ArticleslgStudy

science

Mott–Schottky plot

Mott–Schottky plot is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mott–Schottky plot rather than just read about it. In short: In semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of capacitance ( 1 / C 2 ) {\displaystyle (1/C^{2})} versus the potential difference between bulk semiconductor and bulk electrolyte. In many theories, and in many experimental measurements, the plot is linear.

Mott–Schottky plot — main illustration
Mott–Schottky plot — illustration

Key takeaways

  • Mott–Schottky plot belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Mott–Schottky plot to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Mott–Schottky plot from memory before moving on to harder problems.

Reference excerpt

In semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of capacitance ( 1 / C 2 ) {\displaystyle (1/C^{2})} versus the potential difference between bulk semiconductor and bulk electrolyte. In many theories, and in many experimental measurements, the plot is linear. The use of Mott–Schottky plots to determine system properties (such as flatband potential, doping density or Helmholtz capacitance) is termed Mott–Schottky analysis.

Consider the semiconductor/electrolyte junction shown in Figure 1. Under applied bias voltage V {\displaystyle V} the size of the depletion layer w {\displaystyle w} is

w = [ 2 ε q N D ( V + V bi ) ] 1 / 2 {\displaystyle w={\left\lbrack {\frac {2\varepsilon }{{\mathit {q}}{\mathit {N}}_{D}}}\left(V+{V}_{\text{bi}}\right)\right\rbrack }^{1/2}} (1) Here ε = ε r ε 0 {\displaystyle \varepsilon =\varepsilon _{r}\varepsilon _{0}} is the permittivity, q {\displaystyle q} is the elementary charge, N D {\displaystyle {N}_{D}} is the doping density, V bi {\displaystyle {V}_{\text{bi}}} is the built-in potential. The depletion region contains positive charge compensated by ionic negative charge at the semiconductor surface (in the liquid electrolyte side). Charge separation forms a dielectric capacitor at the interface of the metal/semiconductor contact. We calculate the capacitance for an electrode area A {\displaystyle A} as

C = ∂ Q ∂ V = q N D A ∂ w ∂ V {\displaystyle C={\frac {\partial Q}{\partial V}}={\mathit {q}}{\mathit {N}}_{D}A{\frac {\partial w}{\partial V}}} (2) replacing ∂ w ∂ V {\displaystyle {\frac {\partial w}{\partial V}}} as obtained from equation 1, the result of the capacitance per unit area is

C = A ε w {\displaystyle C=A{\frac {\varepsilon }{w}}} (3) a equation describing the capacitance of a capacitor constructed of two parallel plates both of area A {\displaystyle A} separated by a distance w {\displaystyle w} . Replacing equation (3) in (1) we obtain the result

C − 2 = 2 q A 2 ε N D ( V + V bi ) {\displaystyle {C}^{-2}={\frac {2}{{\mathit {qA}}^{2}{\mathit {\varepsilon N}}_{D}}}\left(V+{V}_{\text{bi}}\right)} (4). Therefore, a representation of the reciprocal square capacitance, is a linear function of the voltage, which constitutes the Mott–Schottky plot as shown in Fig. 1c. The measurement of the Mott–Schottky plot brings us two important pieces of information.

… excerpt ends here. Continue reading the full article.

