【Semiconductor】 📐 08-06. BSIM4 AC/CV Analysis — How to Read Parasitic Capacitance and Frequency Response Correctly”

topics: [“Semiconductor”, “BSIM4”, “SPICE”, “AC Analysis”, “CV Analysis”]

🚀 Introduction

In the previous article, we focused on DC analysis (V–I characteristics).
However, MOSFETs are not devices used only under DC conditions.

• ⚡ High-speed digital circuits
• 🎛 Analog circuits
• 📡 Frequency response and bandwidth design

For all of these applications,
👉 understanding parasitic capacitance and frequency behavior is essential.

In this article, using the BSIM4 model, we systematically explain:

• 📊 AC analysis (frequency response)
• 🧪 CV analysis (capacitance characteristics)

with a clear focus on what can be trusted and what requires caution.

🧭 Difference Between AC Analysis and CV Analysis

🔹 What is AC Analysis?

• Superimposes a small-signal AC excitation around a DC operating point
• Sweeps frequency to evaluate circuit response

What you can observe:

• Small-signal gain
• Phase response
• Bandwidth
• Transconductance $g_m$
• Output resistance $r_o$

👉 AC analysis tells us how fast a circuit can respond.

🔹 What is CV Analysis?

• Evaluates intrinsic capacitance components inside a MOSFET
• Observes how capacitance changes with bias conditions

Typical capacitances:

• Gate capacitance $C_{gg}$
• (Reference) $C_{gs}$, $C_{gd}$, $C_{gb}$

👉 CV characteristics directly affect delay, switching speed, and high-frequency behavior.

🧰 Analysis Environment (SemiDevKit)

This article uses the following tool:

• BSIM4 C–V Extraction Tool (ngspice)
  https://samizo-aitl.github.io/SemiDevKit/bsim/bsim4_analyzer_cv/

Prerequisites

• BSIM4 model cards (educational / analytical)
• ngspice 41 (64-bit)
• Python 3.9+
• matplotlib

⚠️ How to Think About CV Analysis (Important)

In BSIM4, capacitances are defined based on terminal charges.

Physically Meaningful Capacitance

C_{gg} = \frac{dQ_g}{dV_g}

• The derivative of total gate charge
• Uniquely defined by MOS electrostatics

Pitfall: Partitioned Capacitances

BSIM4 can also output:

• $C_{gs}$
• $C_{gd}$
• $C_{gb}$

However, these are:

• Strongly dependent on the charge-partitioning algorithm
• Not guaranteed to satisfy:

C_{gs} + C_{gd} + C_{gb} \neq C_{gg}

👉 Therefore, they are not always suitable as physical CV characteristics.

For this reason, this tool intentionally adopts:

✅ Extraction of $C_{gg}$ only
❌ $C_{gs}$ / $C_{gd}$ / $C_{gb}$ are excluded

This ensures physical interpretability and numerical stability.

🧪 Running CV Analysis

python run_cv.py

This automatically generates and executes:

• NMOS / PMOS
• Temperature corners: LT / RT / HT

for a total of six simulation conditions.

🧩 NMOS / PMOS Terminal Conditions

🔹 NMOS

• S = D = B = 0 V
• Gate sweep: 0 → VDD

🔹 PMOS (Important)

• S = D = B = VDD
• Gate sweep: VDD → 0 V

👉 Matches real device ON/OFF behavior
👉 Ensures physically correct PMOS biasing

📈 CV Analysis Results

■ NMOS C–V (130 nm, RT)

• Accumulation → depletion → inversion
• U-shaped $C_{gg}$–$V_g$ characteristic

■ PMOS C–V (130 nm, RT)

• Sweep from VDD → 0 V
• Consistent with real PMOS operation

📡 AC Analysis: Frequency Response

python run_ac.py

In AC analysis:

• A small AC signal is applied
• Frequency is swept around a DC operating point

This reveals:

• Gain
• Phase
• Bandwidth

👉 If DC analysis is incorrect, AC analysis becomes meaningless
👉 Always follow the order: DC → AC → CV

🧠 Where Do Parasitic Capacitances Come From?

MOSFET parasitic capacitances originate from:

• Gate oxide
• Channel formation
• Gate overlap regions
• Depletion regions

These are exactly the potential and carrier distributions observed in TCAD.

👉 BSIM4 simply compresses this physics into a compact model.

🔗 Relationship with DC Analysis

A critical principle:

AC and CV analyses are completely dependent on the DC operating point

• Incorrect DC → meaningless AC/CV
• Correct DC → meaningful small-signal analysis

👉 Always start from DC correctness.

📝 Summary

• 📊 AC analysis evaluates frequency response
• 🧪 CV analysis evaluates parasitic capacitance
• ⚠️ In BSIM4, only $C_{gg}$ has clear physical meaning
• 🧠 Correct DC analysis is the foundation of everything

To use BSIM4 as a trustworthy model,
you must clearly understand what to look at — and what not to trust.

Next Article 👉

07: MOSFET L/W Scaling and Short-Channel Effects