Micro- and millimeter-scale resonant mass sensors have received widespread attention due to their robust and sensitive performance in a wide range of detection applications. A key performance metric for such systems is the sensitivity of the resonant frequency of a device to changes in mass, which needs to be calibrated. This calibration is complicated by the fact that the position of the added mass on a sensor can have an effect on the measured sensitivity—therefore, a spatial sensitivity mapping is needed. To date, most approaches for experimental sensitivity characterization are based upon the controlled addition of small masses, e.g., the direct attachment of microbeads via atomic force microscopy or the selective microelectrodeposition of material, both of which are time consuming and require specialized equipment. This work proposes a method of experimental spatial sensitivity measurement that uses an inkjet system and standard sensor readout methodology to map the spatially dependent sensitivity of a resonant mass sensor—a significantly easier experimental approach. The methodology is described and demonstrated on a quartz resonator. In the specific case of a Kyocera CX3225 thickness-shear mode resonator, the location of the region of maximum mass sensitivity is experimentally identified.

## Introduction

Microscale devices lend themselves toward sensing applications due to the high sensitivity of their mechanical behavior to changes in system parameters (such as mass, stiffness, or damping), boundary conditions, and various external fields. The promise associated with this high sensitivity has motivated the development of resonant sensors suitable for general mass sensing [15], as well as chemical and biological sensing [610]. As a specific example, prior art exists wherein resonant microscale sensors are used to detect explosive materials [11,12].

One of the most important metrics associated with the performance of a resonant mass sensor is the sensitivity of the resonant frequency of the device to an addition or subtraction of mass, measured in Hertz/picogram or equivalent units. An added mass may have more or less “effective mass” with respect to its effect on the frequency response of a resonator depending on where it is located relative to the vibrational modes of the device. Accordingly, the mass sensitivity of a resonator is spatially dependent. In many cases, the spatial dependence of this metric can be estimated via simulation or analysis. However, with complex resonator geometries or material behavior this can become impractical. In addition, even if the spatially distributed mass sensitivity can be estimated, it is useful to be able to validate such metrics experimentally. Dohn et al. [13,14] demonstrated this by using an etched tungsten tip to load polystyrene microbeads and magnetic microbeads with diameters of 2 μm and 2.8 μm (and masses of 4.4 pg and 14.9 pg), respectively, on various devices and estimating localized mass sensitivity through experimentation. Waggoner and Craighead [15] considered the use of selectively placed gold dots on cantilevers and examined the effect that etching the dots away had on the sensors' frequency responses. This approach allowed for very small test masses (approximately 0.4 pg) but required the researchers to fabricate and test many devices. Nieradka et al. [16] approached the problem of validating mass change and position determination using focused ion beam milling and deposition. However, this work, like those noted above, considered cantilevered beam device geometries.

For platelike devices, tuning forks, or other more complex structures, a second dimension becomes important for deciding the optimal placement of functional compounds and masses. Experimental characterization of mode shapes may be difficult for some device geometries even using state-of-the-art measurement techniques such as laser Doppler vibrometry due to the principal direction of motion, so a method that uses an added or removed mass would be highly desirable. Concretely, the desired outcome is to experimentally produce the differential mass sensitivity
$S(xm,ym)=∂f(xm,ym)∂m$
(1)

where f is a resonant frequency of a device, m is mass, S(xm, ym) is a function with units of Hertz/(unit mass), and xm and ym are the spatial coordinates of a small added mass. Notably, Hillier and Ward [17] used an electrochemical deposition technique with a scanning stage and microelectrode to position and deposit copper on a quartz crystal microbalance device, and used this method to generate a two-dimensional map of differential sensitivity.

