What best practices should be followed when deconvoluting battery electrode spectra? Optimize peak shapes, backgrounds, and constraints.

Use the simplest physically defensible model. For battery-electrode spectra, select peak shapes and backgrounds from the emission physics and measurement conditions—not from whichever combination produces the lowest residual. A mixed Gaussian–Lorentzian profile is often a practical starting point, while metallic or conductive components may require asymmetric peaks and explicitly modeled satellite structure. Backgrounds and fitting constraints must be validated against reference compounds, charging behavior, chemical plausibility, and reproducibility.

The best deconvolution is not the one with the most peaks or the smallest numerical residual. It is the minimum-complexity model that explains the spectrum while respecting known chemical states, instrumental effects, spin–orbit relationships, and realistic peak widths.

Establish the Physical Basis Before Fitting

Define the analytical question

First determine whether the goal is chemical-state identification, relative quantification, or comparison between electrodes and aging conditions. The appropriate model depends on which of these conclusions the fit must support.

A model that is adequate for distinguishing oxidation states may not be sufficiently rigorous for reporting small changes in surface composition. Avoid fitting features that are not relevant to the analytical question.

Confirm energy calibration and charging behavior

Peak positions should not be constrained tightly until the energy scale and charging behavior have been assessed. Battery electrodes can be electrically heterogeneous, and differential charging can broaden, shift, or split features in ways that resemble multiple chemical states.

Use a consistent calibration strategy across samples and report how charging was corrected. If charging varies between regions or samples, rigidly forcing all spectra to the same reference can create misleading chemical shifts.

Inspect the full spectral envelope

Fit the complete chemically relevant envelope before assigning individual components. Survey spectra, neighboring core levels, valence-band features, elemental composition, and known electrode history can help determine whether a proposed component is chemically plausible.

A peak should not be included merely because the residual contains a small local structure. It should correspond to a defensible chemical state, satellite, loss feature, or known instrumental contribution.

Select Peak Shapes That Match the Emission Physics

Start with a mixed Gaussian–Lorentzian profile

A Gaussian–Lorentzian mixture is a reasonable starting point for many insulating interphase compounds and lithium salts. The Gaussian contribution commonly represents instrumental broadening and sample-related inhomogeneity, while the Lorentzian contribution is associated more closely with the intrinsic lifetime width.

The often-used 70:30 Gaussian–Lorentzian mixture can be a practical initial setting, but it should not be treated as a universal physical law. The optimum mixture depends on the instrument, analyzer response, resolution, and fitting convention.

Use asymmetric profiles for metallic contributions

Metallic components and conductive graphite can exhibit asymmetric line shapes because of conduction-electron screening and related final-state effects. A symmetric peak may therefore produce systematic residuals on one side of the feature and incorrectly suggest additional chemical components.

Asymmetric profiles should be introduced only when supported by the material and the observed line shape. They should not be used simply because they improve the fit numerically.

Model satellites and loss features explicitly

Shake-up satellites, plasmon-loss structures, and other high-binding-energy features can be important in transition-metal compounds and conductive materials. These features should be modeled as chemically or physically related to the parent peak rather than treated as independent chemical states.

Where appropriate, constrain their relative position, width, and intensity using reference spectra or established physical behavior. Do not allow satellite peaks to absorb unrelated background or generate artificial oxidation-state assignments.

Keep related peaks internally consistent

Peaks belonging to the same chemical state or spin–orbit multiplet should normally share appropriate constraints on position differences, width, and intensity ratio. Related components should not be allowed to vary independently unless there is evidence of differential charging or another justified effect.

This approach reduces parameter correlation and makes comparisons between samples more reliable.

Choose the Background Model Deliberately

Use Shirley for well-defined envelopes

The Shirley background is commonly suitable for spectra with a clearly defined envelope and reasonably identifiable low- and high-binding-energy endpoints. It is often a practical choice for routine fitting of well-resolved core levels.

However, the endpoints must be selected consistently. A Shirley background can transfer errors in endpoint selection into the fitted peak areas, especially when the spectrum contains broad tails or overlapping components.

Consider a linear background when data quality is limited

A linear background can be preferable when the signal-to-noise ratio is low or when the spectral envelope is heavily overlapped and the data do not support a more elaborate background assumption. It introduces fewer assumptions and can be more stable in poorly resolved regions.

This does not make it intrinsically more accurate. Its suitability should be checked by varying the fitting window and evaluating how strongly the reported peak areas depend on that choice.

Use Tougaard backgrounds for appropriate inelastic-loss structure

A Tougaard-type background can be useful when broad inelastic-loss tails are physically important, particularly for materials and spectral regions where electron scattering contributes substantially to the signal. It should not be described simply as a generic “depth-related” correction.

Tougaard parameters must be selected consistently and justified for the material and measurement. An overly flexible loss background can remove real chemical structure or conceal poorly modeled peaks.

Treat the background as a source of uncertainty

Background choice can substantially affect the relative areas of overlapping interphase components. Therefore, background selection should be included in the uncertainty assessment rather than treated as a purely cosmetic preprocessing step.

