ISRO EC 2023 Q.13: solution and answer

ISRO 2023 · ECQ.13 · 1 mark · MCQ

Which parameter of semiconductor diode exhibits positive temperature co-efficient?

(A)
Reverse leakage current
(B)
Reverse breakdown voltage
(C)
Forward voltage
(D)
None of the above

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Answer and solution

ANSWER

The reverse leakage current has a positive temperature coefficient, option (a).

Official answer: ASource: ISRO's revised and final answer key of 16 February 2024

Reverse leakage current comes from thermally generated minority carriers, so $I_{0} \propto n_{i}^{2} \propto T^{3} e^{- E_{g} / k T}$ . It rises steeply with temperature, roughly doubling for every $10^{\circ} C$ increase. This is a positive temperature coefficient, so (a) qualifies.
Forward voltage at a constant current falls by about $2 mV /^{\circ} C$ . This is a negative coefficient, so (c) is wrong.
Reverse breakdown voltage has no single sign. Zener breakdown (below about $5 V$ ) has a negative coefficient, avalanche breakdown (above about $7 V$ ) has a positive one. Because it is not positive for every diode, it cannot be the parameter singled out in (b).
Since (a) is a positive coefficient in every diode, 'None of the above' in (d) is wrong. The answer is (a).

KEY IDEA

Thermally generated minority carriers make reverse saturation current grow rapidly with temperature, about doubling per $10^{\circ} C$ . Forward voltage falls with temperature at about $2 mV /^{\circ} C$ .

WATCH OUT FOR

Choosing reverse breakdown voltage because avalanche breakdown has a positive coefficient. Zener breakdown has a negative one, so the sign depends on the diode, whereas leakage current always rises with temperature.

From the ISRO EC 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 1 ISRO P-N junction question, with notes