4.2 LW resonator with ZnO nanorods
4.2.3 Effect on mass sensitivity and coupling coefficient
The exact height at which transition from inertial to elastic loading takes place can be obtained by plotting the variation inK2 with hZnO as shown in Fig. 4.5a. As hZnO increases, mode transition occurs when K2 for mode-1 becomes greater than K2 for mode-0, and again
4.2. LW resonator with ZnO nanorods
0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 -1.0
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Elastic loading
Normalizedfrequencyshift(f)
( / s
)
1 m -2
9 m -2
25 m -2
Inertial loading
(a)
200 400 600 800 1000 1200 1400 1600 1800 290
295 300 305 310 315 320 325 330 335 340 345 350
Resonancefrequency(MHz)
h ZnO
(nm)
1 m -2
9 m -2
25 m -2
(b)
Figure 4.4: (a) The normalized values of frequency shift (∆f) as a function of (ω/ωs) obtained using (4.2) for SNRD of 1, 9 and 25 µm−2. (b) Graph showing variation in resonance frequency with ZnO nanorod height for SNRD of 1, 9 and 25µm−2 obtained through FE simulation.
when K2 for mode-2 becomes greater than K2 for mode-1. It is observed that, when SNRD is high (25 µm−2), the K2 values rise and fall sharply near the resonant height, attaining a maximum value of 4.4% at ZnO nanorod height of 475 nm. When SNRD is low (1 µm−2), theK2 value remains stable at about 2.8% over a wide range of nanorod heights. At coupled resonance, the electromechanical coupling coefficient of the device becomes low, attaining a value of 1.74, 1.31, and 1.05% at SNRD of 1, 9 and, 25µm−2 respectively. This lowering ofK2 is an indication of increase in the losses in the device [179], [180]. Typical vibrational mode shapes for SNRD = 9µm−2 showing mode-0, mode-1, and mode-2 athZnO = 400, 1000, and 1600 nm, respectively are presented in Fig. 4.5b–4.5d.
SNRD
Non-coupled resonance Coupled resonance
mode-0 mode-1
Sfmax Kmax2 σT hZnO Sfmax Kmax2 σT hZnO Sfmax Kmax2 σT (m2/kg) (%) (MPa) (nm) (m2/kg) (%) (MPa) (nm) (m2/kg) (%) (MPa)
1 58 2.91 10.5 475 770 1.74 235 1240 710 1.46 215
2.25 71 2.73 12.6 470 835 1.57 300 1225 765 1.43 275
4 89 2.71 19.5 470 928 1.43 348 1210 840 1.38 315
6.25 113 2.5 27.5 465 1045 1.36 435 1200 935 1.34 389
9 135 2.6 30.7 460 1155 1.31 446 1190 1030 1.27 397
12.25 175 2.42 37.6 440 1227 1.28 538 1095 1180 1.25 480
16 221 2.4 41.2 435 1275 1.18 638 1165 1135 1.2 567
20.25 269 2.2 51.4 430 1310 1.09 724 1155 1142 1.18 631
25 291 2.1 55.6 425 1338 1.05 801 1150 1294 1.17 688
Table 4.1: Maximum values of mass sensitivity Sfmax, coupling coefficient Kmax2 and area- averaged stressσT for different SNRD, in the absence of coupled resonance and in the presence of coupled resonance (mode-0 and mode-1).
The mass sensitivity of LW device is obtained by applying the equivalent surface mass density of double-stranded DNA uniformly over the sensor surface. ZnO nanorods of varying height and SNRD are made on the surface of the device. Fig. 4.5ashows the variation in mass sensitivitySf
0 1 2 3 4 5
400 600 800 1000 1200 1400 1600 1800 0
200 400 600 800 1000 1200 1400
mode-1
mode-2
1 m -2
9 m -2
25 m -2
K
2 (%)
mode-0
S f
(m
2 /kg)
h ZnO
(nm)
(a)
(b)
(c)
(d)
Figure 4.5: (a) Variation in coupling coefficient and mass sensitivity of LW resonator with ZnO nanorod height for SNRD = 1, 9, and 25 µm−2. Illustration of the transition of modes in LW resonator as the height of ZnO nanorods increases. Typical vibrational mode shapes for (b) mode-0, (c) mode-1, and (d) mode-2 athZnO = 400, 1000, and 1600 nm, respectively for SNRD
= 9 µm−2 are shown.
