In diode characteristics, the knee (cut-in or threshold) voltage is approximately equal to which fundamental diode parameter?

Introduction / Context:
The knee voltage, also called cut-in or threshold voltage, marks the point on the forward I–V curve of a diode where current starts rising rapidly with small increases in applied voltage. Recognizing what this knee corresponds to helps interpret diode material types like silicon and germanium in practical circuits.

Given Data / Assumptions:

• We discuss a conventional p-n junction diode under forward bias.
• Temperature is nominal and effects like series resistance are modest.
• Typical values: about 0.7 V for silicon and about 0.3 V for germanium at room temperature.

Concept / Approach:
In forward bias, current remains small until the applied forward voltage approximately equals the built-in barrier potential of the junction. At that point, the potential hill opposing majority carrier flow is effectively overcome and current increases steeply. Thus, the knee corresponds to the barrier potential of the diode junction.

Step-by-Step Solution:
1) Consider the diode I–V curve in forward bias.2) Identify the knee region where the slope increases sharply.3) Recognize that this knee appears when the external forward voltage offsets the junction barrier potential.4) Conclude that knee voltage approximates the barrier potential.

Verification / Alternative check:
Comparing measured forward threshold for silicon diodes near 0.7 V with known barrier potentials supports the equivalence in practical usage.

Why Other Options Are Wrong:

• Applied voltage: Generic term, not a parameter equal to the knee point.
• Breakdown voltage: Occurs in reverse bias, unrelated to the forward knee.
• Forward voltage: A broad term; only near the barrier potential does the knee appear. Barrier potential is the precise concept.
• None of the above: Incorrect because barrier potential is correct.

Common Pitfalls:
Confusing forward knee with reverse breakdown is a common error. Also, assuming an exact fixed value ignores temperature and current-level dependence; the knee is approximate and context dependent.

Final Answer:
Barrier potential.