Acoustic Effects of Uneven Polymeric Layers on Tunable SAW Oscillators

Abstract

Surface acoustic wave (SAW) sensors in tunable oscillator configuration, with a deposited polymeric layer, were used to investigate the layer’s impact on the oscillator’s resonant frequency. The SAW oscillators were tuned by means of variable loop amplification. Full-range amplification variation led to a resonant frequency increase of ~1.7 MHz due to the layer’s nonlinear reaction. The layer’s morphology and location resulted in a specific resonant frequency–amplitude dependence. Five types of layers were used to test the causal linkage between the layers’ morphological parameters or positioning and the SAW oscillator’s resonant frequency. The frequency variation trend is almost linear, with a complex minute variation. Small amplitude sigmoids occur at certain attenuation values, due to layer acoustic resonances. Multiple sigmoids were linked with layer resonances of different orders. A good correlation between the layer’s thickness and resonance position was found.

1. Introduction

Surface acoustic wave (SAW) delay lines are finding new applications all across the industry, e.g., wireless sensing [1,2], temperature measurement [3], harsh environment monitoring [4,5,6,7], lab on chip [8], strain monitoring [9], etc. This interest is well justified, given that SAWs are devices with great potential owing to the complex acousto-electrical interactions governing their functionality. For many years, various techniques to bring this potential to actual use were explored [10,11,12,13]. Both frequency variation and amplitude–frequency correlation were evaluated. Furthermore, with a closed-loop oscillator being the most common configuration in which they are deployed, SAW sensors in this configuration inherit all oscillator-specific complexities. It is this specific configuration that enables one of the most interesting applications, which is sensor-based analytics. Additionally, given the extended areas of application outlined above, a technique for extracting complex information from a SAW oscillator would expand its applicability far beyond chemical sensing. As an oscillator at resonance is most sensitive to changes, the idea of a SAW sensor in a multi-frequency oscillator configuration is being diligently pursued by the research community. A recent development that may achieve this goal is the tunable SAW oscillator [14]. In this approach, the oscillator’s resonant frequency changes due to amplitude variation. Due to the chemoselective layer’s non-linear reaction, changing the signal’s amplitude leads to a variation in the oscillator’s resonant frequency. The resulting frequency–amplitude (F-A) characteristic is directly affected by the chemoselective layer’s non-linear acoustic response [14], making it suitable for usage in a gas detection/identification protocol, as well as complex material characterization. However, reliable data can be achieved only by taking into account all elements impacting the detection process outcome. Among these elements, the chemoselective layer’s morphology is of utmost importance. Random thickness variations across the layer’s surface that routinely plague the SAW sensors are immediately revealed by F-A characteristics. This renders a detection-identification protocol inoperable, since establishing a baseline is not possible. To circumvent this problem, it is necessary to identify the frequency–amplitude dependence features that are caused by the layer’s unwanted morphological characteristics.

At this point, we can mention that, besides enabling analytical capabilities, given their dependence on temperature [15,16], an added benefit of such a technique would be eliminating environmental influences, such as temperature variations. Furthermore, it can be applied to other acoustic-based devices with operating modes based on shear oscillation. Quartz crystal micro-balance (QCM) was successfully tested in real-time DNA detection [17] and humidity detection [18]. For applications in molecular biology, the functionality of such a device could be improved by setting up a multi-layer structure with different biochemical functionality in each component sub-layer. Using amplitude variation, the loading degree of each sub-layer could be measured. While such a setup is compatible with an SAW device, a QCM is preferable due to its ability to operate in a liquid environment. Another attractive option is film bulk acoustic resonators (FBARs). This is well justified by their ability to operate at very high frequencies (up to 20 GHz), as well as the notable recent progress in their manufacture [19] and design optimization [20].

This study is intended as a step toward develo** an acoustic wave sensor with analytical capabilities, by investigating the effects of layer morphology on F-A dependence.

