**Question- Diffusion Capacitance of PN Junction diode_________**

**A. Increases linearly with forward bias voltage.****B. Decreases linearly with forward bias voltage.****C. Increases exponentially with forward bias voltage.****D. Decreases exponentially with forward bias voltage.**

**Answer: **

**The correct option is (C)**

The Diffusion Capacitance of the PN Junction Diode increases exponentially with forward bias voltage because diffusion capacitance is proportional to the current flowing through the diode, and the current is exponentially proportional to the forward voltage. A detailed explanation is given below.

**Explanation:**

The diffusion capacitance of a PN junction diode is a crucial parameter that describes the **diode’s ability to store charge under forward bias conditions**.To understand why it increases exponentially with forward bias voltage, let us first discuss the diode and its operation in forward bias and how diffusion capacitance forms.

### Basics of PN Junction Diode

A PN junction diode consists of two semiconductor regions: the p-type and the n-type. The p-type contains an excess of holes (positive charge carriers), while the n-type contains an excess of electrons (negative charge carriers). At the junction of these two regions, a depletion region forms due to the diffusion of carriers, resulting in a barrier that prevents further charge movement under no external voltage.

Forward Bias Condition

When a forward bias voltage is applied (positive to the p-side and negative to the n-side), it reduces the barrier height at the junction, allowing charge carriers (holes and electrons) to diffuse across the junction more readily. The applied voltage essentially “pushes” the carriers over the barrier.

**Diffusion Capacitance**

Diffusion capacitance primarily arises from the excess minority carriers (electrons in the p-side and holes in the n-side) that accumulate in the quasi-neutral regions of the diode under forward bias conditions. These minority carriers are injected from the regions of higher concentration to lower concentration and take some time to recombine with majority carriers. The amount of charge stored in this way, and thus the diffusion capacitance, depends on the rate of injection of these carriers.

### Exponential Increase of Diffusion Capacitance with Forward Voltage Explained

**Carrier Injection**: Under forward bias, as the voltage increases, the barrier lowering allows more carriers to be injected over the barrier into the opposite type regions. This injection of carriers is exponential with respect to the applied forward bias voltage, following the**diode equation 𝐼=𝐼**where 𝐼_{0}(𝑒^{𝑉/𝑉𝑇}−1),*is*current, 𝐼_{0}is the reverse saturation current,*V*is the applied voltage, and*V* is the thermal voltage._{T}**Charge Storage**: The stored charge in the diode, due to the excess minority carriers, is directly proportional to the diode current. Because the current increases exponentially with voltage, so does the charge storage.**Diffusion Capacitance Formula**: The diffusion capacitance 𝐶_{𝑑} is given by the formula 𝐶_{𝑑}=𝜏𝑑𝐼/𝑑𝑉, where*τ*is the minority carrier lifetime and 𝑑𝐼/𝑑𝑉 represents the differential conductance of the diode. Since the diode current 𝐼 increases exponentially with the voltage*V*, the derivative 𝑑𝐼/𝑑𝑉 i*ncreases exponentially*, and hence diffusion capacitance 𝐶_{𝑑 }also increases exponentially.

Thus, the diffusion capacitance of a PN junction diode increases exponentially with the forward bias voltage due to the exponential increase in carrier injection and charge storage under forward bias.

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