How can equivalent circuit analysis of EIS Nyquist plots be used in battery testing systems to evaluate SEI layer growth and interfacial resistance?

Equivalent circuit analysis turns a Nyquist plot into measurable resistance and capacitance values. In a battery testing system, researchers fit the spectrum with elements representing ohmic resistance, SEI-film behavior, charge transfer, and diffusion. By comparing fitted parameters—especially (R_{\mathrm{SEI}}), (R_{\mathrm{ct}}), and their associated capacitances—across cycle number or operating conditions, they can determine whether the SEI is growing, stabilizing, or becoming more resistive.

The key insight is that SEI growth is evaluated from the evolution of a fitted interfacial time constant, not from the semicircle diameter alone. A rising (R_{\mathrm{SEI}}) generally indicates a more resistive or thicker interphase, while a rising total interfacial resistance may also result from slower charge-transfer kinetics, contact degradation, or diffusion changes.

What the Nyquist Plot Reveals

The high-frequency intercept represents ohmic resistance

The first real-axis intercept at high frequency commonly represents the cell’s ohmic resistance, (R_{\mathrm{s}}). It includes contributions from the electrolyte, current collectors, tabs, wiring, and some contact resistances.

A change in (R_{\mathrm{s}}) should not automatically be interpreted as SEI growth. It may instead indicate electrolyte degradation, poor cell assembly, temperature variation, or increased contact resistance.

Semicircles represent interfacial time constants

A semicircle results from a resistive and capacitive process with a characteristic time constant. In a simple model, a parallel resistor-capacitor pair can be written as:

[ R \parallel C ]

The resistance controls the semicircle’s width along the real axis, while the capacitance influences the frequency at which the arc reaches its maximum height.

The low-frequency tail represents diffusion

The low-frequency region commonly appears as a sloped tail associated with Warburg diffusion impedance, (Z_{\mathrm{W}}). It reflects limitations in ion transport through electrode materials, porous structures, or solid electrolytes.

This diffusion response is important for battery performance, but it should be separated from SEI resistance when assessing interfacial film growth.

How Equivalent Circuits Isolate SEI Behavior

A representative battery model

A commonly used model places the major processes in series:

[ R_{\mathrm{s}} + (R_{\mathrm{SEI}} \parallel C_{\mathrm{SEI}})

• (R_{\mathrm{ct}} \parallel C_{\mathrm{dl}})
• Z_{\mathrm{W}} ]

Here:

• (R_{\mathrm{s}}) represents ohmic resistance.
• (R_{\mathrm{SEI}}) represents ionic and electronic resistance through the SEI.
• (C_{\mathrm{SEI}}) represents the SEI’s interfacial or film capacitance.
• (R_{\mathrm{ct}}) represents charge-transfer resistance.
• (C_{\mathrm{dl}}) represents double-layer capacitance.
• (Z_{\mathrm{W}}) represents diffusion behavior.

Real battery spectra often require constant phase elements, or CPEs, instead of ideal capacitors because roughness, porosity, nonuniform current distribution, and distributed reaction rates depress the semicircles.

The SEI semicircle may overlap other processes

In some cells, the SEI response appears primarily at high or intermediate frequencies. In others, it overlaps strongly with charge transfer or contact effects.

Therefore, the statement that one visible semicircle always equals the SEI is too simplistic. The physical assignment must be supported by frequency dependence, control experiments, material knowledge, and the quality of the fitted model.

Fitting separates resistance contributions

Battery testing software typically uses complex nonlinear least-squares fitting to compare measured impedance with the equivalent circuit. The fitting process estimates the values of (R_{\mathrm{s}}), (R_{\mathrm{SEI}}), (R_{\mathrm{ct}}), capacitances or CPE parameters, and diffusion terms.

This deconvolution is especially valuable when multiple semicircles overlap and cannot be measured reliably by visual inspection alone.

How SEI Growth Is Tracked During Battery Testing

Monitor (R_{\mathrm{SEI}}) over cycle number

A progressive increase in fitted (R_{\mathrm{SEI}}) indicates that the interphase is becoming more resistive. This can be consistent with continued SEI formation, thickening, compositional changes, or reduced ionic conductivity through the film.

The trend is more informative than a single measurement. Measurements should be made at controlled state of charge, temperature, rest time, and excitation amplitude.

Track the associated capacitance

The fitted (C_{\mathrm{SEI}}) provides complementary information about the interphase. Changes in capacitance can indicate changes in effective film thickness, dielectric properties, active interfacial area, or film uniformity.

Capacitance should not be interpreted as a direct thickness measurement without additional assumptions. Porous and heterogeneous SEI structures can make the relationship non-unique.

Separate SEI growth from charge-transfer degradation

An increase in (R_{\mathrm{ct}}) means that charge-transfer kinetics have become less favorable, but it does not by itself prove that the SEI has grown.