A useful practice is to refit the data using plausible alternative backgrounds and report whether the chemical conclusion remains unchanged. If the conclusion changes materially, the data do not support the claimed precision.

Apply Constraints That Reflect Chemistry and Instrumentation

Use the minimum number of peaks

Fit only the number of components required to describe the spectrum and support a physical interpretation. Adding unconstrained peaks will almost always improve residuals, but it can produce chemically meaningless assignments.

A statistically better fit is not automatically a scientifically better fit. Model complexity must be justified by independent evidence, such as reference spectra, complementary core levels, electrochemical history, or known reaction products.

Constrain peak positions within defensible ranges

Peak positions should be allowed enough freedom to accommodate charging, calibration uncertainty, and real chemical shifts. They should not be fixed so rigidly that the model hides genuine changes.

At the same time, broad unconstrained position ranges allow peaks to exchange identities during fitting. Use literature and reference-material values as guides, while documenting the allowed ranges and the rationale for deviations.

Constrain FWHM values

Peaks representing comparable chemical environments should generally have similar or related widths. Independent, unconstrained widths can cause one component to become unrealistically broad and absorb neighboring chemistry.

FWHM limits should reflect the instrument resolution, sample heterogeneity, and expected chemistry. A fit requiring extreme widths is often evidence that the peak model, background, or chemical assignment needs reconsideration.

Enforce spin–orbit relationships

For spin–orbit doublets, constrain the energy separation, area ratio, and usually the relationship between component widths according to the relevant core level and reference data. These relationships are among the strongest physical constraints available in XPS fitting.

Do not impose a doublet ratio mechanically when the spectrum is affected by strong overlap, multiplet structure, charging, or other effects that invalidate a simple doublet model. In those cases, explain the deviation rather than silently relaxing every constraint.

Link chemically related parameters

When several peaks represent the same chemical state across a series of samples, use consistent fitting rules and, where justified, shared or linked parameters. This improves comparability and reduces the risk that differences arise solely from fitting freedom.

Constraints should be applied consistently across pristine, cycled, and aged electrodes. Changing the model between samples can create apparent trends that are actually methodological artifacts.

Validate the Fit Beyond the Residual

Examine residual structure

A random-looking residual is preferable to one containing systematic tails, shoulders, or oscillations. Systematic residuals indicate that the background, peak shape, number of components, or calibration may be incorrect.

Do not interpret a low residual alone as evidence that the model is valid. Flexible models can achieve low residuals while violating basic chemical expectations.

Test parameter stability

Perturb starting values, fitting windows, background assumptions, and reasonable parameter bounds. A defensible component should remain reasonably stable under these changes.

If a peak appears or disappears depending on minor fitting choices, report it as uncertain rather than presenting its area or chemical assignment as definitive.

Compare with independent evidence

Assignments should be checked against reference materials, known binding-energy ranges, complementary elements, electrode composition, and expected electrochemical reactions. For transition-metal systems, consider whether multiplet or satellite structure is expected before assigning multiple oxidation-state peaks.

Peak areas alone cannot establish a chemical identity. They become meaningful only when the spectral model is consistent with the material's chemistry and the measurement conditions.

Understanding the Trade-offs

More constraints improve stability but can hide real variation

Strict constraints reduce overfitting and improve reproducibility, but inappropriate constraints can force chemically distinct components into an incorrect model. Constraints must be physically justified rather than selected solely for numerical convenience.

The correct balance is bounded flexibility: enough freedom to represent real sample variation, but not enough freedom to create unsupported components.

More complex backgrounds can increase ambiguity

A sophisticated background may describe inelastic scattering more realistically, but it also introduces additional assumptions and parameter sensitivity. In overlapping battery-electrode spectra, the background can compete directly with broad chemical components.

Use the simplest background that is consistent with the data and the relevant electron-scattering physics. When alternative backgrounds produce materially different conclusions, the result should be reported with appropriate uncertainty.

Better fit statistics do not prove better chemistry

Adding peaks, allowing independent widths, or introducing asymmetry can lower the residual without increasing the reliability of the interpretation. Fit statistics should be used alongside chemical plausibility, parameter stability, and independent validation.

Avoid reporting excessive decimal precision in peak positions, widths, or area percentages when charging, background selection, or overlap dominates the uncertainty.

How to Apply This to Your Project

Use a documented fitting protocol that records the energy calibration, fitting window, background model, peak profiles, constraints, starting values, and sensitivity tests.

• If your primary focus is chemical-state identification: Use the minimum chemically justified peak set, validate assignments with reference and complementary spectra, and avoid interpreting every residual feature as a new species.
• If your primary focus is quantitative comparison: Apply identical backgrounds, peak definitions, and constraints across samples, and include background and model sensitivity in the uncertainty.
• If your primary focus is metallic or conductive phases: Test physically justified asymmetric profiles and satellite or loss structures before adding extra symmetric chemical-state peaks.
• If your primary focus is low-quality or highly overlapped data: Prefer a stable, minimally parameterized model and clearly report when the data cannot uniquely distinguish competing assignments.

A reliable deconvolution is a transparent, constrained chemical model whose conclusions remain stable when reasonable analytical choices are changed.

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