Define Knee and breakdown voltages.

Knee Voltage:

• In the context of semiconductor devices, the knee voltage refers to the voltage at which a significant increase in current flow occurs in a reverse-biased diode.
• It is typically associated with the onset of avalanche breakdown or Zener breakdown.

Derivation of Knee Voltage:

1. Forward Bias: When a diode is forward-biased, the depletion region narrows allowing a significant number of carriers to cross the junction, resulting in a low resistance and high current flow. The voltage drop across the diode is typically small, typically around 0.6-1.0 V for silicon diodes.

2. Reverse Bias: When a diode is reverse-biased, the depletion region widens, creating a barrier for carrier flow. Initially, a small reverse current, known as the leakage current, flows due to minority carriers. As the reverse voltage increases, more carriers are generated due to thermal excitation, leading to a gradual increase in the reverse current.

3. Knee Voltage: As the reverse voltage approaches the knee voltage, the reverse current starts to increase more rapidly. This is because the electric field across the depletion region becomes sufficiently strong to initiate impact ionization or Zener tunneling.

4. Impact Ionization: Under high electric fields, the reverse current increases due to impact ionization. High-energy carriers collide with atoms in the semiconductor lattice, generating additional electron-hole pairs. These newly generated carriers contribute to the reverse current, leading to a rapid increase in current flow.

5. Zener Breakdown: In some diodes, particularly Zener diodes, the knee voltage corresponds to the onset of Zener breakdown. Here, the electric field is strong enough to cause tunneling of electrons from the valence band to the conduction band, resulting in a sudden increase in current.

Breakdown Voltage:

• Breakdown voltage refers to the maximum reverse voltage that a diode can withstand before permanent damage occurs.

Derivation of Breakdown Voltage:

1. Avalanche Breakdown:

• In most diodes, breakdown occurs due to avalanche breakdown.
• As the reverse voltage increases beyond the knee voltage, the impact ionization process becomes more pronounced.
• The newly generated carriers collide with more atoms, creating an exponential increase in the reverse current.
• This leads to a self-sustaining process, known as avalanche breakdown, where the current increases rapidly until the diode is destroyed.

1. Zener Breakdown:

• In Zener diodes, breakdown occurs due to Zener tunneling.
• When the reverse voltage reaches the Zener voltage, which is typically higher than the knee voltage, a large number of electrons tunnel from the valence band to the conduction band.
• This sudden increase in current causes Zener breakdown.
• Zener diodes are designed to operate in this breakdown region, allowing them to regulate voltage.

Conclusion:

• Knee voltage and breakdown voltage are crucial parameters in semiconductor diodes.
• The knee voltage indicates the onset of significant current flow under reverse bias, while the breakdown voltage represents the maximum reverse voltage the diode can withstand.
• Understanding these concepts is essential when analyzing and designing diode circuits.