Cantilever-like micromechanical sensors - Artek

Rep. Prog. Phys. 74 (2011) 036101 A Boisen et al
Figure 1. Schematic of three modes of operation of a cantilever-based sensor. The cantilever is seen from the side. Molecules on one side of
the cantilever cause a change in surface stress which causes the cantilever to deflect (a). Bulk stress changes in the cantilever material can be
used to detect temperature changes caused by a chemical reaction (b). Mass changes are registered by measuring changes in the resonant
frequency of the cantilever (c).
has been interacting with the surface. If an added molecular
layer, for example, contracts compared with the underlying
material, the cantilever will bend towards the molecular
layer. This measuring principle has been used to detect, for
example, prostate-specific antigen (PSA) [22] and to study
antibiotics binding to drug resistant super bugs [23]. A
related technique to study surface stress changes is called
the bending plate technique and was first observed and
applied on wafers of III–V compounds in the 1960s [24].
By introducing the cantilever technique this measurement
principle was significantly improved. Using the bending plate
technique surface stress changes of 1 N m −1 were normally
reported whereas the first measurements of surface stress
changes with micrometre-sized cantilevers were of the order
of 10 −3 Nm −1 . Now, surface stress changes of 10 −6 Nm −1
are routinely observed.
In a second mode of operation the cantilever is used
as a tool to evaluate stress changes in the bulk of the
cantilever material, for example, caused by humidity or
temperature. Stress changes are explored in the realization
of extremely sensitive thermometers. Cantilevers consisting
of two materials with different thermal expansion coefficients
will bend as a function of temperature due to the bimorph effect.
This effect can be used to measure temperature changes down
to 10 −5 K and can, for example, be used to investigate phase
changes in minute amounts of sample [25] (figure 1(b)).
In a third mode of operation the fact that the resonant
frequency of the cantilever depends on the mass of the
cantilever and the resonant frequency drops as the mass
increases is used. Thus, it is possible to make indirect mass
change estimations in the atto- to zepto-gram range [26] by
following the resonant frequency change of the cantilever
(figure 1(c)).
The change in static cantilever deflection or change in
vibrational amplitude is most commonly detected by the
so-called optical leverage technique which is well known from
AFM. The principle will be described in section 4 and basically
a laser is reflected off the backside of the cantilever and onto a
position sensitive diode.
In nearly all experiments performed today a reference
measurement is included. This means that a second cantilever
with identical mechanical performance but without the specific
surface funtionalization is monitored simultaneously. Often
only the differential signals are presented since the use of
reference measurements significantly reduces drift and noise
from, for example, temperature and humidity changes.
3
2.1. Detection of mass changes
In mass sensing, cantilever and bridge shaped geometries
are both commonly used and are in general referred to
as beam-based mass sensors. Both geometries will be
introduced in the following. A cantilever is a singly clamped
beam whereas a bridge is a doubly clamped beam. One
of the ultimate goals of a beam-based mass sensor is the
ability to measure single small molecules which requires
a sensitivity in the sub-zepto-gram (10 −21 g) regime. This
would, for example, make it possible to use a cantilever as a
mass-spectrometer with sensitivity better than commercially
available systems of today. The sensitivity or minimum
detectable mass depends on the ratio between the mass
and the resonant frequency of the beam. Generally, the
resonant frequency increases and the mass decreases when the
dimensions are decreased. Thus, a straightforward approach
to enhance the sensitivity is to decrease the dimensions of the
beam. The feature size of beam-based mass sensors is currently
approaching the nanometre scale. Recently, systems capable
of detecting masses in the atto- and zepto-gram (10 −18 –
10 −21 g) range have been reported [27, 28], and the claim
is that yocto-gram sensitivity is within reach [29]. This is
far better than the reported mass sensitivities of other mass
sensing techniques, such as the quartz crystal microbalance
technique where typical sensitivities are in the nano/picogram
range [30] for a single device. Sensors with a larger
surface area generally have a relatively large distributed mass
resolution (mass resolution per area). For example, socalled
bulk disc resonators with micrometre dimensions now
have similar distributed mass resolution as nanometre-sized
cantilever resonators [31]. As a consequence, nanometresized
resonators are useful when striving to achieve ultrahigh
point mass resolution. In terms of distributed mass
resolution the benefit of miniaturization is less pronounced.
Here, for example, micrometre [32] and nanometre-sized [33]
cantilevers have been reported to have similar distributed mass
sensitivities.
To explain the working principle of a beam-based mass
sensor we will in the following introduce the equations
describing the motion of a beam. Also, the importance of
damping and Q-factor will be introduced.
2.1.1. The eigenfrequency of bending beams. For a thin beam
as depicted in figure 2, rotational inertia and shear deformation
can be neglected. Assuming a linear elastic material and small