An integrated circuit device (e.g., a logic device or a memory device) having (i) a memory cell array which includes a plurality of memory cells (for example, memory cells having electrically floating body transistors) arranged in a matrix of rows and columns, wherein each memory cell includes at least one transistor having a gate, gate dielectric and first, second and body regions, wherein: (i) the gate and gate dielectric are disposed on or above the first semiconductor layer that is disposed on or above an insulating layer or region, (ii) the body region of each transistor is electrically floating, (iii) the transistors of adjacent memory cells include a layout that provides a common first region, and (iv) the first regions of the transistors are comprised of a semiconductor material which is different from the material of the first semiconductor layer. Also disclosed are inventive methods of manufacturing, for example, such integrated circuit devices.