How do you read a Mott–Schottky plot, and how do you translate its capacitance, flat-band potential and doping-density claims accurately? The horizontal axis is usually applied potential, while the vertical axis is reciprocal capacitance squared, often written 1/C² or 1/Csc². Before interpreting the slope or intercept, determine which capacitance was used, whether it was normalised to area and what reference electrode defines the potential.
Mott–Schottky analysis is commonly used to investigate semiconductor interfaces, including photoelectrodes and semiconducting oxides. It can help estimate a flat-band potential and charge-carrier density under an appropriate depletion-layer model. It does not make every straight-looking line a reliable measurement of those properties. Frequency, equivalent-circuit choices, contact effects and interfacial states can all change what the graph means.
This guide explains how to interpret and translate Mott–Schottky graphs for international readers. It moves from axis labels and positive or negative slopes to linear fitting, unit conversions, physical assumptions, worked reading examples and careful scientific wording. The aim is to preserve the distinction between measured capacitance, derived parameters and claims that remain conditional.
The quick answer: a straight line is an interpretation, not the first measurement
A good reading starts from the original AC electrical response. Ask how capacitance was obtained, which capacitance belongs to the space-charge region, and what the graph’s coordinate transformation does. The fitted slope and intercept become physically useful only after the appropriate model and units are established. This order prevents the attractive simplicity of a line from hiding the conditions that generated it.
For a researcher or student translating the figure into another language, retain the mathematical symbols and references while explaining the physical quantities in natural prose. Your reader should be able to reconstruct why increasing 1/C² means decreasing C, which area or permittivity was used, and why a reported flat-band potential may not be a directly observed band energy.
Twenty checks for reading and translating a Mott–Schottky figure
1. Start with the semiconductor–electrolyte junction
When a semiconductor contacts an electrolyte, charge redistribution can create a space-charge region in the solid. Changing the electrode potential can change the width of that region and, in a suitable depletion approximation, its capacitance. Mott–Schottky analysis uses that potential dependence.
Example. In an ideal n-type example, making the electrode more positive over a suitable depletion range may widen depletion and reduce space-charge capacitance. The inverse square therefore increases as the chosen potential convention moves in that direction.
Misreading to avoid. A translated graph that calls every interfacial response ‘double-layer capacitance’ can replace semiconductor physics with a different electrical element. The liquid double layer and semiconductor space-charge region need not behave identically.
Practical verification. Find the sample structure and the author’s capacitance model. Specify whether the analysis concerns a bulk semiconductor, a thin oxide film, a junction or an electrode containing several interfaces.
At this point ask what the instrument actually recorded, what was mathematically transformed, and what the theory makes of that transformation. Keeping those stages visible is especially important for cross-disciplinary readers, because a capacitance graph can look authoritative even when several different physical elements contributed to it. A correct explanation names the assumptions rather than demanding uncritical trust in a plotted line.
2. Do not confuse C, 1/C and 1/C²
The vertical ordinate is often reciprocal square capacitance. It is not the measured capacitance itself, and it is not automatically an impedance magnitude. As C decreases, 1/C² increases, giving the transformed plot a direction that can look counterintuitive.
Example. If one point has capacitance 2 arbitrary units and another has capacitance 1 unit, the reciprocals squared are 0.25 and 1 respectively. The latter appears four times higher in the plotted ordinate, despite representing lower capacitance.
Misreading to avoid. Saying that a rising 1/C² line shows ‘capacitance increasing’ reverses the physical trend. Writing C² where the article means C^-2 is a similarly severe transcription error.
Practical verification. Inspect tick marks, units and mathematical superscripts. Read the axis aloud as ‘inverse capacitance squared’ and test it with a two-point arithmetic example before rewriting the figure legend.
Compare the figure title, axes, legend, methods and equation as one object. A statement can be grammatical and still be wrong if an exponent, reference electrode or capacitance definition differs between those locations. A strong translation checks agreement across the document and retains the author’s degree of certainty when the methods do not settle every interpretation.
3. Total capacitance versus area-normalised capacitance
Some authors use total capacitance C in farads and include electrode area A explicitly in the Mott–Schottky equation. Others divide by area first and use an areal capacitance such as F per square centimetre. Their slopes have different numerical scales.
