Electrochemical Impedance AnalysisImport CSV/TXT data and inspect Nyquist, Bode magnitude, and Bode phase plots.

Basic Equivalent-Circuit AnalysisAnalyze a Randles-type R_s–(R_ct∥C) response and review fit residuals.

Mott–Schottky CharacterizationEstimate semiconductor type, doping density, and flat-band voltage from a manually selected linear region.

FREE COMMUNITY EDITION

Guided Learning Path

Move from impedance fundamentals to equivalent-circuit interpretation and Mott–Schottky parameter extraction.

01Understand EIS 02Review equations 03Import data 04Inspect plots 05Select linear region 06Interpret and export

Learning Objectives

VisualizeConstruct Nyquist, Bode-magnitude, and Bode-phase representations from experimental impedance data.

ExtractEstimate series resistance, charge-transfer resistance, characteristic frequency, and effective capacitance.

ModelCompare a dataset with a basic Randles R_s–(R_ct∥C) response.

EvaluateReview residuals and use them to judge whether the simple circuit is adequate.

DetermineEstimate semiconductor type, doping density, and flat-band voltage from C–V data.

CommunicateExport plot images, processed CSV files, and a local project record.

Introduction

Electrochemical impedance spectroscopy (EIS) applies a small alternating perturbation over a range of frequencies and measures the complex electrical response of a device or material. The complex impedance is written as Z(ω)=Z′(ω)+jZ″(ω). Nyquist plots emphasize resistive and relaxation features, while Bode plots display impedance magnitude and phase over frequency.

Mott–Schottky analysis uses the voltage dependence of depletion capacitance to estimate semiconductor doping density and flat-band voltage. This Community Edition combines basic EIS visualization and Randles-circuit interpretation with single-dataset capacitance–voltage analysis.

Nyquist Representation

The horizontal axis is Z′ and the vertical axis is −Z″. Intercepts and arc diameters can provide first estimates of series and charge-transfer resistances.

Bode Representation

|Z| and phase are plotted against logarithmic frequency. Peaks and transitions reveal characteristic time scales and relaxation processes.

Mott–Schottky Representation

1/C² is plotted against applied voltage. The slope indicates semiconductor type and is used with dielectric constant and area to estimate carrier density.

Theory and Scientific Background

1. Complex impedance

Z(ω)=Z′(ω)+jZ″(ω), |Z|=√(Z′²+Z″²), φ=tan⁻¹(Z″/Z′)

2. Basic Randles response

The Community Edition uses a simple series resistance followed by a parallel charge-transfer resistance and ideal capacitance.

Z(ω)=R_s + R_ct / (1+jωR_ctC)

For an ideal semicircle, the characteristic frequency is approximately f_max=1/(2πR_ctC).

3. Capacitance from impedance

For a predominantly capacitive response, a frequency-dependent effective series capacitance may be estimated from the imaginary impedance.

C(ω)=−1/(ωZ″)

4. Mott–Schottky relation

1/C² = 2(V−V_fb−kT/q)/(qεε₀A²N)

For a positive slope, the toolkit reports n-type behavior; for a negative slope, p-type behavior. The magnitude of carrier density is calculated as N=2/(qεε₀A²|slope|). The flat-band voltage is estimated from the x-intercept with the thermal correction V_fb=−intercept/slope−kT/q.

Model limitation: EIS interpretation is not unique. A good numerical fit does not prove a physical circuit. This Community Edition uses an ideal single-time-constant circuit and basic linear Mott–Schottky analysis. It excludes CPE, Warburg, multiple-circuit, uncertainty, batch, bias-dependent, temperature-dependent, and advanced validation functions listed for paid editions.

1. Impedance Data

Drop CSV/TXT here
or click to choose a file
Expected columns: frequency, Z′, Z″. Common header names are detected automatically.

No impedance dataset loaded.

2. Plot & Circuit Controls

Imaginary sign

Show Randles fit Hover cursor

Basic zoom, pan, hover, and image export are available through each plot toolbar.

3. Extracted EIS Parameters

4. Fit Residuals

Residuals are reported for the basic Randles estimate and are intended as a screening measure.

