睡着 (shuì zháo) means 'to fall asleep' or 'to be asleep'. It's a resultative verb compound composed of 睡 (to sleep) and 着 (zháo, a resultative complement indicating the action has achieved its result). The negative form is 睡不着 (shuì bù zháo, 'can't fall asleep'), and the potential form inserts 得 or 不 between the two characters to express ability or inability. Note that 着 is read zháo here, not zhe, which is the aspect particle.