Hybrid system for complex AC sensing of nanowires

Rossi, Michele; Bennati, Marco; Lombardini, Marta; Ashburn, P.; Morgan, Hywel; Sangiorgi, E.; Tartagni, Marco

doi:10.1109/ulis.2014.6813901

Cited by 1 publication

(3 citation statements)

References 14 publications

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“…If this were not the case, the solution (V,n,p) could not be written in this form and transport models more complicated than the drift-diffusion-Poisson system would have to be used. The small-frequency assumption is the first part of Assumptions 3.1, and it is satisfied in the experiments performed so far (e.g., [14,20,21]).…”

Section: Main Results: the Ac Model Equationsmentioning

confidence: 93%

“…A parallel numerical method was developed in [3]. These mathematical results have then been used to provide quantitative understanding and to optimize sensor design [4,5].More recently, such nanowire field-effect sensors have been fabricated for use in the AC regime and characterized [14,[18][19][20][21]. In the experiments, the electric potentials around the DC equilibrium are small and the frequencies are low enough to ensure that the free charge carriers in the liquid are equilibrated, avoiding spurious signals.…”

mentioning

confidence: 99%

“…More recently, such nanowire field-effect sensors have been fabricated for use in the AC regime and characterized [14,[18][19][20][21]. In the experiments, the electric potentials around the DC equilibrium are small and the frequencies are low enough to ensure that the free charge carriers in the liquid are equilibrated, avoiding spurious signals.…”

mentioning

confidence: 99%

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Analysis of the drift-diffusion-Poisson–Boltzmann system for nanowire and nanopore sensors in the alternating-current regime

Heitzinger¹,

Taghizadeh²

2017

Communications in Mathematical Sciences

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The basic analytical properties of the drift-diffusion-Poisson-Boltzmann system in the alternating-current (AC) regime are shown. The analysis of the AC case differs from the direct-current (DC) case and is based on extending the transport model to the frequency domain and writing the variables as periodic functions of the frequency in a small-signal approximation. We first present the DC and AC model equations to describe the three types of material in nanowire field-effect sensors: The drift-diffusion-Poisson system holds in the semiconductor, the Poisson-Boltzmann equation holds in the electrolyte, and the Poisson equation provides self-consistency. Then the AC model equations are derived. Finally, existence and local uniqueness of the solution of the AC model equations are shown. Real-world applications include nanowire field-effect bio-and gas sensors operating in the AC regime, which were only demonstrated experimentally recently. Furthermore, nanopore sensors are governed by the system of model equations and the analysis as well. 2304 DRIFT-DIFFUSION-POISSON-BOLTZMANN SYSTEM Ω Si Nanowire drift-diffusion-Poisson Ω ox Silicon Dioxide Poisson Ω liq Aqueous Solution Poisson-Boltzmann Γ Boundary Layer Fig. 1.1. Schematic diagram of a cross section of a nanowire field-effect sensor.to the interface conditions used below. In [10], an effective equation for the covariance was derived after homogenization of a random charge distribution at a sensor surface. In [2], existence and uniqueness for the drift-diffusion-Poisson system with interface conditions were shown for the DC regime. A parallel numerical method was developed in [3]. These mathematical results have then been used to provide quantitative understanding and to optimize sensor design [4,5].More recently, such nanowire field-effect sensors have been fabricated for use in the AC regime and characterized [14,[18][19][20][21]. In the experiments, the electric potentials around the DC equilibrium are small and the frequencies are low enough to ensure that the free charge carriers in the liquid are equilibrated, avoiding spurious signals. Nanopore sensors are also described by the same transport equations. Here the particles that move in a self-consistent manner are anions, cations, and target molecules. The principle of a nanopore sensor is similar to the Coulter counter. A schematic diagram is shown in Figure 1.2.In this work, we derive the basic model equations for the AC small-signal regime for affinity-based field-effect sensors from the drift-diffusion-Poisson system. Whenever the frequency ω of the applied current is sufficiently small, the solution of the system of model equations can be written in terms of the real part of exp(iωt). This makes it possible to derive the AC model equations, which are the drift-diffusion-Poisson system governing charge transport coupled to the Poisson-Boltzmann equation for the liquid. The unknowns are the electric potential and the concentrations of the positive and negative charge carriers. After the derivation of the...

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Section: Main Results: the Ac Model Equationsmentioning

confidence: 93%