Example. A curve labelled 1/C² with units F^-2 and one labelled 1/(C/A)² with area factors embedded are not numerically interchangeable. A conversion may involve area squared, not simply one factor of area.
Misreading to avoid. Deleting the area definition because it looks like an experimental detail can invalidate the calculated carrier concentration. A translated expression may then appear dimensionally plausible while yielding a wrong density.
Practical verification. Determine what the authors mean by C and whether it is Csc, a fitted interfacial capacitance, C/A or another quantity. Keep area units explicit throughout the equation and example.
The terminology test is simple: can another scientist use the words to recover the same physical quantity and the same units? Distinctions among potential, energy, capacitance, charge-carrier density and impedance must survive translation. Natural phrasing is valuable, but not when it replaces a defined scientific quantity with a loose synonym that changes what the graph asserts.
4. Potential means a defined reference, not an absolute number
The horizontal axis may be E versus Ag/AgCl, saturated calomel, reversible hydrogen electrode or another scale. Reference offsets depend on calibration conditions, composition and temperature. A Mott–Schottky intercept is meaningful only with its scale.
Example. A flat-band estimate of 0.2 V versus one reference electrode cannot be reported as 0.2 V versus every other reference. Even when two publications use the same numeral, their energy alignments may differ.
Misreading to avoid. Dropping ‘versus’ and the reference name makes a graph more readable but less scientifically meaningful. Equating electrode potential with a universal conduction-band energy is another common overstatement.
Practical verification. Copy the reference electrode name and any reported conversion equation. Use an explicitly stated calibration instead of inventing a generic conversion factor.
For teaching, invite readers to identify three sentences: one about a measured electrical response, one about a model-based parameter, and one about an unresolved limitation. Their ordering reveals whether the explanation is scientifically balanced. Students learn more from a carefully qualified parameter estimate than from a bold but untraceable number.
5. Positive and negative slopes require the full context
In a simple depletion-capacitance treatment, the sign of a suitably defined Mott–Schottky slope is often used as a clue to n-type or p-type behaviour. But sign conventions, mixed interfaces and nonideal response can complicate the conclusion.
Example. A positive linear region can be consistent with n-type behaviour in the usual potential convention, while a negative region may be consistent with p-type behaviour. That does not make each isolated sign a definitive material classification.
Misreading to avoid. A graph can have positive and negative segments because multiple processes contribute, not necessarily because the material transforms into two ideal semiconductor types as the scan proceeds.
Practical verification. Retain the sign and potential direction exactly. Translate a qualified phrase such as ‘consistent with n-type behaviour’ without upgrading it to an unqualified material identity.
Whenever an assumption is disputed in the literature, treat it as an assumption rather than an obscure footnote. Some Mott–Schottky analyses work well for their intended systems while others are complicated by contacts and mobile charges. Explaining the boundary helps readers decide whether the same method can be transferred to a different semiconductor, device or electrolyte.
6. The slope carries an assumed carrier-density model
For an ideal planar n-type depletion layer using total capacitance, a common relation has slope m = 2/(q εr ε0 N_D A²) for the graph of 1/C² against potential. With areal capacitance, the area factor is treated differently.
Example. A steeper correctly normalised slope corresponds to a lower extracted donor concentration in this simple model, assuming charge, permittivity, area and fitting regime are otherwise fixed. The symbol N_D denotes a model-derived density.
Misreading to avoid. It is easy to turn ‘carrier density calculated from the Mott–Schottky slope’ into ‘carriers counted directly’. The instrument measures an electrical response; a mathematical model supplies the density estimate.
Practical verification. Trace each constant and unit. Confirm whether εr is measured, assumed or taken from literature, and whether the calculation used SI metres or centimetres for area and density.
Reproducibility depends on mundane detail: the stated electrode area, voltage reference, frequency, fit interval, environmental condition and units. These are not decorative labels. When a translation preserves them, a reader can examine an alternative model or recalculate the derived value; when it drops them, the result becomes a difficult-to-check assertion.
