Sekhemkhet was likely son of Pharaoh Djoser, however, he was his successor. Sekhemkhet is also known as Djosertety. His name wasn't mentioned in any list of Pharaohs, but a sign with his name was discovered in Wadi Maghareh in the Sinai Peninsula. His name wasn't translated correctly, so it is possible, that his name was mistakenly associated with a Pharaoh of Archaic period Semerkhet.
Sekhemkhet ruled for 6 years in Egypt
According to the Turin King List Sekhemkhet ruled for 6 years. There is Sekhemkhet's pyramid in Saqqara (it is a step pyramid as well as the Djoser's). Unfortunately there isn't more preserved information about this Pharaoh, except two rock inscriptions in Wadi Maghareh in the Sinai peninsula.
Considering tha fact, that a period of decline of absolutist power followed after Sekhemkhet and following Pharaohs were insignificant and weak, Sekhemkhet was probably murdered.
Sekhemkhet - a detail from Wadi Magrareh in the Sinai peninsula