Channel Length Modulation in MOSFETs: Concept, Equation, and Impact on Circuits

In MOSFETs, the assumption of a perfectly flat saturation region is only an approximation. In reality, the drain current slightly increases with V_DS even in saturation. This phenomenon is known as channel length modulation. It is a key non-ideal effect in MOSFET operation and an important topic in analog design interviews.

1. Ideal MOSFET Saturation

In the ideal case (without channel length modulation), the MOSFET drain current in saturation is given by:

I_D = (1/2) μ_n C_ox (W/L) (V_GS – V_TH)²

This implies that once V_DS > V_GS – V_TH, the current is constant and independent of V_DS.

2. Real Behavior – Channel Length Modulation

In practice, as V_DS increases, the depletion region at the drain expands into the channel, effectively reducing the channel length (L). Since I_D ∝ 1/L, the current increases slightly with V_DS. This effect is called channel length modulation.

3. Modified Equation

With channel length modulation, the saturation current equation becomes:

I_D = (1/2) μ_n C_ox (W/L) (V_GS – V_TH)² (1 + λV_DS)

Where λ (lambda) is the channel length modulation parameter, typically small (e.g., 0.01–0.05 V⁻¹).

4. Output Resistance

Channel length modulation introduces a finite slope in the I_D–V_DS curve in saturation, which corresponds to a finite output resistance (r_o):

r_o = 1 / (λ I_D)

Thus, higher I_D or larger λ reduces output resistance, degrading amplifier gain.

5. Impact on Circuits

• Decreases intrinsic gain: Since gain A_v ≈ g_mr_o, finite r_o reduces amplifier gain.
• Affects current mirrors: Output current depends on V_DS, reducing accuracy.
• More significant in short-channel devices: As L shrinks in modern technologies, channel length modulation becomes more pronounced.

6. Techniques to Minimize Channel Length Modulation

• Use cascode configurations to increase output resistance.
• Use longer channel lengths in critical analog devices.
• Employ feedback techniques in analog design to stabilize gain.

7. Interview Questions on Channel Length Modulation

• What is channel length modulation and why does it occur?
• Derive the modified drain current equation with λ.
• How does channel length modulation affect output resistance?
• Why is channel length modulation more severe in short-channel technologies?
• What circuit techniques help reduce its effect?

Conclusion

Channel length modulation is an unavoidable non-ideal effect in MOSFETs that reduces output resistance and amplifier gain. Understanding its impact and methods to counteract it is critical for analog and mixed-signal design engineers, and it is a frequent interview question in the semiconductor industry.