7. The x-intercept is not the whole flat-band story
Extrapolating a valid linear segment to reciprocal capacitance squared equal to zero gives a characteristic potential. In ideal derivations, a thermal term involving kT/q may separate that intercept from the flat-band potential, depending on equation convention.
Example. At room temperature the thermal-voltage scale kT/q is approximately 0.026 V, a small quantity that can matter in a precise comparison. A source may include, omit or approximate it and should describe the choice.
Misreading to avoid. Calling the x-intercept exactly Efb in every context conceals the derivation. A plotted intercept from an arbitrary fit window may also be far less certain than the printed number suggests.
Practical verification. Write the equation actually used by the authors, inspect whether the thermal term is retained and state whether the value is an extrapolated estimate. Avoid silently changing the sign of the correction.
At this point ask what the instrument actually recorded, what was mathematically transformed, and what the theory makes of that transformation. Keeping those stages visible is especially important for cross-disciplinary readers, because a capacitance graph can look authoritative even when several different physical elements contributed to it. A correct explanation names the assumptions rather than demanding uncritical trust in a plotted line.
8. Frequency determines what capacitance responds
Capacitance is often extracted from impedance measured at a chosen AC frequency. Surface traps, slow ions, contact processes and dielectric relaxation can respond differently at different frequencies, changing the apparent Mott–Schottky slope.
Example. A plot made at 1 kHz may differ from one at 100 Hz for the same sample. That disagreement is useful diagnostic evidence rather than proof that one plot is necessarily fraudulent.
Misreading to avoid. Translating ‘Mott–Schottky curve’ while omitting the measurement frequency can hide a crucial condition. Assuming the highest available frequency always isolates an ideal space-charge capacitance is also unsafe.
Practical verification. State the applied perturbation frequency, amplitude if supplied and any reported frequency-dependence checks. Explain when the authors selected a frequency because the response appeared most stable.
Compare the figure title, axes, legend, methods and equation as one object. A statement can be grammatical and still be wrong if an exponent, reference electrode or capacitance definition differs between those locations. A strong translation checks agreement across the document and retains the author’s degree of certainty when the methods do not settle every interpretation.
9. Equivalent-circuit extraction is a modelling decision
An instrument measures complex impedance or a related AC response. Capacitance may then be calculated through a series or parallel equivalent-circuit assumption, or obtained from fitting a more elaborate circuit. Different choices can change C.
Example. The same complex impedance point does not automatically map to an identical capacitance in a series RC and parallel RC interpretation. In a system with substantial resistance or dispersion, that difference may affect the slope.
Misreading to avoid. Calling a fitted capacitance an instrument’s ‘direct measurement of depletion width’ skips several model steps. The reader deserves to know which electrical interpretation connects the raw response to the plotted ordinate.
Practical verification. Inspect the equivalent circuit, fitting window and phase-angle behaviour. Keep the reported model name and parameter notation with the graph, especially when several capacitance-like elements are present.
The terminology test is simple: can another scientist use the words to recover the same physical quantity and the same units? Distinctions among potential, energy, capacitance, charge-carrier density and impedance must survive translation. Natural phrasing is valuable, but not when it replaces a defined scientific quantity with a loose synonym that changes what the graph asserts.
10. Series resistance and contacts can distort the line
Ohmic resistance in solution, films, substrates or electrical contacts can affect measured impedance. Resistive contributions may make an apparent capacitance vary with bias and frequency even if depletion physics is not the sole cause.
Example. A thin semiconducting film deposited on a conductive substrate can have a contact contribution that is easy to overlook. If a plot changes after changing a contacting layer, interpreting all change as donor-density variation is premature.
Misreading to avoid. A translation that says ‘carrier concentration doubled’ may be unjustifiably strong when the reported result is only a fitted slope change under an untested circuit.
Practical verification. Check substrate, contact geometry, series-resistance correction and reported impedance fit quality. Preserve cautious wording when the experiment has not isolated the space-charge contribution.
For teaching, invite readers to identify three sentences: one about a measured electrical response, one about a model-based parameter, and one about an unresolved limitation. Their ordering reveals whether the explanation is scientifically balanced. Students learn more from a carefully qualified parameter estimate than from a bold but untraceable number.
