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A semiconductor device such as a DRAM memory device is disclosed. A substrate 12 of semiconductor material is provided with energy band modifying means in the form of a box region 38 and is covered by an insulating layer 14. A semiconductor layer 16 has source 18 and drain 20 regions formed therein to define bodies 22 of respective field effect transistors. The box region 38 is more heavily doped than the adjacent body 22, but less highly doped than the corresponding source 18 and drain 20, and modifies the valence and/or conduction band of the body 22 to increase the amount of electrical charge which can be stored in the body 22.