming a gate contact opening in at least one layer of insulating material exposing a second gate structure;
• forming an initial gate-to-source/drain (GSD) contact structure in said gate-to-source/drain GSD contact opening conductively coupled to said conductive source/drain contact structure and said first gate structure;
• forming an initial gate contact structure in said gate contact opening conductively coupled to said second gate structure, wherein an upper surface of each of said initial gate-to-source/drain GSD contact structure and said initial gate contact structure is positioned at a first level, and said first conductive source/drain contact structure has an insulating source/drain cap positioned above at least a portion of an upper surface of said conductive source/drain contact structure;
• performing a recess etching process on said initial gate-to-source/drain GSD contact structure and said initial gate contact structure at a same first time to form a recessed GSD contact structure and a recessed gate contact structure, wherein a recessed upper surface of each of said recessed GSD contact structure and said recessed gate contact structure is positioned at a second level that is below said first level, said second level is at a level that is above a level of an upper surface of said insulating source/drain cap, and said second level is below an uppermost surface of said at least one layer of insulating material;
• and
• forming first and second separate conductive contact structures at a same second time, said first conductive contact structure being positioned above and conductively coupled to said gate contact structure, said second conductive contact being positioned above and conductively coupled to a second conductive source/drain contact structure.