11. Interfacial traps and states add another response
Electronic states at surfaces and interfaces can store or exchange charge. Their charging behaviour may contribute capacitance that depends on potential, frequency and illumination, producing nonideal or curved Mott–Schottky plots.
Example. A region that bends upward may reflect additional states or a change of which process dominates rather than a simple shift in constant bulk carrier density. It cannot safely be extrapolated like an ideal straight line without justification.
Misreading to avoid. Calling every curved region ‘experimental noise’ hides a possible physical mechanism. But claiming that curvature proves a specific trap is also stronger than the figure alone allows.
Practical verification. Describe what is visibly curved, identify which model the paper applies and state whether independent measurements constrain the proposed surface-state explanation.
Whenever an assumption is disputed in the literature, treat it as an assumption rather than an obscure footnote. Some Mott–Schottky analyses work well for their intended systems while others are complicated by contacts and mobile charges. Explaining the boundary helps readers decide whether the same method can be transferred to a different semiconductor, device or electrolyte.
12. Choose the linear fitting interval transparently
A Mott–Schottky graph may contain several quasi-linear segments, flat regions and curvature. Estimated slopes and intercepts depend on which points are fitted and on the weighting and regression method.
Example. A line fitted only to the steepest three points can yield a different intercept from one fitted across a broader stable region. Without a stated interval, a displayed flat-band potential is difficult to reproduce.
Misreading to avoid. Saying ‘the plot gives Efb’ masks the fact that someone chose a model and a fitting range. Never turn a selectively fitted trend into a universal property of all potentials.
Practical verification. Preserve the plotted fitting range, measurement spacing and whether error bars were used. If no fit method is given, explain the estimate’s limited reproducibility.
Reproducibility depends on mundane detail: the stated electrode area, voltage reference, frequency, fit interval, environmental condition and units. These are not decorative labels. When a translation preserves them, a reader can examine an alternative model or recalculate the derived value; when it drops them, the result becomes a difficult-to-check assertion.
13. Keep dielectric permittivity explicit
The Mott–Schottky density equation contains the material’s relative dielectric permittivity εr and vacuum permittivity ε0. Literature values may depend on composition, phase, frequency, direction and temperature.
Example. An assumed εr of 50 and a more appropriate value of 100 produce different inferred densities from the same slope. The numerical density should therefore be linked to the permittivity used.
Misreading to avoid. Reporting a donor density as a pure observation without naming an assumed dielectric constant can give readers unjustified confidence in its accuracy.
Practical verification. Check the dielectric value, source and units, and whether anisotropy or composite structure matters. Where uncertainty is substantial, retain a conditional statement about the model-dependent estimate.
At this point ask what the instrument actually recorded, what was mathematically transformed, and what the theory makes of that transformation. Keeping those stages visible is especially important for cross-disciplinary readers, because a capacitance graph can look authoritative even when several different physical elements contributed to it. A correct explanation names the assumptions rather than demanding uncritical trust in a plotted line.
14. Distinguish bulk density from apparent effective density
Real materials can have grain boundaries, defects, porous surfaces, multilayer contacts and nonuniform doping. The simple planar depletion formula assumes more uniform behaviour than many functional electrodes provide.
Example. A nanostructured photoelectrode may have an impressive apparent slope but a geometric area far removed from its electrochemically accessible interface. Labelling its derived number an ‘effective’ donor density may be more defensible.
Misreading to avoid. Calling the extracted number an exact count of dopants per cubic centimetre in every grain can be inaccurate when multiple capacitances contribute.
Practical verification. Ask what physical volume the capacitance probes and whether the geometry supports the standard model. Preserve ‘apparent’, ‘estimated’ and similar qualifiers when authors use them.
Compare the figure title, axes, legend, methods and equation as one object. A statement can be grammatical and still be wrong if an exponent, reference electrode or capacitance definition differs between those locations. A strong translation checks agreement across the document and retains the author’s degree of certainty when the methods do not settle every interpretation.
15. Light changes semiconductor interfaces
Photoelectrochemical experiments may measure capacitance in darkness or illumination. Photogenerated carriers, surface reactions and changed occupancy can alter the electrical response, which is why light conditions belong in the caption.
