My 6D has a "Manual Sensor" cleaning setting in the menu that states the mirror locks up exposing the sensor and has this warning: "The surface of the image sensor is extremely delicate. If the sensor needs to be cleaned directly, having it done by a Canon Service Center is recommended." It seems to suggest when manually cleaning the sensor you're actually cleaning the surface of the sensor. By either way, I would exercise as much care as possible when performing a cleaning.

Personally, if I was going to attempt to clean the sensor myself, I would purchase a sensor cleaning kit that is specifically made foe the purpose. However, as long as my Camera is under warranty, I'd send it to a Canon Service center.