Which type of special-purpose diode has the characteristics of a voltage-controlled capacitor

A varactor diode (variable capacitor diode) is designed to act as a voltage-controlled capacitor. By changing the reverse bias voltage, you change the width of the depletion region, which changes the capacitance. Tunnel diodes exhibit negative resistance, Schottky diodes have low forward drop, and Zener diodes are used for voltage regulation.