In our previous research, a large area layer with an average thickness of 0.5 μm was used. While the proposed model in [14] was successfully used to fit the experimental data, it failed to work for smaller area layers of the same material presented in this paper. The aim of this study is to lay the groundwork for the development of this model by outlining the interactions that characterize a layer of non-uniform thickness. In doing so, we will establish in as much detail as possible the effects of the layer’s thickness variation on F-A characteristics. We presumed that while layer thickness and thickness variation amplitude are determinants in the interaction’s outcome, the location with regard to input/output interdigital transducers (IDTs) also plays an important role. Thus, a two-part experiment was envisioned, firstly, to test the location impact by placing identical layers at different locations on the waves’ paths, and secondly, to test the layers of different morphologies. The necessity to isolate the location’s impact required the use of small-diameter layers. Additionally, a small diameter facilitated more accurate layer surface map**. On the other hand, measurable acoustic effects are the result of thick layers; thus, we opted for a small area and thick layers of polyethyleneimine (PEI). It is expected that the magnitude of unevenness effects is proportional to thickness gradients, so a high gradient of thickness variation due to the small radius of layers is an added benefit.

2. Materials and Methods

Five types of PEI layers were used for investigating the layer morphology and position impact on a tunable SAW closed loop oscillator. In the following description, the layer’s type will be referred to by a capital letter from A to E.

Typically, the morphology of a PEI layer is characterized by thickness variation across its surface. This is both due to random processes during deposition, and, in case of viscous polymers, due to post-deposition fragmentation effects (the so-called “shark skin” effect). To avoid the formation of a layer with complex random relief during deposition was another reason why we opted for small-area layers. Additionally, a small area confers morphological stability, preventing the post-deposition formation of random relief.

To acquire F-A data, we used a setup similar to that presented in [14]. Briefly, the SAW oscillator loop amplification was reduced using a PC-controlled potentiometer. The potentiometer was actuated by a high-precision rotary stage and, for each attenuation value, the corresponding frequency was measured by a CNT-90 frequency counter. A computer program was developed using LabView 2013 IDE (National Instruments, Austin, TX, USA) for measurement process automation and data acquisition, integrating the functionality of both the rotary stage controller and frequency counter. This way, we acquired A-F data at a rigorously identical signal attenuation for each measurement. To identify the relevant morphological parameters of the layers, their thicknesses were measured with an **-100 non-contact interferential profilometer made by Ambios Technology Inc. (Santa Cruz, CA, USA). To establish the positioning impact on F-A dependence, it was first necessary to deposit layers with identical F-A characteristics. For this purpose, a FinnTip 10 (Thermo Fisher Scientific Waltham, MA, USA) pipette tip was dipped into PEI solution, allowing a small quantity of liquid to be retained by capillary forces. The retained solution was transferred onto the SAW device by slightly touching the lower tip opening to the piezo-active area. Previous to the deposition process, an extremely thin (<10 kHz) hydrophobic layer was applied on the piezo-active surface. This prevented the uncontrolled expansion of the PEI solution droplet on the surface, resulting in the formation of a reproducible layer after solvent evaporation. To verify the reproducibility of the coating, the deposition technique was tested multiple times. As a reproducibility criterion, the identity of F-A characteristics corresponding to deposited layers was considered. Once the deposition technique for the reproducible layer was established, it was used to deposit one type A layer at distances from the input IDT of 1, 2.5, 5, and 7.5 mm. The type A layers were deposited by the described technique using 5% by weight PEI ethanol solution.

To determine the layer’s morphology impact on F-A characteristics, one layer of each type was deposited on the piezo-active area’s center, followed by F-A characteristics and layer thickness measurements. The type B layer was deposited by the same technique as type A, but using 1% by weight PEI solution. Type C, D, and E layers were deposited following the same procedure except for the final step, which consisted of drop-casting 0.4, 0.6, and 0.8 μL 1% by weight PEI solution.

The shape of the A, C, D, and E layers was circular, with radii of 2.1, 1.5, 1.6, 2, 2.8 mm. Type B developed a contiguous irregular shape circumscribed inside a circular area of 1.5 mm diameter.

