Proposal of Exponentially Sensitive Stress Based Sensor Using Flexure-fet

In this paper, we demonstrate that a Flexure-FET [1] (flexure sensitive field effect transistor) can dramatically enhance the sensitivity of stress based chem-bio sensors. A Flexure-FET translates any change in the stress of the suspended gate into corresponding change in the drain current of the integrated transistor, thereby offering direct electrical readout of the sensor signal. Moreover, when the gate is biased close to pull-in and the transistor in sub-threshold regime, the sensor is exponentially sensitive to stress change. In contrast, all classical nanomechanical sensors are limited to linear sensitivity and need complex optical instrumentation for sensing. The simplicity and exponential sensitivity of Flexure-FET may broaden applications of stress-based chem-bio sensors. Motivation/Background: Stress based nanomechanical sensors involving either a cantilever (Fig. 1(a)) or a fixed-fixed beam (Fig. 1(b)) have shown great promise for bio-molecules sensing [2], vapor/gas sensing [3][4], pH sensing[5], etc. In these sensors, interaction of stimuli (i.e., surface adsorption of bio or gas molecules) with the sensing layer introduces a stress in the cantilever and fixed-fixed beam (Figs. 1(a)-(b)). This stress bends the cantilever (tip deflection y) and changes the resonance frequency (f). The strength of the stimuli is determined by measuring the changes in y or f. Unfortunately, the sensor response is at best linear. For example, static mode cantilever sensors follow Stoney’s equation y ∝ Δσ [6], Δσ being the change in surface stress in N/m. Similarly, a cantilever based pH sensors respond only linearly to pH change (Fig. 1(c)) [5]. On the other hand, one finds that f ∝ Δσ (Δσ = σ − σc with σ being the stress in the beam and σc being the critical buckling stress) for a fixed-fixed beam both below [7] and above buckling transition [8]. The sub-linear response suggested by theory is consistent with the experimental data [3] of buckled-beam vapor sensors (Fig. 1(d)). This linear/sublinear response of nanomechanical sensors therefore makes detection of small amount of stimuli very difficult. Moreover, they typically need complex optical instrumentation for measurement of y or f, making their integration with hand-held devices difficult. Therefore, a simpler readout scheme and super-linear response is needed to broaden applications of stress based sensors. Proposal of Flexure-FET for Stress based Sensing: The classical limits of stress based sensors can be circumvented and super-linear response can be achieved by a new class of criticalpoint sensors known as Flexure-FET (Fig. 1(e)) [1]. A FlexureFET consists of a movable gate suspended above the channel of a field effect transistor (Fig. 1(e)), which is structurally similar to a NEMFET[9] or resonant gate transistor[10]. Initially, a carefully chosen gate voltage biases the gate close to the pull-in Fig. 1: Stress based nanomechanical sensors and their response. Schematic of (a) static mode cantilever sensor and (b) resonant mode fixed-fixed beam sensor. (c) Response of cantilever based pH sensor with linear change in the deflection (y) due to pH change [5]. Symbols denote the experimental data and dotted line highlights the linear response. (d) Response of buckled-beam based vapor sensor [3] with sub-linear change in the resonance frequency (f ∝ Δσ) due to change in the stress (Δσ). Symbols denote the experimental data and solid line corresponds to f ∝ Δσ. (g) Schematic of Flexure-FET. (h) Exponential sensitivity (S) of Flexure-FET towards stress change (Δσ). IDS1 is the drain current at zero stress and IDS2 is the drain current after stress change. point (but bias lower than the pull-in voltage). As an example of vapor sensor, reaction of water vapor with hygroscopic polymer coated on the gate introduces a compressive stress in the gate due to swelling of the polymer. As a result, gate further bends towards the dielectric increasing the drain current of the transistor. Thus, a simple electrical measurement of the change Proceedings of 2013 Nanomechanical Sensing Workshop Ankit Jain and Muhammad Ashraful Alam Stanford University, Stanford, CA in drain current directly correlates to the signal induced by water vapor. Indeed, we predict that optimally designed and appropriately biased Flexure-FET can achieve orders of magnitude change in the drain current for small change of stress (Fig. 1(f)) and therefore can achieve super-linear sensitivity beyond the reach of classical nanomechanical sensors. Response of Flexure-FET to Stress Change: The response of Flexure-FET is governed by the Euler-Bernoulli equation that is given by-