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.

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:

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