The resonator below, operating in length-extensional mode, is used to implement a sensitive mass sensor.
For a resonant mass sensor, the sensitivity is quantified as the ratio of normalized frequency variation (in
ppm) over mass unit:
Sensitivity $(\frac{ppm}{kg}) \approx \frac{(\frac{\Delta f}{f_0})}{\Delta M}$
a) Identify the best location for placement of the functionalization material (where the mass can be
attached to the resonator), to achieve the maximum sensitivity.
b) Derive the sensitivity as a function of resonators dimension, density, and Young's modulus. Calculate
the sensitivity when the resonator is made from Si and SiO$_2$. Which material is better to enhance the
sensitivity of mass sensing?
c) Considering the sensitivity of resonator frequency to temperature variations, which material is better
for implementation of highly sensitive resonant mass sensor?
W
H
L
Material
Doped Si
SiO$_2$
E (GPa)
140
67
Density (kg/m³)
2320
2650
TCF (ppm/C)
-5
65
