A Zener diode
A Zener diode has a negative temperature coefficient of breakdown voltage.
The mechanism of Zener breakdown is the quantum tunneling of electrons. In a Zener diode, the depletion region width is very small due to very highly doped n and p regions. This makes the depletion region width very narrow, which creates a high electric field across it on application of reverse bias. On application of a suitable reverse bias across the diode, this high electric field causes the breaking of covalent bonds in the lattice, to liberate electron-hole pairs, and then pulls the carriers in the respective directions of the field.
The concerned electric field is directed from n side to p side, so minority electrons in the p side are drawn by this field to the n side, and minority holes in the n side are drawn to the p side.
As temperature increases, the thermal vibration of the lattice atoms increases, increasing the vibrational energy of the constituent electrons. This additional vibrational energy makes it easier for an electron to escape from the covalent bond, under the influence of the existing electric field.
Thus, with increased temperature, we have a large generation of minority carriers and their subsequent movement in the respective directions, at a lower value of reverse bias voltage. In other words, Zener breakdown voltage decreases with increase of temperature, as temperature facilitates breakdown.
Thus, the temperature coefficient of the Zener breakdown voltage is negative.