The diffusion capacitance of a diode is an important parameter for understanding its dynamic behavior, especially at high frequencies. This type of capacitance is associated with charge storage in a diode’s depletion and neutral regions due to the diffusion of carriers.
When a P-N junction is forward-biased, a type of capacitance called diffusion capacitance or CD comes into play. The CD is much larger than the transition capacitance. When a P-N junction is forward biased, the potential barrier is reduced, allowing electrons from the N-side to enter the P-side and holes from the P-side to enter the N-side. These charge carriers diffuse away from the junction and gradually recombine. The density of charge carriers is highest near the junction and decreases exponentially with distance. Therefore, a charge is stored on both sides of the junction when forward-biased. The amount of stored charge varies with the applied potential, similar to a true capacitor. To describe this, we use an incremental capacitance called the diffusion or storage capacitance CD, which is given by the equation CD = dQ/dV. Here, dQ represents the change in the number of minority carriers stored outside the depletion region when a change in voltage across the diode, dV, is applied.
Diffusion Capacitance Formula
Diffusion Capacitance Formula Derivation
If the mean lifetime of charge carriers is τ, then a flow of charge Q will produce a diode current I.
The diode current equation is.
Putting the value of I from equation(2) in equation(1), we get,
The diffusion capacitance is,
Putting the value of Q from equation(3) in equation(4), we get,
For a forward bias voltage that exceeds a few tenths of a volt,
The diffusion Capacitance is
The capacitance(CD) is proportional to the forward current through the diode as the number of majority carriers injected into the depletion region increases with the forward current.
Solved Problem
Calculate the diffusion capacitance of a silicon diode at room temperature (300 K) when it is forward-biased at 0.7 V. Assume the following parameters:
- Saturation current (Is): 1×10−14 A
- Minority carrier lifetime (τ): 1μs = 1×10−6 s
- Electron charge (q): 1.6×10−19 C
- Boltzmann constant (k): 1.38×10−23 J/K
Solution Steps
1. Calculate the Forward Current (I): The current through a forward-biased diode can be calculated using the diode equation:
2. Calculate the diode Capacitance
These values indicate that the diffusion capacitance is significantly large, typical for diodes in forward bias, due to the exponential increase in charge carrier concentration at higher forward voltages. This capacitance must be considered in high-frequency applications where the dynamic behavior of the diode impacts circuit performance.
Conclusion
Diffusion capacitance is a key characteristic of diodes operating under forward bias conditions. It arises due to the storage of excess minority carriers that are injected into the neutral regions of the diode when it is forward-biased. This form of capacitance is significant because it can dominate the overall capacitance of the diode, particularly at high frequencies or under conditions of rapid current changes.