Comparing (R_{\mathrm{SEI}}) and (R_{\mathrm{ct}}) separately helps distinguish mechanisms:

• Increasing (R_{\mathrm{SEI}}) with stable (R_{\mathrm{ct}}): likely increasing film resistance.
• Stable (R_{\mathrm{SEI}}) with increasing (R_{\mathrm{ct}}): likely slower reaction kinetics or loss of active interface.
• Both increasing: possible combined SEI evolution, electrode degradation, contact loss, or electrolyte-related aging.

Calculate total interfacial resistance

A practical performance metric is the combined interfacial contribution:

[ R_{\mathrm{interface}} \approx R_{\mathrm{SEI}} + R_{\mathrm{ct}} ]

This quantity connects impedance behavior with polarization and power capability. However, it should not replace the individual fitted parameters when the purpose is mechanistic diagnosis.

Using EIS to Evaluate Materials and Cell Processing

Compare electrolyte additives

EIS measurements before and after cycling can reveal whether an additive produces a more stable interphase.

A desirable formulation may show limited growth in (R_{\mathrm{SEI}}), stable charge-transfer resistance, and reduced impedance increase over repeated cycles. A lower initial resistance is not always sufficient if the resistance grows rapidly during aging.

Evaluate surface coatings

Metal, carbon, ceramic, or polymer coatings can be assessed by comparing fitted interfacial parameters with an uncoated reference.

The most useful comparison includes initial impedance, rate of resistance growth, changes in (C_{\mathrm{SEI}}) or CPE behavior, and preservation of the charge-transfer response.

Diagnose electrode and assembly quality

Impedance fitting can also expose problems originating upstream of electrochemical operation. Slurry nonuniformity, inadequate electrode pressing, poor current-collector contact, and inconsistent cell assembly can increase (R_{\mathrm{s}}) or create additional interfacial time constants.

This prevents researchers from incorrectly attributing every impedance increase to SEI chemistry.

Compare cells at controlled conditions

SEI-related impedance is strongly affected by temperature, state of charge, electrode potential, formation history, and rest period.

Reliable comparisons require the same test protocol across cells. Otherwise, an apparent change in (R_{\mathrm{SEI}}) may reflect a measurement-condition difference rather than actual layer growth.

Understanding the Trade-offs

A larger semicircle is not automatically SEI growth

A semicircle’s diameter reflects the resistance of the process represented by the selected circuit element. If the arc contains both SEI and charge-transfer responses, its diameter is a combined quantity.

Only a validated equivalent circuit can justify assigning part of that diameter specifically to (R_{\mathrm{SEI}}).

Equivalent circuits are interpretive models

An equivalent circuit is not a direct image of the physical interface. Different circuits can sometimes fit the same spectrum with similar statistical quality but different physical interpretations.

Model selection should therefore consider electrochemical plausibility, parameter stability, residuals, repeatability, and whether the circuit explains changes across multiple conditions.

Ideal capacitors may be inadequate

Battery interfaces are rarely uniform enough to behave as ideal capacitors. Depressed semicircles often require CPEs, and porous electrodes may exhibit distributed time constants.

Using an overly simple (R \parallel C) model can produce misleading resistance or capacitance values even when the visual fit appears acceptable.

Low-frequency data are slow and noisy

The low-frequency region requires long measurement times and is sensitive to battery drift, temperature changes, and nonstationary behavior. A changing battery state during the scan can distort the Warburg response and influence the fitted interfacial parameters.

Measurements should use a sufficiently small perturbation and verify that the cell remains approximately linear and stationary during acquisition.

Making the Right Choice for Your Goal

Use equivalent circuit analysis as a controlled comparison method rather than as a standalone proof of SEI chemistry.

• If your primary focus is SEI growth: Track (R_{\mathrm{SEI}}) and (C_{\mathrm{SEI}}) or their CPE equivalents over cycle number under identical temperature, state-of-charge, and rest conditions.
• If your primary focus is interfacial kinetics: Track (R_{\mathrm{ct}}) separately from (R_{\mathrm{SEI}}), because a larger charge-transfer resistance indicates slower reaction kinetics rather than necessarily a thicker SEI.
• If your primary focus is electrolyte or coating development: Compare resistance growth rates, not only initial impedance, and include an untreated reference cell.
• If your primary focus is cell manufacturing: Examine (R_{\mathrm{s}}), additional high-frequency features, and fitting repeatability to identify electrolyte, contact, pressing, or assembly problems.
• If your primary focus is mechanistic confidence: Validate the circuit with frequency-resolved residuals, alternative plausible models, replicate cells, and complementary post-mortem or materials characterization.

With disciplined modeling and controlled measurements, EIS converts impedance evolution into actionable evidence about SEI stability, interfacial resistance, and battery aging.

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