Subthreshold Conduction in MOSFETs: Concept, Equation, and Design Impact

In an ideal MOSFET, when the gate-to-source voltage (V_GS) is less than the threshold voltage (V_TH), the device is considered OFF. However, in reality, a small but significant current still flows even when V_GS < V_TH. This current is known as subthreshold conduction or weak inversion current. It plays a key role in low-power circuits and leakage analysis, and is an important topic in analog and VLSI interviews.

1. What is Subthreshold Conduction?

Subthreshold conduction occurs due to diffusion of carriers between the source and drain when the surface potential is not high enough to form a strong inversion channel. Even though the transistor is “off,” the depletion region allows minority carriers to diffuse, resulting in a small drain current.

This current behaves exponentially with respect to gate voltage rather than quadratically as in strong inversion.

2. Subthreshold Current Equation

The drain current in the subthreshold (weak inversion) region is expressed as:

I_D = I₀ exp((V_GS – V_TH)/(nV_T)) (1 – exp(–V_DS/V_T))

Where:

• I₀ = current constant depending on device geometry
• V_T = thermal voltage (≈ 26 mV at 300 K)
• n = subthreshold slope factor (typically 1.3–1.5)

For large V_DS, the term (1 – exp(–V_DS/V_T)) ≈ 1, so the current simplifies to:

I_D ≈ I₀ exp((V_GS – V_TH)/(nV_T))

3. Subthreshold Slope (S)

The subthreshold slope defines how effectively the transistor can switch from OFF to ON state. It is given by:

S = (dV_GS / d(log I_D)) = n × 60 mV/decade at 300 K

Where n depends on the oxide capacitance and depletion capacitance:

n = 1 + (C_dep/C_ox)

Ideal value of S is 60 mV/dec, but practical MOSFETs show 70–100 mV/dec due to non-idealities.

4. Factors Affecting Subthreshold Conduction

• Temperature: Higher temperature increases V_T and hence subthreshold current.
• Channel Length: Shorter channels increase DIBL, reducing effective threshold voltage and increasing leakage.
• Body Bias: Reverse body bias increases V_TH, reducing subthreshold current.
• Oxide Thickness: Thinner oxides increase gate control and reduce leakage.

5. Impact on Analog Design

Although subthreshold current is undesirable in digital circuits due to leakage, it can be useful in analog design, especially in ultra-low-power applications.

• Low-Power Amplifiers: Operating transistors in weak inversion provides very high transconductance per unit current.
• Low-Noise Circuits: Weak inversion can offer better noise efficiency for small-signal applications.
• Leakage Trade-Off: Designers must balance performance and leakage in mixed-signal ICs.

6. Comparison Between Strong and Weak Inversion

7. Interview Questions

• What causes subthreshold conduction in a MOSFET?
• Explain subthreshold slope and its significance.
• Why is the subthreshold current exponential in V_GS?
• What factors determine the subthreshold slope factor (n)?
• How can subthreshold operation be used beneficially in analog design?

Conclusion

Subthreshold conduction is a critical non-ideality in MOSFETs that becomes more prominent with technology scaling. While it increases leakage in digital circuits, analog designers often exploit it for ultra-low-power operation. Understanding its exponential behavior, slope, and temperature dependence is essential for any analog or VLSI engineer.