Vth Calculator (Linear Extrapolation at Max gm)

Tooling to extract MOS threshold voltage (Vth) from measured Id–Vg sweeps and analyze its temperature and Vds dependence.

• Method: linear extrapolation at the point of extreme transconductance gm
  • NMOS: choose Vg at maximum gm, draw tangent to Id–Vg at that point, Vth is intercept with Id=0
  • PMOS: choose Vg at minimum gm (gm is negative), same tangent rule, Vth negative
• Features:
  • Per-file visualization (GUI) and batch processing (CLI) across all chips/temperatures
  • NEW: Vth derivative analysis vs temperature and Vds with 3D plots, heatmaps, and contour plots
  • NEW: Automated analysis with comprehensive Makefile

Table of Contents

• Get the code
• Requirements and installation
• Dataset layout
• Quick Start
• Makefile Guide
• Basic Vth Extraction
• Vth Derivative Analysis
• Algorithm Details
• Troubleshooting
• Advanced Usage

Get the code

git clone https://github.com/abestable/vthcalculator.git
cd vthcalculator

Requirements and installation (venv recommended)

• Python 3.8+
• Create a virtual environment and install dependencies:

python3 -m venv .venv
source .venv/bin/activate
pip install -U pip
# Use numpy < 2 to avoid ABI issues with some distro matplotlib builds
pip install "numpy<2" pandas matplotlib
# For GUI on Debian/Ubuntu systems, if missing:
# sudo apt-get install -y python3-tk

Dataset layout

The repo includes only canonical measurement files to keep it lean:

• Under chip*/.../{Nmos,Pmos}/ only 1.txt, 2.txt, 3.txt, 4.txt and their *.bmp are tracked.
• The script accepts any folder hierarchy; it scans recursively.
• Each .txt must be tab-separated with header: Index Vg Id Time Vd and blocks of constant Vd.

Quick Start

GUI Mode

Launch interactive viewer to inspect a single file, select block Vd, choose Vth extraction method, and see Id/gm, tangent and Vth:

make gui

Notes:

• The GUI auto-selects the closest Vd to 0.1 V for NMOS and 1.1 V for PMOS.
• NEW: Choose between Traditional, Sqrt, and Hybrid Vth extraction methods.
• Hover the cursor over plots to read (Vg, Id) or (Vg, gm).
• Close the window to free the shell.
• See GUI_Usage_Guide.md for detailed instructions.

Automated Analysis (Recommended)

Use the Makefile for automated Vth analysis and derivative analysis:

# Show all available commands
make help

# === BASIC VTH EXTRACTION ===
make gui          # Interactive GUI for single file analysis
make batch        # Standard batch processing (all chips, summary, plots)
make batch-daniele # Batch processing with Daniele comparison

# === DERIVATIVE ANALYSIS ===
make derivative   # Derivative analysis for all devices (NMOS + PMOS)
make derivative-nmos # Derivative analysis for NMOS only
make derivative-pmos # Derivative analysis for PMOS only
make plots        # Generate English version of all derivative plots

# === UTILITY ===
make quick-all    # Quick derivative analysis (uses existing data)
make list         # List all generated files
make clean        # Clean all generated files

Makefile Guide

The Makefile provides comprehensive automation for all Vth analysis workflows.

Available Targets

Basic Vth Extraction

make gui

• Use case: Inspect individual measurement files
• Features: Select Vd blocks, visualize Id/gm curves, see tangent and Vth
• Output: Interactive plots

make batch

• Use case: Standard Vth extraction for all devices
• Output files:
  • vth_all.csv: Per-file results
  • vth_summary.csv: Summary by device
  • vth_by_chip.csv: Pivot by chip
  • vth_nmos_vs_temp.png: NMOS plots
  • vth_pmos_vs_temp.png: PMOS plots

make batch-daniele

• Use case: Compare results with reference measurements
• Additional outputs:
  • vth_compare_clean.csv: Comparison results
  • vth_compare_clean_status.csv: PASS/FAIL status

Derivative Analysis

make derivative

• Use case: Analyze dVth/dT vs temperature and Vds
• Output files:
  • all_chips_complete_data.csv: Complete Vth data
  • all_chips_complete_derivative.csv: Calculated derivatives
  • all_chips_complete_3d.pdf: 3D scatter plot
  • all_chips_complete_heatmap.pdf: 2D heatmap
  • all_chips_complete_contour.pdf: Contour plot

make derivative-nmos / make derivative-pmos

• Output prefix: nmos_derivative / pmos_derivative

make plots

• Use case: Generate English version of all derivative plots
• Output prefix: *_english

Legacy Targets (Backward Compatibility)

• make all → make derivative
• make nmos → make derivative-nmos
• make pmos → make derivative-pmos

Utility Targets

make quick-all

• Use case: Fast re-analysis without re-extracting data
• Behavior: Uses existing all_chips_vth_all_vds.csv if present

make list

• Output: Shows basic Vth files and derivative analysis files

make clean / make clean-data

• Removes: All files / CSV files only
• Keeps: Nothing / PDF and PNG visualization files

