A storage device includes a non-volatile memory, a volatile memory and a controller. The volatile memory supports a normal mode and a self-refresh mode. The controller is configured to store data for a host in the non-volatile memory while using the volatile memory in the normal mode and, in response to receiving a power-down command from the host, to deactivate at least part of the storage device and to switch the volatile memory from the normal mode to the self-refresh mode.