Solar-cell characterisation: I–V, Mott-Schottky, EIS and IMVS
1 Theory
The I–V curve of a solar cell
Under illumination the p–n junction (or the equivalent structure in a dye-sensitised/perovskite cell) generates a photocurrent; the I–V curve is the diode equation in shifted form: I = I_ph − I₀[exp(qV/nkT) − 1] − (V + I·R_s)/R_sh. Characteristic quantities: short-circuit current (I_sc), open-circuit voltage (V_oc), maximum power point, fill factor (FF = P_max/(I_sc·V_oc)) and efficiency (η = P_max/P_light). Series resistance R_s flattens the curve near V_oc, shunt resistance R_sh adds a slope near I_sc. The standard test condition is AM1.5G, 100 mW/cm², 25 °C; scan direction and rate must be reported for cells showing hysteresis (perovskites).
Mott–Schottky analysis
At the semiconductor/electrolyte or semiconductor/metal interface the space-charge capacitance depends on potential: 1/C² = (2/(ε·ε₀·q·N_D·A²))·(E − E_fb − kT/q). The slope of the 1/C²–E plot gives the doping density (N_D; positive slope n-type, negative p-type), the intercept the flat-band potential (E_fb). The measurement is made by EIS at a single frequency (typically 1 kHz) or by frequency sweep; frequency dependence points to the presence of surface states.
EIS, IMPS and IMVS
Under illumination EIS gives the carrier recombination resistance and chemical capacitance; the recombination lifetime τ = R_rec·C_µ. In intensity-modulated photocurrent (IMPS) and photovoltage (IMVS) spectroscopy the light intensity is modulated sinusoidally with small amplitude; IMPS gives the carrier collection/transit time, IMVS the recombination lifetime directly — in dye-sensitised and perovskite cells in particular the diffusion length is calculated from the ratio of the two.
Photoelectrochemistry
On water-splitting photoelectrodes (TiO₂, BiVO₄, Fe₂O₃) the photocurrent–potential curve is taken under chopped illumination; the photocurrent onset potential, transient spikes (surface recombination) and the applied-bias photon-to-current efficiency (ABPE) are evaluated. The incident photon-to-electron conversion efficiency (IPCE) is measured against wavelength.
2 Application in measurement
From light/dark I–V curves the open-circuit voltage, short-circuit current, fill factor and efficiency are obtained; from the Mott-Schottky plot (1/C² vs E) the flat-band potential and carrier density. At the semiconductor/electrolyte interface Mott-Schottky is measured by potential-dependent EIS (SPEIS).
EIS separates the recombination resistance and chemical capacitance in DSSC/perovskite/organic cells (Bisquert models). IMVS/IMPS give electron lifetime and transport time with modulated light; the analogue inputs and synchronous EIS mode of the SP-300 support these measurements.
In photoelectrochemical water splitting LSV + chopped light and EIS are used together.
Key equations
Mott-Schottky: 1/C² = (2/(εε₀eN_D·A²))·(E − E_fb − kT/e)
3 Applicability
Where it applies
- New absorber/interface materials, perovskite and DSSC development, photoelectrochemical water splitting, I–V in module quality control.
Limits and caveats
- Mott–Schottky rests on the assumption of a flat, homogeneous, doped semiconductor; on nanostructured or heavily doped films the quantitative N_D may be unreliable.
- In perovskites ion movement complicates EIS at low frequency; model selection is debated.
4 What did the application notes find?
- Photovoltaic AN24 — Shows recording the polarisation (I–V) curve of a solar cell under illumination and calculation of the doping density and flat-band potential by Mott–Schottky analysis in the dark.
- Photovoltaic AN30 — Shows the set-up of an IMVS measurement (modulated LED, potentiostat synchronisation) and reading the recombination lifetime from the spectrum.
- Photovoltaic AN35 — Shows direct plotting of the capacitance–voltage curve from EIS data; the use of this curve for the doping profile in semiconductor characterisation.
- Battery AN18 — Shows the automatic acquisition of a potential-dependent series of spectra with staircase potentiostatic EIS (SPEIS) and its sequential fitting with Z Fit; the data source of Mott–Schottky and C–V analyses.
5 Which instruments perform this measurement?
References
- article K. Gelderman, L. Lee, S. W. Donne. Flat-Band Potential of a Semiconductor: Using the Mott–Schottky Equation. J. Chem. Educ. 84, 685, 2007. doi:10.1021/ed084p685
- article F. Fabregat-Santiago, G. Garcia-Belmonte, I. Mora-Seró, J. Bisquert. Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopy. Phys. Chem. Chem. Phys. 13, 9083–9118, 2011. doi:10.1039/c0cp02249g
- book A. J. Bard, L. R. Faulkner, H. S. White. Electrochemical Methods: Fundamentals and Applications (3rd ed.). Wiley, 2022.