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 .