A conventional DRAM needs to be refreshed at an interval of several tens of milliseconds to hold data, which results in large power consumption. In addition, a transistor therein is frequently turned on and off; thus, deterioration of the transistor is also a problem. These problems become significant as the memory capacity increases and transistor miniaturization advances. A transistor is provided which includes a wide-gap semiconductor and has a trench structure including a trench for a gate electrode and a trench for element isolation. Even when the distance between a source electrode and a drain electrode is decreased, the occurrence of a short-channel effect can be suppressed by setting the depth of the trench for the gate electrode as appropriate.