Example. A Mott–Schottky series measured under two illumination states is not automatically evidence of a permanent chemical change to donor concentration. The device may simply be in two operating states.
Misreading to avoid. The misleading translation is ‘light doped the material’ when the source shows only a light-dependent capacitance response. Doping, carrier population and illumination are different concepts.
Practical verification. Write whether the experiment was dark, illuminated or alternated between states. Preserve light wavelength, intensity and stabilization procedures if they were controlled.
The terminology test is simple: can another scientist use the words to recover the same physical quantity and the same units? Distinctions among potential, energy, capacitance, charge-carrier density and impedance must survive translation. Natural phrasing is valuable, but not when it replaces a defined scientific quantity with a loose synonym that changes what the graph asserts.
16. Hysteresis exposes history dependence
Capacitance recorded while scanning potential upward may not retrace when scanning downward if ions, traps, interfaces or material states relax on comparable timescales. The measurement history becomes part of the meaning.
Example. Two opposite-direction sweeps forming a loop indicate a path-dependent electrical response under those conditions. The loop alone does not identify the responsible physical process.
Misreading to avoid. A single fitted line copied from one sweep direction may hide the difference between forward and reverse scans. This can make an extracted intercept look more stable than it is.
Practical verification. Preserve scan direction, delay at each bias and conditioning history. If hysteresis exists, avoid reporting one intercept as an entirely history-independent property without evidence.
For teaching, invite readers to identify three sentences: one about a measured electrical response, one about a model-based parameter, and one about an unresolved limitation. Their ordering reveals whether the explanation is scientifically balanced. Students learn more from a carefully qualified parameter estimate than from a bold but untraceable number.
17. Temperature and electrolyte are experimental variables
Electrolyte composition, ionic strength, pH and temperature can influence interfacial charge distribution and measured potential. A fair comparison needs the surrounding chemical conditions as well as the material identity.
Example. Two studies may disagree on a flat-band estimate because their reference scales or electrolytes differ, even before accounting for semiconductor composition. A small potential offset is not always a meaningful performance ranking.
Misreading to avoid. It is misleading to present several flat-band values in a comparison table without naming the measurement conditions. That can make methodological variation look like a material property.
Practical verification. Keep the electrolyte, pH, temperature, pretreatment and reference electrode near the reported value. Use consistent units without erasing the original conditions.
Whenever an assumption is disputed in the literature, treat it as an assumption rather than an obscure footnote. Some Mott–Schottky analyses work well for their intended systems while others are complicated by contacts and mobile charges. Explaining the boundary helps readers decide whether the same method can be transferred to a different semiconductor, device or electrolyte.
18. A straight line is necessary for a simple fit, not sufficient proof
A linear region of 1/C² against E is compatible with a depletion capacitance model, but some contact and injection phenomena can mimic apparently linear behaviour. Independent physical characterization may be necessary.
Example. In certain photoanodes, an apparent capacitance step can arise from charge injection at a contact, complicating conventional Mott–Schottky doping estimates. A visually tidy graph alone cannot discriminate these mechanisms.
Misreading to avoid. Words such as ‘proves the doping density’ should not replace a source’s more limited ‘estimated under the depletion approximation’. A line does not validate the model that produced it.
Practical verification. Compare frequency behaviour, thickness series, contacts, impedance spectra and independent material evidence where available. Describe the measured line and the inferred parameters separately.
Reproducibility depends on mundane detail: the stated electrode area, voltage reference, frequency, fit interval, environmental condition and units. These are not decorative labels. When a translation preserves them, a reader can examine an alternative model or recalculate the derived value; when it drops them, the result becomes a difficult-to-check assertion.
19. Make uncertainty and units readable
Carrier density may be given in cm^-3 or m^-3, capacitance in F or F cm^-2, and potential versus a named electrode. Powers of ten and negative exponents make technical writing vulnerable to very large conversion errors.
Example. A density of 10^19 cm^-3 is 10^25 m^-3, not 10^13 m^-3. A graph label that loses the exponent or the ‘per cubic centimetre’ phrase destroys the quantitative meaning.
