A semiconductor memory cell includes a floating body region configured to be charged to a level indicative of a state of the memory cell; a first region in electrical contact with said floating body region; a second region in electrical contact with said floating body region and spaced apart from said first region; a gate positioned between said first and second regions; and a back-bias region configured to inject charge into or extract charge out of said floating body region to maintain said state of the memory cell. Application of back bias to the back bias region offsets charge leakage out of the floating body and performs a holding operation on the cell. The cell may be a multi-level cell. Arrays of memory cells are disclosed for making a memory device.