The analysis of the F-A characteristics was based on the model developed in [21]. We adopted the same method as in [21]: x and z in-plane with the piezo-active area, with z along the acoustic wave propagation direction. A layer deposited on the piezo-active area of a SAW device undergoes two shear x- and z-polarized oscillations and one y-polarized compression oscillation. These waves are reflected back to the layer–substrate interface, where they interfere with surface waves on the substrate. The outcome of the interference is given by the phase difference Φj between the two oscillations. The oscillation amplitude and velocity of a dissipating layer are given by a complex bulk K modulus and shear G modulus. The wave velocity on a coated SAW sensor is determined by the layer’s mass load and the layer–substrate oscillation interference, and is given by [21]:

$$\frac{\mathsf{\Delta }\mathrm{v}}{\mathrm{v}}=-\mathfrak{I}\left({\sum }_{\mathrm{j}=\mathrm{x},\mathrm{y},\mathrm{z}}\frac{{\mathrm{c}}_{\mathrm{j}}{\mathsf{\beta }}_{\mathrm{j}}{\mathrm{M}}_{\mathrm{j}}}{\mathsf{\omega }}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(\mathrm{i}{\mathsf{\beta }}_{\mathrm{j}}\mathrm{h}\right)\right)$$

(1)

where

$${\mathsf{\beta }}_{\mathrm{j}}=\mathsf{\omega }{\left[\frac{\mathsf{\rho }-\frac{{\mathrm{E}}_{\mathrm{j}}}{{{\mathrm{v}}_0}^2}}{{\mathrm{M}}_{\mathrm{j}}}\right]}^{\frac{1}{2}}$$

(2)

and

$${\mathrm{E}}_{\mathrm{x}}=\mathrm{G},{\mathrm{E}}_{\mathrm{y}}\approx 0,{\mathrm{E}}_{\mathrm{z}}=\frac{4\mathrm{G}\left(3\mathrm{K}+\mathrm{G}\right)}{3\mathrm{K}+4\mathrm{G}}$$

(3)

In Equations (1)–(3), Im represents the imaginary part of the expression; index j gives the oscillation’s polarization; ‘i’ is the imaginary unit; c_j is the SAW–film coupling parameter [21]; ‘tanh’ is the hyperbolic tangent function, where ‘ω’ is the wave pulsation 2 × π × f with ‘f’ the oscillation frequency of the SAW; ‘h’ is the layer thickness; v₀ is surface acoustic wave velocity of un-coated SAW; ρ is the layer density; and M_x = M_z = G, M_y = K. In this model, phase difference Φj = R_e(iβ_jh), where R_e represents the real part of the expression in parenthesis.

While the equality Δf/f₀ = Δv/v₀ holds only if the layer covers the entire area between the interdigital transducers [21], which is not our case, the resonant frequency variation tracks that of the SAW propagation velocity modeled by Equation (1), thus allowing qualitative evaluation.

3. Results and Discussion

For statistically meaningful layer characterization, multiple interferential images were taken, and thickness-related parameters were subsequently obtained by computer image processing. Pixel statistics were made, in which the pixel color values were replaced by their thickness values according to the image color scale.

As in the example in Figure 1, the layer’s profile is that of a convex meniscus, with in-layer dips and peaks of various amplitude.

Due to the profilometer’s viewing area being limited to 504 µm × 504 µm area, only 504 µm from the layer’s margin could be probed. However, interference profiling provided crucial information for identifying the origin of the observed F-A features.

Histograms for layers thickness and thickness gradients are presented in Figure 2.

In the above-thickness histograms, an abrupt ending toward small values, common to all layers, is visible. This is not surprising, given that the polymer solution droplet assumed a lenticular shape before solvent evaporation. As a result, the layer ends abruptly at the droplet’s limit. The thickness lower limit seems to be the result of both solution concentration and droplet volume. In the case of the type B layer, the thickness lower limit is situated at 0.3 µm, with a maximum around 0.65 µm. Apart from the type B layer, all other layers present thicknesses no less than 1 µm. Owing to its different deposition techniques, the type A layer is characterized by a thickness distribution with three local maxima, at 2, 3, and 6 µm. The type C and D layers are virtually identical in thickness distribution, both starting at 1 µm, with the most consistent values up to 3.5 µm, and a smaller fraction that gradually diminishes up to ~5 µm. The type E layer presents a close resemblance with type C and D, except a ~0.5 μm shift toward higher thicknesses. Additionally, it has two maxima centered around 2.7 μm and 3.5 µm.

