【Semiconductor】 📈 08-05. Reading MOSFET DC Characteristics with BSIM4 — Vg–Id / Vd–Id Analysis

topics: [“Semiconductor”, “BSIM4”, “SPICE”, “DC Analysis”, “MOSFET”]

🧭 Introduction

In the previous article, we covered BSIM4 model generation using Paramus.
Once a model card is created, there is one essential next step:

Verify what kind of V–I characteristics the model actually exhibits.

In this article, we use DC analysis with a BSIM4 MOSFET model to visualize:

• Gate voltage sweep: $V_g$ – $I_d$ characteristics
• Drain voltage sweep: $V_d$ – $I_d$ characteristics

Through these plots, we organize the basic MOSFET operation and the
physical meaning of model parameters.

🔍 What Is DC Analysis?

DC analysis evaluates the steady-state voltage–current (V–I) relationship,
ignoring time-dependent effects.

For MOSFETs, the two most important DC characteristics are:

• $V_g$ – $I_d$ (transfer characteristics)
• $V_d$ – $I_d$ (output characteristics)

These characteristics are the starting point for:

• Device understanding
• Model validation
• Circuit design and evaluation

They are the most fundamental and essential characteristics.

🧰 Analysis Environment (SemiDevKit)

In this article, we use the BSIM4 DC Analyzer included in SemiDevKit.

🔗 Tool Page
BSIM4_ANALYZER_DC | SemiDevKit

Features

• Automated DC analysis using BSIM4 × ngspice × Python
• NMOS / PMOS (130 nm) support
• Automatic plotting of $V_g$–$I_d$ and $V_d$–$I_d$
• Automatic extraction of $V_t$, $g_{m,\max}$, $I_{d,\mathrm{lin}}$, $I_{d,\mathrm{sat}}$
• Designed for education, with a view toward future commercial-grade analysis tools

Prerequisites

• BSIM4 model card (generated by Paramus)
• ngspice
• Python 3.10 or later

📉 Vg–Id Analysis (Gate Voltage Sweep)

How to Run

cd bsim/bsim4_analyzer_dc/run
python run_vgid.py

This script automatically performs:

1. SPICE netlist generation
2. ngspice execution
3. Numerical data extraction
4. Linear and logarithmic plotting

NMOS: $V_g$ – $I_d$ Characteristics (Example)

• Horizontal axis: gate voltage $V_g$
• Vertical axis: drain current $I_d$

From this plot, you can extract:

• Threshold voltage $V_t$
• Subthreshold region behavior
• On-current level
• Gate control capability
  ($g_m = \partial I_d / \partial V_g$)

What you observed in TCAD as “channel formation”
appears here directly as V–I characteristics.

PMOS: $V_g$ – $I_d$ Characteristics

For PMOS, characteristics are plotted using SPICE polarity conventions.
Temperature-dependent changes in $|V_t|$ and mobility can also be observed.

📊 Vd–Id Analysis (Drain Voltage Sweep)

How to Run

cd bsim/bsim4_analyzer_dc/run
python run_vdid.py

NMOS: $V_d$ – $I_d$ Characteristics (Example)

• Horizontal axis: drain voltage $V_d$
• Vertical axis: drain current $I_d$

From this plot, you can clearly identify:

• Linear region (low $V_d$)
• Saturation region
• Channel-length modulation (output resistance $r_o$)

These are the operating regions of a MOSFET,
clearly revealed by DC analysis.

PMOS: $V_d$ – $I_d$ Characteristics

This analysis is also useful for:

• Extracting $I_{d,\mathrm{lin}}$ and $I_{d,\mathrm{sat}}$
• Comparing short-channel effects

🧠 Linking DC Characteristics to Physical Models

The V–I characteristics obtained from DC analysis are not black boxes.

All of these are connected through the consistent flow:

TCAD → BSIM4 → SPICE

🧪 Why DC Analysis Is So Important

DC analysis is more than just plotting characteristics.

It serves as a sanity check to confirm that:

• The model is not broken
• Parameters are physically reasonable
• There are no abnormal voltage or temperature dependencies

AC analysis, CV analysis, and reliability analysis
all assume that DC characteristics are correct.

📝 Summary

• DC analysis is fundamental to MOSFET understanding
• $V_g$ – $I_d$ and $V_d$ – $I_d$ must always be checked
• The meaning of BSIM4 appears directly in V–I characteristics
• SemiDevKit enables automated and reproducible analysis

▶ Next Article

👉 06: BSIM4 AC / CV Analysis — Parasitic Capacitance and Frequency Response

Understanding BSIM4 starts with DC analysis.
The ability to read models is the ability to connect circuits and physics.