5. Community Export & Project

Projects are saved in this browser using local storage. The Community Edition does not provide cloud project management or version history.

Basic AI-Style Guidance

Nyquist Plot

Bode Magnitude

Bode Phase

Randles-Fit Residuals

Imported Data Preview

Capacitance & Mott–Schottky Analyzer

Load or paste one voltage–capacitance dataset. Select the linear region manually by setting its starting and ending voltages.

1. C–V Data

Drop C–V CSV/TXT here
or click to choose a file
Expected columns: voltage and capacitance.

No C–V dataset loaded.

2. Device & Fit Inputs

Area (cm²) Relative ε

Temperature (K)

Linear region start (V)Linear region end (V)

3. Extracted Parameters

Capacitance–Voltage Plot

Mott–Schottky Plot

Interactive Concept Explorer

Select a concept to review its role in impedance or Mott–Schottky analysis.

Choose a term above.
The explanation will appear here.

User Guide

1. Import impedance data

Load CSV/TXT data containing frequency, real impedance, and imaginary impedance. Use the demo dataset to test the workflow.

2. Analyze EIS response

Inspect Nyquist and Bode plots, then run the basic Randles analysis to estimate R_s, R_ct, characteristic frequency, and capacitance.

3. Review residuals

Use residual trends and RMS error as a preliminary indication of whether the single-time-constant model represents the data adequately.

4. Import C–V data

Load a single voltage–capacitance dataset and enter the active area, relative dielectric constant, and temperature.

5. Select a linear region

Set the starting and ending voltages for the region that appears linear in the 1/C² versus V plot.

6. Export results

Download plot PNGs and processed CSV files, or save one project locally in the current browser.

Upgrade beyond the Community Edition

Access CPE and Warburg elements, multiple equivalent circuits, advanced fitting statistics, multi-region Mott–Schottky analysis, frequency/bias mapping, dataset comparison, uncertainty analysis, AI circuit recommendations, and publication-ready reports.

Searchable Glossary

Selected References and Further Reading

E. Barsoukov and J. R. Macdonald (eds.), Impedance Spectroscopy: Theory, Experiment, and Applications, 3rd ed., Wiley (2018).
M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, 2nd ed., Wiley (2017).
A. J. Bard and L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, 2nd ed., Wiley (2001).
S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley (2007), for depletion capacitance and semiconductor junction analysis.
J. Bisquert, Nanostructured Energy Devices: Equilibrium Concepts and Kinetics, CRC Press (2014).

Use experimental conditions and literature appropriate to the particular material system. Equivalent-circuit assignments and Mott–Schottky assumptions should be justified independently.

About, License, and Citation

Toolkit Scope

Browser-based basic impedance visualization, ideal Randles analysis, capacitance evaluation, and single-region Mott–Schottky parameter extraction.

Community License

Personal and educational use; non-commercial only. Confirm licensing before commercial or institutional deployment.

Version and Author

NexSolveAI Research Toolkit™ 03 Community Edition v1.0, developed by Dr. Muhammad Hassan Sayyad.

Suggested Citation

Sayyad, M. H. (2026). NexSolveAI Research Toolkit™ 03: Impedance & Mott–Schottky Analyzer, Community Edition v1.0. NexSolveAI.

Scientific-use notice

The extracted parameters are preliminary estimates. Validate sign conventions, units, equivalent-circuit selection, area, dielectric constant, frequency, bias range, and linear-region selection before using results in scholarly work.

Edition Comparison

NexSolveAI Research Toolkit™ 03: Impedance & Mott–Schottky Analyzer

Compare the Community, Research and Professional Editions for Nyquist and Bode analysis, equivalent-circuit modelling, capacitance evaluation, doping-density determination and flat-band-voltage extraction.