Misreading to avoid. A careful editor must not change an exponent to match what seems plausible. Apparent anomalies need a source check, not an invisible repair.
Practical verification. Retain scientific notation and dimensional units exactly, then verify transformations algebraically. State the uncertainty type and the fit precision if reported; do not invent error bars.
At this point ask what the instrument actually recorded, what was mathematically transformed, and what the theory makes of that transformation. Keeping those stages visible is especially important for cross-disciplinary readers, because a capacitance graph can look authoritative even when several different physical elements contributed to it. A correct explanation names the assumptions rather than demanding uncritical trust in a plotted line.
20. Write the claim at the strength of the evidence
A technically responsible translation says what was plotted, which segment was fitted, which model was assumed and what the resulting estimate means. The strongest claim may require independent confirmation.
Example. A suitable sentence is ‘The approximately linear region was fitted with the depletion-capacitance model, yielding an apparent flat-band estimate and donor concentration under the stated dielectric and area assumptions.’
Misreading to avoid. An unsuitable sentence says ‘the graph measures the exact band edge and dopant count’. It turns a parameter extraction with limitations into a direct observation.
Practical verification. Mark measured quantities, derived values and physical hypotheses in separate clauses. Preserve every qualifier that tells the reader how strongly the source supports the conclusion.
Compare the figure title, axes, legend, methods and equation as one object. A statement can be grammatical and still be wrong if an exponent, reference electrode or capacitance definition differs between those locations. A strong translation checks agreement across the document and retains the author’s degree of certainty when the methods do not settle every interpretation.
Worked reading: finding a slope and an intercept without claiming too much
Take a hypothetical plot in which the plotted reciprocal square capacitance is 4 arbitrary units at 0.30 V versus a specified reference and 8 units at 0.50 V versus the same reference. If those points lie in an appropriate linear region, the line has slope (8 − 4)/(0.50 − 0.30) = 20 plotted units per volt. Extrapolating this idealised line to a vertical-axis value of zero gives 0.10 V. Those arithmetic steps are valid for the invented example; they are not sufficient to establish a physical flat-band potential.
The next task is to identify what the vertical units mean. Were values calculated from total capacitance in farads or area-normalised capacitance? Did the researchers use an appropriate semiconductor permittivity and a defensible depletion approximation? Does the instrument’s measured impedance support isolating the space-charge capacitance? Without these details, no credible numerical donor concentration follows from the slope. Writing ‘apparent linear intercept of 0.10 V versus the reported reference’ is more accurate than assigning an unverified absolute band energy.
Suppose the same electrode produces a noticeably different slope at another frequency. A responsible account does not simply average the two slopes or choose the one yielding a familiar carrier density. It reports that the extracted capacitance is frequency-dependent and discusses whether the ideal model is suitable. The example demonstrates a general language skill: distinguish a correct numerical transformation from a physical interpretation that still requires evidence.
A reusable caption format
Use this text-first caption pattern: ‘Mott–Schottky plot of [defined capacitance transformation] against [electrode potential and reference] measured in [electrolyte and condition] at [frequency and perturbation amplitude]. The fitted interval [state range] gives [slope and intercept]. Under [named model, area and dielectric assumptions], the authors estimate [derived parameter and uncertainty].’ Every bracket must be supported by the figure or methods, not filled with plausible-looking inventions.
Where the source does not identify the capacitance model, do not write an equation as if you know it. Label the gap: ‘The plot is presented as 1/C² versus potential; the procedure used to extract C is not specified in the supplied material.’ Such transparency is essential when a translation may be reused by teachers, researchers or technicians who did not see the original experiment.
Questions readers ask
What is a Mott–Schottky plot?
It is generally a graph of reciprocal square capacitance versus applied electrical potential, used under an interfacial capacitance model to infer semiconductor properties. Its value depends on what capacitance was extracted and whether depletion-layer assumptions are credible.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Does a positive slope always prove n-type conductivity?
A positive slope is often associated with n-type depletion behaviour under the usual convention. It is not proof independent of reference scale, circuit interpretation, traps and other contributions. A comparison with complementary electrical or photoelectrochemical data may be needed.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Is the x-axis intercept exactly the flat-band potential?