Workflow Examples

Complete Analysis Workflow

# 1. Start with basic Vth extraction
make batch

# 2. Run derivative analysis
make derivative

# 3. Generate English plots
make plots

# 4. View results
make list

Quick Iteration Workflow

# 1. First run (extracts data)
make derivative

# 2. Subsequent runs (uses existing data)
make quick-all

# 3. Clean and start over
make clean
make derivative

Comparison Workflow

# 1. Run with Daniele comparison
make batch-daniele

# 2. Check comparison results
ls -la vth_compare_clean*.csv

# 3. Run derivative analysis
make derivative

Basic Vth Extraction

Using Makefile (Recommended)

# Standard batch processing
make batch

# Batch processing with Daniele comparison
make batch-daniele

Manual Commands

Run over all chips/temperatures, extract Vth at low/high drain bias and produce CSVs and plots (from repo root):

python3 scripts/extract_vth.py . \
  --run_all \
  --vd 0.1 \
  --out ./vth_all.csv \
  --summary-out ./vth_summary.csv \
  --plots-outdir .

Outputs:

• vth_all.csv: one row per input file (and closest block to target Vd)
• vth_summary.csv: grouped by temperature, device (nmos/pmos), device_index with count/mean/std/min/max
• vth_by_chip.csv: pivot by chip per (temperature, device_label) with per-chip values and overall avg/std
• vth_nmos_vs_temp.png, vth_pmos_vs_temp.png: mean ± std vs temperature, one series per device index

Comparison against a reference CSV (e.g., Daniele)

If you have a reference table with columns like temperature, device, avg, stdev (temperature in K, device such as nmos1, pmos4), pass it to produce comparison files automatically:

Using Makefile:

make batch-daniele

Manual command:

python3 scripts/extract_vth.py . \
  --run_all \
  --out ./vth_all.csv \
  --summary-out ./vth_summary.csv \
  --plots-outdir . \
  --daniele-csv ./RisultatiDaniele.csv \
  --compare-threshold 0.01

Additional outputs:

• vth_compare_clean.csv: columns temperature, device_label, abe_avg_V, abe_std_V, daniele_avg_V, daniele_std_V, delta_avg_V, delta_std_V
• vth_compare_clean_status.csv: same plus status with PASS/FAIL if any absolute delta exceeds the threshold (default 0.01 V)

Vth Derivative Analysis

Overview

The derivative analysis feature calculates dVth/dT (threshold voltage derivative with respect to temperature) for different Vds values and generates comprehensive visualizations.

Features

• 3D Plots: Interactive 3D visualization of dVth/dT vs temperature and Vds
• Heatmaps: Color-coded 2D representation showing sensitivity regions
• Contour Plots: Level curves for detailed analysis
• Data Filtering: Automatically excludes Vds=0 for NMOS and Vds=1.2V for PMOS
• Multi-language: Support for both Italian and English plot labels (use make plots for English)

Generated Files

For each analysis, you get:

• *_data.csv: Complete Vth data for all Vds values
• *_derivative.csv: Calculated dVth/dT values with columns:
  • device: nmos/pmos
  • temperature: temperature in K
  • vds: drain-source voltage in V
  • vth: threshold voltage in V
  • dvth_dt: derivative dVth/dT in V/K
• *_3d.pdf: 3D scatter plot
• *_heatmap.pdf: 2D heatmap visualization
• *_contour.pdf: Contour plot with temperature on X-axis, Vds on Y-axis

Key Results

NMOS Behavior

• Range: -0.000579 to 0.000192 V/K
• General Trend: Negative dVth/dT (Vth decreases with temperature)
• Vds Dependence: Becomes less negative (more positive) with higher Vds
• Exceptions: Some positive values at low Vds and low temperatures

PMOS Behavior

• Range: 0.000143 to 0.000771 V/K
• General Trend: Always positive dVth/dT (Vth increases with temperature)
• Vds Dependence: Increases with higher Vds

Data Filtering

• NMOS: Vds=0 excluded
• PMOS: Vds=1.2V excluded
• Temperature Range: 85K - 295K

Manual Commands

# Extract Vth data for all chips
python3 scripts/extract_vth.py chip3 --all-vd --out chip3_vth_all_vds.csv
python3 scripts/extract_vth.py chip4 --all-vd --out chip4_vth_all_vds.csv
python3 scripts/extract_vth.py chip5 --all-vd --out chip5_vth_all_vds.csv

# Combine data
head -1 chip3_vth_all_vds.csv > all_chips_vth_all_vds.csv
tail -n +2 chip3_vth_all_vds.csv >> all_chips_vth_all_vds.csv
tail -n +2 chip4_vth_all_vds.csv >> all_chips_vth_all_vds.csv
tail -n +2 chip5_vth_all_vds.csv >> all_chips_vth_all_vds.csv

# Run derivative analysis (Italian labels by default)
python3 scripts/vth_derivative_vs_vds_temp.py . --device-type both --output-prefix my_analysis --skip-extraction

# For English labels, use the Makefile:
# make plots

Algorithm Details

Vth Extraction

• Id units are parsed from pA/nA/uA/mA/A; Vg/Vd from mV/V and normalized to SI units.
• gm is computed numerically via np.gradient(|Id|, Vg) with a floor to avoid subthreshold noise.
• Selection of the tangent point:
  • NMOS: index of maximum gm
  • PMOS: index of minimum gm
• Tangent slope is gm(Vg*) and passes through (Vg*, |Id|(Vg*)); Vth = Vg* − |Id|/gm (sign applied: NMOS +, PMOS −).
• Target Vd for extraction: NMOS 0.1 V, PMOS 1.1 V (closest block is chosen per file).

