Calibration of High-Frequency Impedance Spectroscopy Measurements with Nanocapacitor Arrays

High frequency impedance spectroscopy (HFIS) biosensors based on nano-electrode arrays (NEA) demonstrated the capability to overcome the screening limits set by the Electrical Double Layer (EDL), thus enabling label-free detection and imaging of analytes far above the sensor surface [1,2]. In order to achieve quantitatively accurate results, a precise understanding and modeling of the signal transduction chain is necessary. With reference to the CMOS array platform in [1], capacitance is measured by CBCM. Hence, the nanoelectrodes are alternatively charged and discharged by two switch transistors (Fig.1, a), which are activated by non-overlapping clocks with typically 1 ns floating time between the two phases. The column readout circuits integrate and average over multiple cycles the charging current to obtain a capacitance information. The output signal is interpreted in terms of a switching capacitance (CSW), modeled by charge-pump analysis of an equivalent C-RC circuit excited by a square wave (EDL capacitance CS in series to a parallel RECE representing the bulk electrolyte [1]; CS, RE and CE are extracted with the biosensor simulator ENBIOS [3]), good agreement is obtained between experiments and simulations over a broad range of frequencies and electrolyte salt concentrations [1]. Residual discrepancies, however, require explanation and this is the main contribution of our abstract. To this end, we firstly, consider the role of leakage currents (ILEAK) in the sensor cell (due to subthreshold conduction of the inactive switch). The leakage current implies overestimating the column current IM (and hence the capacitance). Due to the large number of cells connected on each column, a value as large as 20pA is estimated for ILEAK, and measurements are corrected by compensating for it. Then, we consider the voltage waveforms at the nanoelectrode, as obtained by Spice simulations with Predictive Technology Models (PTM) of the sensor cell readout circuit (Fig.1 (b) for a 10mM electrolyte). Charge repartition between the nanoelectrode’s node and CGS/CGD capacitance of the switching transistors during the float time distorts the otherwise square-waveform. For electrolytes with high salt concentration this effect is mitigated (due to the larger load capacitance). To account for this effect, we extract the harmonic content of the waveform by Fourier expansion of the waveform (Fig.1, b). Then, ENBIOS simulations at all harmonic frequencies are used to reconstruct the capacitance response to the actual waveform (CF). Fig.1 (c) compares experiments (corrected for leakage) and simulations (CSW or CF). The impact of leakage is modest, whereas CF exhibits an improved agreement with experiments at high frequency, where waveform glitches are more relevant. These corrections highlight the importance of leakage and harmonic content of the input waveforms to achieve quantitatively accurate interpretation of NEA HFIS biosensor experiments. Further work is necessary to extend these results to electrolytes with physiological salinity.