In the right column of Figure 2, histograms for layer thickness gradients are shown. Consistent thickness differences are present in all five types of layers. The thickness gradient distribution clearly splits the layers into two distinct groups: A and B with thickness gradient histogram maxima at less than 0.03 µm; and C, D, and E with thickness gradient distribution maxima at more than 0.03 µm. Additionally, types A and B present insignificant thickness variations above 0.15 µm, while types C, D, and E exhibit important areas with gradients higher than 0.2 µm. While most of it is due to the increasing thickness toward the layer’s center, it is clear that in-layer thickness irregularities also account for a significant proportion of gradients, as can be seen in Figure 1.

Figure 3 depicts an F-A characteristic corresponding to a B-type layer placed on the piezo active area center. The oscillator’s resonant frequency shows a steady increase with signal amplitude attenuation, with a shallow sigmoid occurrence. While common to all layer types, sigmoid amplitude and position varies. The sigmoid positioning is the result of layer resonances, which are dependent on thickness.

Multiple mini plateaus occur, and they could indicate spontaneous signal amplitude modulation. This is because zones of increased frequency stability were connected with carrier envelope resonances of a delay line oscillator [22].

The overall profile of the F-A is that of an increase in resonant frequency with attenuation, with full-range attenuation variation leading to an increase in the resonant frequency of ~1.7 MHz. This can be explained by the non-Newtonian behavior of the polymers, consisting of decreasing viscosity η and shear loss modulus G″ with shear rate [23,24]:

$$\mathsf{\eta }=\frac{{\mathrm{G}}^{″}}{\mathsf{\omega }}\text{∼}\frac{1}{\dot{\mathsf{\gamma }}\left(\mathrm{t}\right)}$$

(4)

where $\dot{\mathsf{\gamma }}$(t) is the shear rate.

As the signal’s amplitude decreases due to attenuation, the shear rate $\dot{\mathsf{\gamma }}$(t) decreases, also leading to increased viscosity and shear loss module G″. Considering the dependence of β_z on G″, this leads to the observed increase in resonant frequency.

Additionally, the layer’s acoustic reaction contributes to sha** the F-A characteristic. As the layer’s acoustic impedance changes due to the amplitude scan, so does the phase shift Φ_z of the reflected oscillations. While Φ_z = R_e(β_zh) [21], the loss modulus variation will cause a change in phase difference Φ_z due to relation (3), which mingles the pure complex loss modulus G″ in the real part of β_z. Thus, loss modulus variation nevertheless exerts a measurable influence on the Φ_z, consequently changing F-A characteristics.

Based on the above, the resonant frequency variation should be attributed to amplitude-driven changes in PEI shear loss module. This can be direct, due to β_z dependence on G″, or indirect, via non-gravimetrical effects, namely interference between the layer’s shear oscillation and acoustic waves at the layer–SAW interface. The existence of acoustical effects is further confirmed by the presence of the sigmoid shapes at 110, 165, and 185 attenuations. Additionally, the orientation of the sigmoid is consistent with an increase in phase difference [21] implied by relations (3) and (4).

Type A layer was used to determine the correlation between the layer’s position and F-A characteristic features. Isolating the positioning influence from other factors imposed the use of layers of identical F-A characteristics. As mentioned before, the deposition process reproducibility was tested by comparing the F-A characteristics of four type A layers. Figure 4 depicts the F-A characteristic of four type A layers placed in the center of the piezo-active area. Multiple common elements can be noted, the most significant being the sigmoidal region in the 100–120 a.u. attenuation range. The sigmoid consists of two regions of similar inclination separated by a mini plateau. Mini plateaus are present at both sigmoid ends. Many other plateaus occur with F-A characteristics, and most of them are similar in size and, aside from a small vertical shift, position.

