A demateralisation circuit was an essential part of a Type 40 TARDIS which enabled it to dematerialise from normal space into the Vortex and rematerialise later back into it. (DW: Terror of the Autons) It did the slowly appear/disappear in universe(s), and a fast appear/disappear in the Vortex. (This is shown on the 2005-2010 opening title animation, where it appears at the beginning and disappears before the name of the episode is shown.)
During his exile on Earth, the Time Lords removed the "dematerialisation codes" from the Doctor's mind and made the dematerialisation circuit of his TARDIS inactive. He therefore coveted the working dematerialisation circuit of the Master's TARDIS (DW: Terror of the Autons, The Mind of Evil, EDA: The Eight Doctors). Once the Time Lords had rescinded his exile after his defeat of the renegade Time Lord Omega, the Time Lords restored this knowledge to the Doctor memory. (DW: The Three Doctors)