Temperature Dependence of Reverse Saturation Current: A silicon p–n junction at 20 °C has a reverse saturation current of 10 pA. Approximate the reverse saturation current at 40 °C for the same bias.
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A30 pA
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B40 pA
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C50 pA
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D60 pA
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E20 pA
Answer
Correct Answer: 40 pA
Explanation
Introduction / Context:The reverse saturation current (Is) of a p–n junction diode is highly temperature dependent. A widely used engineering rule of thumb states that Is doubles for approximately every 10 °C rise in temperature. This approximation is useful for predicting leakage current increases with temperature.
Given Data / Assumptions:
- Diode type: silicon p–n junction.
- Temperature T1 = 20 °C, reverse saturation current Is1 = 10 pA.
- Temperature T2 = 40 °C.
- Approximation: Is doubles for each 10 °C rise.
Concept / Approach:
From 20 °C to 40 °C is a 20 °C rise, which corresponds to two 10 °C steps. Therefore, the reverse saturation current doubles twice.
Step-by-Step Solution:
Step 1: Start with Is1 = 10 pA at 20 °C.Step 2: At 30 °C, Is ≈ 20 pA.Step 3: At 40 °C, Is ≈ 40 pA.Verification / Alternative check:
More exact models use Is ∝ T^3 * exp(−Eg / (kT)), but for small temperature intervals the doubling rule is sufficiently accurate, confirming ~40 pA.
Why Other Options Are Wrong:
- 30 pA: correct for ~15 °C rise, not 20 °C.
- 50 pA, 60 pA: overestimates doubling effect.
- 20 pA: corresponds to 30 °C, not 40 °C.
Common Pitfalls:
- Forgetting the 'doubles every 10 °C' rule.
- Confusing silicon with germanium behavior.
Final Answer:
40 pA