The F-A characteristics in Figure 4 can be divided into three regions. First, the 0–65 a.u. attenuation is characterized by the A1 layer departure from the profile of the other three layers. From 65 to 160 a.u. attenuation, the F-A is characterized by a high degree of coincidence, both in features and position. In the last portion, the coincidence departure is most notable, both in features and position. This could indicate higher system instability at lower amplification, which exacerbated the differences in layer morphology. In the 0–100 a.u. attenuation range, the A2, A3, and A4 layers are virtually indistinguishable, their superposition being almost perfect. The A1 layer presents a vertical shift of ~30 kHz in the 0–25 and 45–65 a.u. attenuation ranges. Overall, Figure 1 proves that the deposition technique produces layers with similar F-A characteristics, supporting the validity of positioning impact investigation based on type A layers.

Figure 5 depicts the F-A characteristics corresponding to the four distances from input IDT at which a type A layer was placed. It is worth noting that, despite clear differences, the F-A characteristics still retain significant common elements, confirming the layers’ quasi-identical morphology.

While consistent efforts to preserve the experiment’s integrity were made, there are some differences arising from occurrences out of our control, as is visible in both Figure 4 and Figure 5. The presence of these random features will render our evaluation more difficult. To avoid drawing unfounded conclusions, we will limit ourselves to considering only major elements and parameters such as frequency variation rate, sigmoids, etc.

Aside from a relatively small vertical shift, the first three characteristics are parallel. Surprisingly, and in opposition to the resonant frequency increasing with attenuation, as the signal amplitude presumably increases with proximity to the IDT input, the characteristics are shifted vertically toward higher frequencies. At this point, the most certain information we possess is the increase in frequency at lower signal amplitudes. This is supported by the values in

Table 1. Relation between layer position and total frequency variation.

Distance from input IDT (mm)	1	2.5	5	7.5
Frequency variation (Hz)	1,705,990.5	1,743,723.5	1,750,369.5	1,590,019.1

, which indicate a lower frequency variation range for the 1, 2.5, and 7.5 mm layers. Thus, we are compelled to assume that this vertical shift is also caused by a decrease in the signal’s amplitude, which implies the existence of a wave energy loss mechanism. In order to explain this behavior, the energy loss must be highly dependent on the layer’s location. At this stage, it seems that the layer exerts a lens-like effect on SAW’s wavefront, increasing its divergence. Also at this stage, it seems that the layer convex contour exerts a lens-like effect on SAW’s wavefront, strongly increasing its convergence. After passing the focus point, the wavefront expands, diminishing its energy in a distance-dependent manner, thus lowering the signal’s amplitude at receiving IDT. In turn, this causes a general decrease in signal amplitude all across the system, including a decrease in the oscillation amplitude of layers. This hypothesis can also explain the anomalous 7.5 mm F-A characteristics. The anomaly consists of the vertical shift toward lower frequencies (equivalent to layer oscillation with higher amplitudes) while being placed further from the emitting IDT (lower SAW amplitude due to attenuation). That means that the amplitude attenuation with distance is outweighed by the reduction in divergence-induced energy loss due to the shorter distance to the reception IDT, with the net result being an increase in SAW amplitude. Nevertheless, this does not explain the lower frequency variation range for the 7.5 mm layer and the diminished sigmoid amplitude.

In conclusion, displacement from the central position results in both a frequency shift and decrease in the frequency variation range due to reduced oscillation amplitude. It can be seen in Table 1 that the trend is well-defined, and it is the result of two distance-dependent wave energy loss mechanisms: layer-induced wavefront divergence, and wave attenuation with distance. Maximum frequency variation corresponds to the center position, 1.75 MHz, which corresponds to a minimum in wave energy loss.

F-A for all five layers can be seen in Figure 6. There are two elements that differentiate the F-A dependence: frequency increase rates and layer resonance position.

A good correlation between layer thicknesses and the position of layer resonances can be observed in Figure 6. In the cases of type C, D, and E layers, the layer resonance is situated virtually at the same frequency, which is consistent with their measured thickness.