The x-axis intercept is obtained by extrapolating the fitted line. The reported flat-band potential may involve a thermal correction and other model conventions. The chosen fitting interval and potential reference also matter. State the exact definition used in the source.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Why do curves differ at 100 Hz and 1 kHz?
Different physical processes respond at different frequencies. Traps, ions, contacts, resistance and dielectric relaxation may influence the extracted capacitance. Report the frequency and compare full impedance behaviour before declaring one curve intrinsically correct.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
What units should donor density use?
Both cm^-3 and m^-3 are common. Their numerical values differ by a factor of one million because one cubic metre contains one million cubic centimetres. When translating, retain exponent and unit together, and check which area units the density equation used.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Can I compute doping density from the slope alone?
Not reliably. You also need the actual equation, whether total or area-normalised capacitance was used, charge, dielectric permittivity, area if applicable and consistent units. You must also assess whether the plotted response represents the relevant space-charge capacitance.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Why is my Mott–Schottky plot curved?
Curvature can result from nonideal depletion, states, multiple interfaces, resistance, light effects and measurement protocol. It should be described as observed curvature before one mechanism is assigned. A numerical fit alone does not establish its cause.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
How should I describe uncertain flat-band data?
Use phrases such as ‘estimated flat-band potential’ or ‘apparent donor density under the stated capacitance model’. Name the chosen linear region, potential reference and uncertainty source. This is clearer, not weaker, scientific communication.
The most useful next check is to return to the methods and units, then ask which part of the answer is observation and which part is the consequence of a model. Keeping that distinction visible makes a translated explanation more helpful to newcomers without hiding the conditions that experts need for independent evaluation.
Terminology and notation glossary
Mott–Schottky plot. Potential-dependent reciprocal-square-capacitance representation. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Space-charge capacitance, Csc. Capacitance attributed to charge redistribution within the semiconductor. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Flat-band potential, Efb. Potential associated with the defined no-band-bending condition, inferred under a model. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Donor density, ND. Estimated density of electron-donating centres in a suitable n-type model. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Acceptor density, NA. Estimated acceptor density in a suitable p-type model. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
εr and ε0. Relative permittivity of the material and permittivity of free space. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Reference electrode. Measurement reference for applied potential; must be named. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
1/C². Inverse square capacitance, not capacitance squared. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Linear fit. Numerical estimation using selected data points over a stated interval. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Frequency dispersion. Change in measured response as the AC measurement frequency changes. Preserve the corresponding mathematical symbol in every language version, and check that its unit, definition and role agree across the axis label, equation and caption.
Further reading and adjacent learning routes
Read EIS Bode plots — a linked route for deeper explanation, related measurements or checking technical language in context.
Read EIS Nyquist plots — a linked route for deeper explanation, related measurements or checking technical language in context.
Translation and meaning across languages — a linked route for deeper explanation, related measurements or checking technical language in context.
Cross-linguistic vocabulary transfer — a linked route for deeper explanation, related measurements or checking technical language in context.
How to translate correctly — a linked route for deeper explanation, related measurements or checking technical language in context.
English learning map — a linked route for deeper explanation, related measurements or checking technical language in context.
Mott–Schottky analysis (Metrohm) — a linked route for deeper explanation, related measurements or checking technical language in context.
Frequency choice and effects (Catalysts research) — a linked route for deeper explanation, related measurements or checking technical language in context.
Limits to photoanode Mott–Schottky inference — a linked route for deeper explanation, related measurements or checking technical language in context.
Final checklist
Before publishing a Mott–Schottky explanation, inspect the potential reference, capacitance definition, inverse-square transformation, frequency, perturbation amplitude, fit interval, slope sign, thermal correction, permittivity, electrode area, units, sample architecture, light conditions and model limits. Confirm that every reported carrier density and flat-band potential retains its status as a derived quantity. If evidence is missing, preserve that limitation instead of silently strengthening a claim.
The best translation does more than pronounce the symbols. It shows what the graph means, how a researcher obtained the numbers and where the interpretation may fail. That combination turns an apparently simple straight-line plot into a reliable learning resource.