Feature	Community Edition FREE	Research Edition Request Quote	Professional Edition Request Quote
01 Impedance Data Import	CSV, TXT	CSV, TXT, XLSX	CSV, TXT, XLSX + Batch Import
02 Nyquist Plot	✓	✓	✓
03 Bode Magnitude Plot	✓	✓	✓
04 Bode Phase Plot	✓	✓	✓
05 Interactive Plot Controls	Basic zoom and cursor	Advanced controls	Advanced + synchronized plots
06 Equivalent-Circuit Library	Basic circuits	Extended circuit library	Extended + custom circuit builder
07 Randles Circuit Analysis	✓	✓	✓
08 Constant Phase Element (CPE)	✕	✓	✓
09 Warburg Diffusion Element	✕	✓	✓
10 Equivalent-Circuit Fitting	Single basic model	Multiple models	Automated multi-model fitting
11 Fit-Quality Statistics	Basic residuals	Residuals + χ²	Advanced statistics + confidence intervals
12 Series Resistance Extraction	✓	✓	✓
13 Charge-Transfer Resistance Extraction	✓	✓	✓
14 Recombination Resistance Analysis	✕	✓	✓
15 Capacitance Extraction	Basic	Advanced	Advanced + frequency/bias mapping
16 Capacitance–Frequency Analysis	✓	✓	✓
17 Capacitance–Voltage Analysis	Single dataset	Multiple datasets	Batch datasets + comparison
18 Mott–Schottky Plot	✓	✓	✓
19 Linear-Region Selection	Manual	Manual + assisted	Automatic + manual refinement
20 Doping Density Extraction	Single-region estimate	Multi-region analysis	Automated analysis + uncertainty
21 Flat-Band Voltage Extraction	Basic linear fit	Advanced linear fit	Automated extraction + confidence limits
22 Semiconductor-Type Identification	Basic indication	✓	✓
23 Dielectric Constant & Area Inputs	Manual entry	Saved project parameters	Material database + project presets
24 Frequency-Dependent Parameter Mapping	✕	✓	✓
25 Bias-Dependent Impedance Comparison	✕	Up to 10 datasets	Unlimited datasets
26 Temperature-Dependent Analysis	✕	✓	✓
27 Device / Sample Comparison	✕	Up to 10 samples	Unlimited samples
28 Automated Data Validation	Basic	Advanced	Advanced + anomaly detection
29 AI-Assisted Circuit Recommendation	✕	✕	✓
30 AI-Powered Interpretation	Basic guidance	Advanced interpretation	Expert insights with explanations
31 Research Report Generation	Summary	Detailed report	Publication-ready report
32 Export	PNG, CSV	PNG, SVG, CSV, XLSX, JSON	PNG, SVG, CSV, XLSX, JSON + PDF Report
33 Project Saving & Reopening	Local project	Multiple projects	Unlimited projects + version history
34 Priority Support	Community Forum	Email Support	Priority Email + Live Support
35 Commercial / Research Use	Non-commercial only	✓ Allowed	✓ Allowed
36 License	Personal / Educational	Commercial Research License	Commercial / Enterprise License

Guided Learning Path

Learning Objectives

Introduction

Nyquist Representation

Bode Representation

Mott–Schottky Representation

Theory and Scientific Background

1. Complex impedance

2. Basic Randles response

3. Capacitance from impedance

4. Mott–Schottky relation

1. Impedance Data

2. Plot & Circuit Controls

3. Extracted EIS Parameters

4. Fit Residuals

5. Community Export & Project

Basic AI-Style Guidance

Nyquist Plot

Bode Magnitude

Bode Phase

Randles-Fit Residuals

Imported Data Preview

Capacitance & Mott–Schottky Analyzer

1. C–V Data

2. Device & Fit Inputs

3. Extracted Parameters

Capacitance–Voltage Plot

Mott–Schottky Plot

Interactive Concept Explorer

User Guide

1. Import impedance data

2. Analyze EIS response

3. Review residuals

4. Import C–V data

5. Select a linear region

6. Export results

Upgrade beyond the Community Edition

Searchable Glossary

Related NexSolveAI Research Toolkits™

Toolkit™ 01

Toolkit™ 02

Toolkit™ 04

Selected References and Further Reading

About, License, and Citation

Toolkit Scope

Community License

Version and Author

Suggested Citation

Scientific-use notice

Edition Comparison

NexSolveAI Research Toolkit™ 03: Impedance & Mott–Schottky Analyzer

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