Comparing the resonances of type B and any of the C, D, or E layers, the frequency spacing is not large enough to accommodate two different harmonics. Thus, it is probable that the lower resonance (in layers C, D, and E) is a second-order resonance. Given that the phase difference between reflected and substrate acoustic waves marks is n × π/2 (n = 1, 3, 5, ...) at layer resonance for a second-order layer resonance, the corresponding thickness ratio between the two layers should be 3. It should be noted that the sigmoids for the type C, D, and E layers are well defined and virtually identical. This suggests that the associated layer thickness causing this resonance is situated in an overlap** region of the type C, D, and E thickness histograms. The most probable thickness value is ~2.4 μm, leading to a very plausible (based on the thickness histogram in Figure 2 for the type B layer) thickness resonance value of 0.8 μm for sigmoids on type B F-A characteristic at 59.9 and 60.2 MHz. The 2.4 μm value for layer thickness is compatible with type A layer thickness distribution, and its departure from the thickness distribution maximum at 2 μm could account for the not-so-well-defined sigmoid shape.

Considering that the type B layer is the thinnest layer, the sigmoid around 59.3 MHz can be regarded as anomalous. This could be explained by the fact that the inner areas of the type B layer might be thick enough to accommodate the corresponding higher-order resonance. This explanation is thus far consistent with the our experimental data interpretation.

Kee** in mind that the thickness distributions, as shown in Figure 2, are kept from probing the layers outer areas, and thickness distribution could be shifted toward higher values, this fits very well with type C, D, and E morphologies.

A striking quasi-total F-A similitude can be noted for the type C, D, and E layers, in spite of their different area and masses. While this correlates well with their similar morphology, as revealed by thickness-related parameters in Figure 2, it raises questions about the impact of size and mass on F-A characteristics. In this case, the two parameters have antagonistic effects on signal amplitude. On the one hand, a larger quantity of material will dissipate proportionally more energy. On the other hand, a higher radius layer will focus the wavefront less sharply, followed by a less pronounced divergence. Thus, the size impact for type C, D, and E layers may have been diminished due to the two effects canceling each other. As a result, the oscillation amplitude is almost identical for the C, D, and E layers, which is manifested in their F-A quasi-identical shape.

Aside from layer resonance position, the F-A differ in frequency variation rate, which is visibly smaller for C, D, and E-type layers. This signifies that the layers undergo overall lower amplitude oscillations, i.e., the amplitude variation range is smaller. While the amplitude attenuation caused by the added mass accounts for the different slopes, this does not explain the lower sigmoidal amplitudes for C, D, and E characteristics. Since the lower sigmoidal frequency excursion is the hallmark of higher loss parameter [21], this could signify the presence of an additional wave energy loss mechanism. Such a mechanism could be due to shear wave interference among adjacent areas of different thicknesses. Thus, the shear oscillatory energy returned by a portion of a given thickness will undergo attenuation by interference with neighboring portions of different thicknesses, proportional to the border length and phase difference between the two shear oscillations. This interpretation is very well supported by the thickness gradient histogram, as shown in Figure 2, which is highest for the C, D, and E layers.

4. Conclusions

PEI layers were deposited on SAW devices and used to determine the causal linkage between layer morphology and positioning, as well as F-A features. Identifying the morphology features responsible for F-A parameters was enabled by the deposition of PEI layers with reduced area. Thus, a causal connection between morphological features and F-A parameters was possible. As the reproduction of F-A for distinct layers of the same type was possible, this enabled the effects of the layer’s positioning on F-A characteristics to be isolated. The results strongly suggest the existence of a position-dependent energy loss mechanism, presumably due to layer-induced wavefront divergence.

F-A features specific to each type of layer were explained by resonances of layer areas of different thicknesses and by the presence of energy loss mechanisms via layer-induced wave divergence, and inter-layer shear wave interference, due to differences in layer thickness.

Notably, while a liability for gas detection, this method dependence on layer characteristics could constitute the basis for an advanced material testing method. Additionally, combined with the wireless capabilities of SAW devices, this could provide an accessible early warning method for an advanced process monitoring method.

The future development of this method is conditioned by a process to circumvent its dependence on layer morphology. Develo** better layer deposition techniques with higher morphology reproducibility might not be always possible, nor economically viable. Thus, the development of computational methods could prove instrumental in implementing a detection/identification protocol based on this method. In this respect, the most important result is the dependence on the attenuation of the terms outside the hyperbolic tangent in Equation 2, which is nonexistent in the model used in [14], this is a very important consideration for future model development.