A highly sensitive co-resonant cantilever sensor for materials research: Application to nanomaterial characterization
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INVITED PAPER A highly sensitive co-resonant cantilever sensor for materials research: Application to nanomaterial characterization Julia Körnera) Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah 84112, USA (Received 24 May 2018; accepted 1 August 2018)
Dynamic-mode cantilever sensors are used in many different applications but especially in materials research to study properties of novel (nano)materials. Decreasing sample sizes require an increase in sensitivity of the analysis tools. For cantilever-based methods that is achieved through a reduction in cantilever dimensions. However, the increase in sensitivity has to be balanced with the detectability as also for a small cantilever a reliable detection of its oscillatory state has to be ensured. A recently introduced co-resonant measurement principle for cantilever sensors addresses this challenge by coupling and eigenfrequency matching of a micro- and a nanocantilever. Here, the sensor concept is reviewed with focus on the application in materials research by the instructive example of an iron-filled carbon nanotube, giving insight into the features and benefits of the sensor concept and demonstrating the reliable derivation of magnetic sample properties. I. INTRODUCTION
Dynamic-mode cantilever sensors are employed for many different applications, ranging from the use as mass sensors in biology,1–3 and gas sensors (‘artificial nose’)4 to the study of novel materials.5–7 In materials research, mainly scanning probe methods and cantilever magnetometry are used. In the former case, the cantilever is equipped with an interaction tip and is scanned across the sample surface.8 In cantilever magnetometry, the sample is placed onto the cantilever and subject to a known interaction which in many cases is a magnetic field.9 Many different samples have been studied by cantilever magnetometry which included magnetite rocks,10 thin ferromagnetic layers,11–13 nanowires,14–17 small magnetic particles6 as well as magnetotactic bacteria.6 In contrast to the static mode where the static bending of the cantilever beam is evaluated, the dynamic mode makes use of the change of oscillatory properties of a cantilever excited to oscillations at or close to its resonance frequency. The change of the beam’s oscillatory state, i.e., amplitude, phase, resonance frequency, due to an interaction is usually detected by laser-based methods (deflectometry, interferometry). This signal can then be related to the properties of the sample under investigation.18 With decreasing sample size and increasingly weak interactions, the sensitivity of dynamic-mode cantilever sensors has to be increased. The usually used frequency shift signal Dx is related to an external interaction by:
Dx ¼ x0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffi ( Dk k þ Dk k 2k Dm meff þ Dm meff 2meff
for Dm 0 for Dk 0
; ð1Þ
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2018.295
where Dk represents an external force gradient along the oscil
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