In
semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of
capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
versus the potential difference between bulk
semiconductor
A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...
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
the size of the depletion layer
is
(1)
Here
is the permittivity,
is the elementary charge,
is the doping density,
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
In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
at the interface of the metal/semiconductor contact. We calculate the capacitance for an electrode area
as
(2)
replacing
as obtained from equation 1, the result of the
capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized ar ...
per unit area is
(3)
a equation describing the capacitance of a capacitor constructed of two parallel plates both of area
separated by a distance
.
Replacing equation (3) in (1) we obtain the result
(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.
# The slope gives the
doping (semiconductor) density (provided that the
dielectric constant is known).
# The intercept to the ''x'' axis provides the built-in potential, or the flatband potential (as here the surface barrier has been flattened) and allows establishing the semiconductor conduction band level with respect to the reference of potential.
In liquid junction the reference of potential is normally a standard
reference electrode
A reference electrode is an electrode which has a stable and well-known electrode potential. The high stability of the electrode potential is usually reached by employing a redox system with constant (buffered or saturated) concentrations of each ...
. In solid junctions, we can take as a reference the metal Fermi level, if the
work function
In solid-state physics, the work function (sometimes spelt workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" ...
is known, which provides a full energy diagram in the physical scale. The Mott–Schottky plot is sensitive to the electrode surface in contact with solution, see Figure 2.
A more accurate analysis considering the statistics of electrons provides the following result for the size of the depletion region
(5)
in this case the
Mott–Schottky equation is
(6)
When the interfacial barrier is of the order
, special care has to be taken to interpret the capacitance measurement. In fact at these small voltages the capacitance makes a peak that can be used for the determination of the built-in voltage.
The Mott–Schottky analysis can more generally resolve a variable
doping profile in the semiconductor as follows
(7)
The derivative gives the doping at the edge of the depletion region,
. This method only provides a spatial resolution of the order of a
Debye length
In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
systems where more than one process gives a substantial kinetic response, it is necessary to adopt
Electrochemical Impedance Spectroscopy
Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 200 ...
that resolves the different capacitances in the system.
For example, in the presence of a surface state at the semiconductor/electrolyte interface, the spectra show two arcs, one at low frequency and another one at high frequency. The depletion capacitance leading to Mott–Schottky plot is situated in the high frequency arc, as the depletion capacitance is a dielectric capacitance. On the other hand, the low frequency feature corresponds to the
chemical capacitance of the surface states. The surface state charging produces a plateau as indicated in Fig. 1d. Similarly, defect levels in the gap affect the changes of capacitance and conductance.
Another widely used method to scan deep levels in Schottky barriers is termed
admittance spectroscopy and consists on measuring the capacitance at a fixed frequency while varying the temperature.
Surface photovoltage technique or potentiostatically induced Burstein-Moss shifts
can be used to determine the position of the band edges.
References
{{DEFAULTSORT:Mott Schottky plot
Semiconductors