Experimental Common Tools: (2) Frequency Response Analysis

Editor : Sapien

Every breath that you take,
Any sound that you make,
Is a whisper in my ear.

– From “You Take My Breath Away”, sung by Queen

 Frequency Response Analysis (FRA) is a common AC technique for nonlinear device characterization. While the I-V characterizaton is basically a DC technique for measurement at steady-state conditions, further information on device characteristics at dynamic conditions can be obtained by using FRA. For a linear electrical system, for instance, the resistance is the characteristic parameter measured by DC technique, while the capacitance and inductance can be further obtained by using AC measurement.

 If a periodic stimulus is applied to a system as an input signal, then the output signal can be considered as a periodic response of the input, and the relation between output vs. input we call as a response function. In the electrical system, the response function is impedance(Z) when periodic input is current and output is voltage, and admittance(Y) when periodic input is voltage and output is current. In FRA, a sinusoidal waveform is generally used as periodic stimulus, and its magnitude is usually set to be relatively small to DC bias when systems are nonlinear and the periodic stimulus is required to be a small perturbation. The frequency of the sinusoidal waveform is a key variable in FRA.

 The impedance as a response function in the electrical system, when represented in frequency domain, is a complex function of frequency including real part and imaginary part, or expressed in terms of magnitude and phase. The impedance spectroscopy (IS) is a set of complex impedance measurements at different frequencies in a specific frequency range.

 The equivalent circuit is a model generating frequency dependent impedance function. A combination of linear or nonlinear circuit elements, which has physical relevance to modeled electrical process, can be expressed in a mathematical way as a complex impedance function with characteristic parameters of corresponding circuit elements. These characteristic parameters can be determined by numerical fitting of experimentally measured impedance spectrum data using complex nonlinear least square regression algorithm.

 FRA technique has been widely used in characterization of electrochemical systems. Many of electrochemical processes such as Faradaic process, various polarization phenomena, charge transfer at the interface, charge conduction in the electrolyte and diffusion process through solid-state material has been modeled and used as equivalent circuit elements. FRA is applicable to, and plays key role for characterization of battery, electrochemical double layer capacitor, dye-sensitized solar cell, fuel cell and many other electrochemical systems.

 FRA has also been used for characterization of semiconductor device, especially for capacitance measurement. Organic semiconductor devices such as OLED, OPV and OTFT have thin multi-layered structure and require device optimization through parametrization of charge transport (mobility and capacitance) in the layer and across the interface. FRA is also useful in characterization of dielectric, ferroelectric, and piezoelectric devices.

 Optically coupled devices like solar cell, photo diode and LED having optical input or output can be characterized using response functions analogous to electrical systems. Intensity modulated photocurrent spectroscopy (IMPS) and intensity modulated photovoltage spectroscopy (IMVS) measure quasi-impedance spectra from current or voltage output with respect to modulated optical input, and these methods can be categorized as FRA technique.