Derivative Calculation

1. Data Grouping: Groups data by device type and Vds value
2. Temperature Averaging: Averages Vth values for duplicate temperatures
3. Numerical Differentiation: Uses np.gradient() to calculate dVth/dT
4. Filtering: Removes infinite and NaN values
5. Validation: Ensures at least 2 temperature points per device/Vds combination

Visualization Features

• 3D Plots: Interactive scatter plots with different colors for each device
• Heatmaps: Color-coded matrices with RdBu_r colormap
• Contour Plots: Level curves with black dots showing actual data points
• Multi-language: Support for Italian and English labels (use make plots for English)

Troubleshooting

Common Issues

"No .txt files found"

• Cause: No measurement files in the expected locations
• Solution: Ensure chip3/, chip4/, chip5/ directories exist with measurement files

"ModuleNotFoundError: No module named 'pandas'"

• Cause: Missing Python dependencies
• Solution: Install required packages: pip install pandas matplotlib numpy

"No existing data found"

• Cause: Running make quick-all without previous data extraction
• Solution: Run make derivative first to extract data

GUI doesn't start

• Cause: Missing tkinter
• Solution: Install python3-tk package

"No data found" in derivative analysis

• Cause: Insufficient temperature points (at least 2) for each device/Vds
• Solution: Ensure sufficient temperature measurements

"Infinite values" in derivative calculation

• Cause: Duplicate temperature measurements
• Solution: Check for duplicate temperature points

Debug Commands

# Check file structure
ls -la chip*/

# Check Python dependencies
python3 -c "import pandas, matplotlib, numpy; print('OK')"

# Check generated files
make list

# Check data extraction
ls -la *_vth_all_vds.csv

# Check derivative calculation
head -10 *_derivative.csv

# Verify plot generation
ls -la *.pdf

# Clean and restart
make clean
make batch

Advanced Usage

Custom Analysis

# Manual extraction for specific chip
python3 scripts/extract_vth.py chip3 --all-vd --out chip3_only.csv

# Manual derivative analysis (Italian labels by default)
python3 scripts/vth_derivative_vs_vds_temp.py . --device-type nmos --output-prefix custom_nmos --skip-extraction

# For English labels, use the Makefile:
# make plots

# Compare different chips (Italian labels by default)
python3 scripts/extract_vth.py chip3 --all-vd --out chip3_only.csv
python3 scripts/vth_derivative_vs_vds_temp.py . --device-type both --output-prefix chip3_analysis --skip-extraction

# For English labels, use the Makefile:
# make plots

Data Analysis

# View derivative statistics
python3 -c "
import pandas as pd
df = pd.read_csv('all_chips_complete_derivative.csv')
print('NMOS dVth/dT range:', df[df['device']=='nmos']['dvth_dt'].min(), 'to', df[df['device']=='nmos']['dvth_dt'].max())
print('PMOS dVth/dT range:', df[df['device']=='pmos']['dvth_dt'].min(), 'to', df[df['device']=='pmos']['dvth_dt'].max())
"

# View detailed statistics
python3 -c "
import pandas as pd
df = pd.read_csv('all_chips_complete_derivative.csv')
print('NMOS statistics:')
print(df[df['device']=='nmos']['dvth_dt'].describe())
print('\nPMOS statistics:')
print(df[df['device']=='pmos']['dvth_dt'].describe())
"

Performance Tips

1. Use make quick-all for iterative analysis
2. Use make clean-data to keep plots but remove large CSV files
3. Use make derivative-nmos or make derivative-pmos** for device-specific analysis
4. Use make list to check what files are generated

Integration with Git

The Makefile is designed to work well with Git:

• Generated files are not tracked by Git (add to .gitignore)
• Use make clean before commits to remove temporary files
• The Makefile itself is tracked and versioned

Physical Interpretation

Physical Meaning

• Negative dVth/dT: Vth decreases with temperature (typical for NMOS)
• Positive dVth/dT: Vth increases with temperature (typical for PMOS)
• Vds Dependence: Shows how temperature sensitivity varies with operating conditions

Design Implications

• Temperature Compensation: Understanding dVth/dT helps design temperature-compensated circuits
• Process Variation: Different devices may show different temperature sensitivity
• Operating Conditions: Vds affects temperature sensitivity significantly