Question

The I-V characteristic of a semiconductor diode in forward bias is a/an:

• A. straight line
• B. parabolic curve
• C. exponentially decreasing curve
• D. exponentially increasing curve
• E. sinusoidal curve

Hint:

Diode forward current follows exponential law \( I \propto e^V \), not linear Ohm’s law.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks about the relationship between current (I) and voltage (V) for a semiconductor p-n junction diode when it is forward-biased. Forward bias occurs when the positive terminal of a voltage source is connected to the p-type material and the negative terminal to the n-type material.
Step 2: Key Formula or Approach:
The current-voltage relationship for an ideal p-n junction diode is given by the Shockley diode equation:
\[ I = I_s \left( e^{\frac{qV}{nkT}} - 1 \right) \] where:
- I is the diode current.
- \( I_s \) is the reverse bias saturation current (a very small constant).
- q is the magnitude of the electron charge.
- V is the voltage across the diode.
- n is the ideality factor (typically between 1 and 2).
- k is the Boltzmann constant.
- T is the absolute temperature.
We need to analyze the behavior of this equation under forward bias conditions.
Step 3: Detailed Explanation:
In forward bias, the applied voltage V is positive. The term \( \frac{qV}{nkT} \) is positive and typically much greater than 1, especially once the voltage exceeds the knee voltage (around 0.7 V for silicon).
When \( e^{\frac{qV}{nkT}} \gg 1 \), the '\(-1\)' term in the Shockley equation becomes negligible. The equation can be approximated as:
\[ I \approx I_s e^{\frac{qV}{nkT}} \] This equation shows that the forward current (I) increases exponentially with the applied forward voltage (V).
When plotted on an I-V graph, this relationship results in a curve that is initially very flat (for small V) and then rises very steeply in an exponential fashion after a certain threshold voltage (the knee or cut-in voltage) is reached.
Therefore, the I-V characteristic is an exponentially increasing curve.
- A straight line (A) would imply a linear relationship (I \( \propto \) V), which is characteristic of an ohmic resistor, not a diode.
- Parabolic (B), decreasing (C), and sinusoidal (E) curves do not describe the diode's behavior.
Step 4: Final Answer:
The I-V characteristic of a semiconductor diode in forward bias is an exponentially increasing curve. This corresponds to option (D).