Mott-Schottky Analysis

Semiconductors are intrinsic to modern life, but they stand to play an even greater role in the coming energy transition. Several techniques are employed in the pursuit of improved materials for energy production and storage. One particularly popular method for studying the electronic properties of potential new semiconducting materials is Mott-Schottky Analysis. The technique can be best understood as an extension of electrochemical impedance spectroscopy (EIS). By performing EIS at a range of different DC bias or offset potentials, the reciprocal of the square capacitance can be derived from the data and then plotted against the DC offset itself, producing a so-called Mott-Schottky Plot. From such a plot, critical parameters such as the carrier concentration, the doping profile, and the flatband potential can be conveniently extracted.

This technique is popular across different fields, as it is versatile, non-destructive, and relatively fast. Compared to other options, Mott-Schottky Analysis also requires relatively little specialist equipment. This Application Note presents an example of Mott-Schottky measurement on a popular semiconducting material using VIONIC powered by INTELLO.

It is important to note that semiconductors exhibit quite different electrochemical behavior when compared to the traditional well-conducting electrode materials (e.g., glassy carbon or platinum). Namely, semiconductor electrochemistry is complicated by the appearance of a space charge region that extends from the surface into the material itself. During a Mott-Schottky measurement, it is the capacitance of the space charge region which is probed. This region is related to the redistribution of charge that occurs when the material is placed in contact with the electrolyte. The energy levels of the valence and conduction bands within the space charge region are distorted (a process called «band bending») so that the fermi level of the semiconductor matches the redox potential of the electrolyte/redox system. The degree of band bending can be artificially adjusted using a potentiostat. Logically, there must be an applied potential where no band bending occurs – this is termed the «flatband potential» (E_FB). This is a useful parameter that gives information about the energy levels within the semiconductor and how to best optimize the operating conditions of the semiconducting material.

It is possible to relate the flatband potential and also, conveniently, the doping density (carrier concentration) to the capacitance of the space charge region by the Mott-Schottky equation, shown here:

where 𝜀 is the dielectric constant of the material, 𝜀₀ (8.85E − 12 F m⁻¹) is the vacuum permittivity, A (m) is the exposed area of the material, e (1.60E − 19 C) is the electronic charge, N_D is the doping density, E is the applied DC offset, E_FB is the flatband potential, k (1.38E − 23 J K⁻¹) is the Boltzmann constant, and T (K) is the temperature.

It should be clear from the above that a plot of 1/C_SC² vs E allows both N_D and E_FB to be calculated from the slope and the intercept at the x-axis, respectively:  

Note that EIS can be used to obtain the capacitance of the space charge region assuming that the chosen frequency is sufficiently high (kHz), such that the following equations are true:

where −Z" is the imaginary impedance, 𝜔 is the angular frequency, R_s is the serial (uncompensated) resistance, 1/C_s² is the capacitance if modelled by a serial connection of R_s-C_s, and 1/C_p² is the capacitance if modelled by a parallel connection of R_s-C_p / R_P.

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A 250 mL three-electrode cell was employed for this application study. As the working electrode, an FTO-coated (fluorine-doped tin oxide) glass slide (25 × 25 × 1 mm, RedoxMe) was used. The slides were washed with ultrapure water before use and then mounted on a sample holder (RedoxMe). The counter electrode consisted of two Pt sheet electrodes shorted together to increase the overall surface area. (PT.SHEET, Metrohm). The reference electrode used was Ag/AgCl (6.0733.100, Metrohm). The electrolyte (0.1 mol/L NaCl) was not purged and was exposed to the ambient air.

From these results and the equations above, the flatband potential was determined from the intercept as -1.61 V (vs. 3 mol/L Ag/AgCl or -1.40 V vs. SHE). Comparable values have been reported for FTO in the literature [2].

Assuming the dielectric constant is also known (here taken as 2.137 from [3]), the doping density can be calculated from the slope using the previous equation as 2.90 × 10²¹ cm^-3. This is also comparable to the doping densities reported in scientific literature [1,3].