A semiconductor memory includes p-type MOS transistors (11) dispersed in one-to-one correspondence with sense amplifiers (4−1-4−n) to activate their corresponding sense amplifiers, and a p-type MOS transistor (12) to activate the sense amplifiers (4−1-4−n). After the p-type MOS transistors (11) are overdriven by an external voltage (VCC) higher than a memory stored voltage, the p-type MOS transistor (12) is driven by an internal step-down voltage (VII) that is the memory stored voltage. This increases the driving capability per sense amplifier in comparison with a conventional method and further increases the speed of sense operation in comparison with a simple overdriving method.