Illustrations

Mott–Schottky plot: Figure 1. (a) Shows an energy diagram of n-type semiconductor in contact with redox electrolyte at the left side (yellow), and with a metallic ohmic contact at the right side. Ec is the conduction band edge energy, Ev is the valence band energy of the semiconductor. By equilibration of the Fermi level in the semiconductor, EF, and the redox energy of electrolyte, Eredox, a Schottky barrier is formed at the semiconductor/electrolyte interface. The vertical size of the barrier in the energy diagram corresponds to the built-in potential Vbi. In the spatial axis the equilibration of Fermi levels produces a space charge region or depletion region of size w. A positive voltage applied to the back contact in (b) raises the Fermi level of electrons EFn, and decreases the size of the depletion region. Consequently, the capacitance of the junction increases, and the reciprocal square capacitance decreases forming a linear Mott–Schottky plot in (c). The intercept with the x-axis shows the flatband situation, that reveals the built-in potential, depending on the reference of voltage in the electrolyte side. (d) In the presence of a surface state of density Nss, when the Fermi level reaches the bandgap state level, it is discharged and a plateau occurs depending on the value of the Helmholtz layer capacitance CH at the electrolyte side of the junction. When the surface state is charged the Mott–Schottky lines continues, but the flatband potential is modified according to the extent of unpinning of the Fermi level. Adapted from[1]
Figure 1. (a) Shows an energy diagram of n-type semiconductor in contact with redox electrolyte at the left side (yellow), and with a metallic ohmic contact at the right side. Ec is the conduction band edge energy, Ev is the valence band energy of the semiconductor. By equilibration of the Fermi level in the semiconductor, EF, and the redox energy of electrolyte, Eredox, a Schottky barrier is formed at the semiconductor/electrolyte interface. The vertical size of the barrier in the energy diagram corresponds to the built-in potential Vbi. In the spatial axis the equilibration of Fermi levels produces a space charge region or depletion region of size w. A positive voltage applied to the back contact in (b) raises the Fermi level of electrons EFn, and decreases the size of the depletion region. Consequently, the capacitance of the junction increases, and the reciprocal square capacitance decreases forming a linear Mott–Schottky plot in (c). The intercept with the x-axis shows the flatband situation, that reveals the built-in potential, depending on the reference of voltage in the electrolyte side. (d) In the presence of a surface state of density Nss, when the Fermi level reaches the bandgap state level, it is discharged and a plateau occurs depending on the value of the Helmholtz layer capacitance CH at the electrolyte side of the junction. When the surface state is charged the Mott–Schottky lines continues, but the flatband potential is modified according to the extent of unpinning of the Fermi level. Adapted from[1]
Mott–Schottky plot: Figure 2. Mott–Schottky plot of a fluorine-doped tin oxide (FTO) semiconductor electrode measured in aqueous electrolyte at different pH, with respect to standard Ag/AgCl electrode. Changing the pH modifies the apparent flatband potential by 570 mV corresponding to a 59 mV displacement per unit of pH. From the slope the donor density ND = 1.1 × 1021 cm−3 is determined. Then the same sample is measured after nanostructured TiO2 is deposited on top of FTO. The observed change of slope is due to the decrease of the surface in direct contact with the electrolyte.
Figure 2. Mott–Schottky plot of a fluorine-doped tin oxide (FTO) semiconductor electrode measured in aqueous electrolyte at different pH, with respect to standard Ag/AgCl electrode. Changing the pH modifies the apparent flatband potential by 570 mV corresponding to a 59 mV displacement per unit of pH. From the slope the donor density ND = 1.1 × 1021 cm−3 is determined. Then the same sample is measured after nanostructured TiO2 is deposited on top of FTO. The observed change of slope is due to the decrease of the surface in direct contact with the electrolyte.

Worked examples

Example 1 — a first encounter with Mott–Schottky plot

Start with the simplest possible case. Write down what Mott–Schottky plot claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mott–Schottky plot before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mott–Schottky plot ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mott–Schottky plot

In research
Mott–Schottky plot appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Mott–Schottky plot in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Mott–Schottky plot is common in secondary-school and first-year university syllabi. It links to neighbouring topics Semiconductors, so understanding it makes those chapters shorter.
In everyday life
Look for Mott–Schottky plot outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Mott–Schottky plot” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Mott–Schottky plot in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Mott–Schottky plot means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Mott–Schottky plot out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mott–Schottky plot in simple terms?

In semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of capacitance ( 1 / C 2 ) {\displaystyle (1/C^{2})} versus the potential difference between bulk semiconductor and bulk electrolyte. In many theories, and in many experimental measurements, the plot is l…

Why does Mott–Schottky plot matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mott–Schottky plot?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mott–Schottky plot.

Tags

  • Semiconductors

Keep exploring