versus ZnO nanorod height for SNRD of 1, 9, and 25 µm−2. Considering the case when SNRD
= 1µm−2, in the absence of coupled resonance (athZnO = 800 nm) the mass sensitivity is about 58 m2kg−1 which is close to the mass sensitivity of a plain SiO2 based LW device obtained in the previous chapter. However, in the presence of coupled resonance at nanorod heights of 475 and 1240 nm, mass sensitivity increases to 770 and 710 m2kg−1 respectively. As the nanorod packing density on the surface of the device increases, the mass sensitivity at coupled resonant height also rises.
The stress profile of the area of contact between nanorods and substrate with six ZnO nanorods corresponding to SNRD = 1µm−2is plotted in Fig. 4.6aand4.6bforhZnO = 475 nm and 800 nm, respectively. The magnitude of total stress at the contact surface in the xz plane is represented in the form of color bars and normalized projections. Overall, the stress values at the edges of the contact area between nanorod and substrate, along the x direction are high in comparison to other regions. In the presence of coupled resonance at hZnO = 475 nm, the stress at the edges of the contact area goes above 26 GPa significantly greater than the stress
4.2. LW resonator with ZnO nanorods
(a) (b)
400 600 800 1000 1200 1400 1600 1800 0
25 50 75 100 125 150 175 200 225 250
T
(MPa)
h ZnO
(nm)
(c)
Figure 4.6: Stress profile of the active area of the sensor surface with six ZnO nanorods corre- sponding to SNRD = 1µm−2. The magnitude of total stress over the contact surface in thexz plane is represented in the form of color bars and normalized projections for (a) in the presence of coupled resonance (hZnO= 475 nm) and (b) in the absence of coupled resonance (hZnO= 800 nm). The figure shows large vertical stress at the edges of the contact area between nanorod and substrate and it greatly increases at the resonant heighthZnO = 475 nm. (c) Plot of magnitude of total stress averaged over the entire top surface of the sensor versus ZnO nanorod height for SNRD of 1µm−2.
of 0.6 GPa observed in the absence of coupled resonance at hZnO = 800 nm. The magnitude of total stress averaged over the entire top surface area of the sensor (σT) in the xz plane is calculated for SNRD of 1 µm−2 for varying heights of nanorods as shown in Fig. 4.6c. Away from the coupled resonance, the average stress on the surface is about 15 MPa, but near the resonant height, it reaches above 235 MPa.
The maximum values of mass sensitivitySfmax, coupling coefficientKmax2 and area-averaged stress σT for different SNRD, in the presence of coupled resonance (mode-0 and mode-1), and in the absence of coupled resonance are listed in Table4.1. It is noted that in the absence of coupled resonance,Sf increases with SNRD and attains a maximum value of 291 m2kg−1 for SNRD of 25µm−2, i.e. about six times greater than the mass sensitivity of a plain LW device.
However, this rise is mainly due to the enhanced inertial mass loading caused by the increase in surface area provided by nanorods for the analyte to attach. On the other hand, in the presence
of coupled resonance,Sf increases to 1338 m2kg−1 for SNRD = 25µm−2, that is about 25 times greater than the mass sensitivity of a plain LW device (section3.3.1, Table3.1). The significant increase in the mass sensitivity due to coupled resonance can be attributed to the increase in the contact stiffness of the composite resonator. In the presence of coupled resonance, with increasing SNRD, the mass sensitivity of the device also increases considering both mode-0 and mode-1. Although the mass sensitivity and average stress at SNRD = 25 µm−2 are high, the coupling coefficient falls to a low value of 1.05 and 1.17 for mode-0 and mode-1 respectively.
Thus, the increase in mass sensitivity comes at the cost of a decrease in coupling coefficient and increase in the losses in the device. The advantage of coupled resonance can be highlighted from the observation that even a low SNRD of 1 µm−2 can offer an increase in mass sensitivity by about fifteen times compared to a plain SiO2 based LW device. The presence of ZnO nanorods of appropriate size on LW sensor will not only provide ample surface area but will also resonate in unison with the device to cause coupled resonance leading to an extremely sensitive biosensing device.