A dematerialisation circuit was an essential part of a TARDIS which enabled it to dematerialise from normal space into the Time Vortex and rematerialise back from it. (TV: Terror of the Autons) The Doctor's Type-40 TARDIS used a Mark I model, and the Master's TARDIS used a Mark II.
During his exile on Earth, the Time Lords removed the dematerialisation codes from the Third Doctor's mind and made the dematerialisation circuit of his TARDIS inactive. He coveted the working dematerialisation circuit of the Master's TARDIS, and switched his defective circuit with the Master's. Although he learned he could not use the circuit with his TARDIS, the Doctor was cheered to realise the Master was now as trapped on Earth as he. (TV: Terror of the Autons, The Mind of Evil, PROSE: The Eight Doctors) Once the Time Lords had rescinded the Doctor's exile as thanks for his defeat of the renegade Time Lord Omega, they also restored his knowledge of the dematerialisation codes and provided him with a new circuit. (TV: The Three Doctors)