The Body Effect in MOSFETs: Concept, Equation, and Impact on Circuit Design

In an ideal MOSFET, the threshold voltage (V_TH) is fixed and depends only on the gate oxide and channel doping. However, in real devices, the potential difference between the body (substrate) and the source affects the threshold voltage. This phenomenon is known as the Body Effect or Bulk Effect. It is an essential concept for analog designers, as it directly influences biasing, gain, and matching in integrated circuits.

1. What is the Body Effect?

The body effect arises because the substrate acts as a second gate that influences the channel. When the source-to-body voltage (V_SB) is nonzero, the depletion region under the channel changes, altering the voltage required to invert the surface.

In most cases, the body (or bulk) is tied to the lowest potential in the circuit (ground for NMOS, V_DD for PMOS). If the source voltage rises above the body potential, a reverse bias develops across the source-body junction, increasing the depletion width and therefore the threshold voltage.

2. Mathematical Expression for Body Effect

The threshold voltage considering the body effect is given by:

V_TH = V_TH0 + γ(√|2ϕ_F + V_SB| – √|2ϕ_F|)

Where:

• V_TH0: Threshold voltage when V_SB = 0
• γ: Body effect coefficient = √(2qε_siN_A)/C_ox
• ϕ_F: Fermi potential
• V_SB: Source-to-body voltage

As V_SB increases, the term under the square root grows, thus increasing V_TH.

3. Physical Explanation

When the source-body junction becomes more reverse-biased, more charge is required at the gate to invert the channel. This means a higher V_GS is needed to turn the MOSFET ON. In effect, the device becomes less sensitive to gate voltage variations and requires more voltage to conduct.

4. Impact on Analog Design

The body effect introduces several challenges in analog circuits:

• Bias Shift: The threshold voltage varies with V_SB, altering bias currents in current mirrors and amplifiers.
• Gain Reduction: Changes in V_TH reduce transconductance (g_m), decreasing voltage gain.
• Mismatch: Devices with different source voltages will have different V_TH, leading to offset errors in differential pairs.
• Output Swing Limitation: In source followers, the body effect limits how close the output can approach the gate voltage.

5. Body Effect in NMOS and PMOS

• For NMOS: The body is tied to the lowest potential (usually ground). As the source rises, V_SB increases, causing V_TH to increase.
• For PMOS: The body is tied to V_DD. When the source goes below the body potential, the threshold magnitude increases (|V_TH| increases).

6. Design Techniques to Reduce Body Effect

• Use body ties: In full-custom ICs, the body can be tied to the source to eliminate V_SB.
• Use isolated wells: In twin-well or triple-well processes, the body potential can be independently controlled.
• Use differential architectures: Minimizes mismatch due to common-mode body bias variations.
• Longer channel devices: Reduce body effect sensitivity in precision circuits.

7. Impact on Circuit Examples

Source Follower: The body effect increases the voltage drop between input and output, typically by 0.2–0.4 V, limiting output swing.

Differential Pair: Mismatch in source potential leads to different threshold voltages, introducing offset and degrading common-mode rejection.

Current Mirrors: Variation in threshold voltage due to V_SB causes unequal currents, lowering mirror accuracy.

8. Interview Questions on Body Effect

• What is the body effect in MOSFETs and why does it occur?
• How does V_SB influence the threshold voltage?
• Why is the body effect more significant in analog design?
• What methods are used to eliminate or reduce body effect?
• How does body effect impact the performance of a source follower?

Conclusion

The body effect is a fundamental non-ideality in MOSFETs that modifies the threshold voltage based on the body-source bias. In analog and mixed-signal design, it impacts gain, bias stability, and matching. A good designer must understand and mitigate its effects using proper layout and circuit techniques. In interviews, this topic often appears in discussions on biasing, current mirrors, and source followers.