INSTRUMENTATION AND EXPERIMENTATION - Nanoindentation with Biological Applications - page 55

length, width, and thickness are varied to achieve a range of spring
constants ( k ) on the order of 50 N/m < k < 0.001 N/m. The macroscopic
shape of these cantilevers is typically rectangular (diving board) or
triangular (V-shaped); the latter profile is typical of low-stiffness
cantilevers and reduces cantilever torsion during scanning in contact
mode. The actual probe that contacts the biomaterial surface is located at
the distal end of the cantilever, and typically extends 1 μm normal to the
cantilever.
Just as in the case of instrumented indenters, this force transducer
must be calibrated prior to use. As these force transducers are
microscale, thin, mass-produced devices, there is considerable variation
in residual stress and even feature sizes among a wafer of fabricated
cantilevers. Thus, the nominal stiffness of an individual cantilever can
vary to factors of 2, 5 and even 10 from the nominal spring constant
classifications of the vendor. Calibration of the cantilever k prior to
indentation experiments is critical to conversion of the cantilever
deflection ), and can be conducted in two steps. First,

one must establish the sensitivity of the cantilever, in terms of
photodiode output voltage per unit cantilever deflection. This is termed
the Optical Lever Sensitivity (OLS) in units of [V/m], and is measured
simply by displacing the cantilever toward a rigid and hard surface ( e.g .,
glass). When contact occurs, the cantilever free-end will deflect 1 nm for
every 1 nm of the calibrated piezoactuator, so the cantilever deflection in
photodiode [V] is easily converted to [m] via the slope of the cantilever
deflection

δ to force ( P = k δ

vs. cantilever base displacement D relation. For the relative
laser and photodiode positions typical of commercial AFMs, changes in
cantilever deflection of 0.1 Å are readily measurable, and precision is
limited by thermal fluctuations. Second, one must establish the stiffness
of the cantilever by displacing it a (now calibrated) distance under a
known force. One facile approach is to measure the deflection of the
cantilever as it oscillates in air, acquiring the power spectral density
function or fast Fourier transform of these oscillation frequencies and
amplitudes. By fitting a simple harmonic oscillator model to the
resonance peak of this spectrum, one can quickly and reliably establish
the force transducer calibration constant k . Note that although k is a
property of the cantilever and it has been shown that the force resolution

δ