Inkjet printing is a known method for applying functional and polymer materials to microscale devices [1821]. It is also used in other circumstances to aerosolize compounds [22]. With inkjet printing, drop size control can be made repeatable and reliable, if the correct material and nozzle are chosen [23]. The chief contribution of this work is the development and application of an inkjet deposition-based method suitable for characterizing the spatially dependent sensitivity of resonant mass sensors. The proposed approach is to estimate S(xm, ym) by using a precision inkjet deposition system constructed for device functionalization. This is advantageous because the system designed for functionalizing a mass or chemical sensor can also be used to calibrate it and map its sensitivity. Precisely controlled drops can be deposited accurately using the inkjet system and allowed to dry so that the solvent in the ink evaporates, and an inert material dissolved in the fluid is left as a deposit. The resulting change in the resonant frequency can then be evaluated. The experimental techniques employed herein are described in the Methodology section, and the corresponding results are interpreted in the Results and Discussion section. The work concludes with a brief overview and suggestions for research extensions.

## Methodology

### Experimental Setup.

The custom deposition system comprised of an X–Y motion stage (Anorad-XKY-C-150-150-AAA0 stage controlled by an Anorad-CM-2 controller) and a custom mounted HP (Hewlett-Packard, Corvallis, OR) Thermal Inkjet Printing System (TIPS), with printing commands provided through in-house software. An aqueous Canon thermal inkjet printing ink was used as the deposition material. The designed drop weight for aqueous inks for the selected nozzle was 28,000 pg, with the corresponding solids loading per drop being 6100 pg.

Because aqueous inks can have a long drying time, a temperature-controlled hot air tool was used to dry the drop on the sensor. This hot air tool (normally used for hot air soldering rework) was set to 100 °C and allowed to run at 50% of its maximum fan speed for 5–10 s at a time.

An Edmund Optics EO-1312 Color USB 3.0 Camera mounted with a 2× primary magnification, 65 mm working distance compact telecentric lens was used for imaging the sensor (with a 2.62 μm/pixel resolution) to determine drop placement locations. For the experiment conducted here, the resonant sensor was characterized using a circuit based on two Texas Instruments LMH6609 amplifiers, with one configured as a drive amplifier for the crystal and the other configured as a transimpedance amplifier with a 2 pF capacitor in parallel with a 43 Ω resistor in the feedback path. The circuit was excited and measured using a Zurich Instruments HF2LI lock-in amplifier, which had phase-locked loop (PLL) functionality. A schematic of the entire experimental system can be seen in Fig. 1.

Fig. 1
Fig. 1

### Experimental Procedure.

The CX3225 resonator is a 16 MHz member of a quartz crystal family produced by Kyocera. While the intended use of the device is as part of a crystal oscillator circuit for clock signal generation, the device is under investigation for use in mass sensing applications due to its small size and surface mount packaging (3.2 mm × 2.5 mm). Internally, the device is a bulk-acoustic wave crystal operating in the fundamental thickness shear mode, mounted to a ceramic substrate. The experimental procedure consisted of decapping a new CX3225 resonator in order to make it accessible for inkjet printing and mass sensing. A CX3225 sensor in this state is shown in Fig. 2. An initial frequency sweep was performed using the HF2LI amplifier. The results of the frequency sweep can be seen in Fig. 3. Based on the results of this frequency sweep, the magnitude and phase of the response at resonance were identified, and the phase was used to allow the PLL to adjust the frequency input to the resonator and track resonance. The corresponding modulator settings, output frequency, and phase error were continuously recorded with a sampling rate of 55 Hz. The PLL loop parameters (proportional and integral) were tuned using the Zurich Instruments ziControl PLL advisor software.

Fig. 2
Fig. 2
Fig. 3
Fig. 3

After the PLL was configured to track the resonant frequency, the experiment continued into the iterative deposition phase. First, in order to prevent the “first drop problem” effects common in inkjet systems [24], the inkjet deposition system was commanded to print an array of 30 drops onto a “sacrificial” substrate, a small piece of absorbent paper, and in the same continuous motion commanded to print a single drop at a location on the resonator. The 30 drop array consisted of three lines of drops spaced 0.2 mm apart, and the experimental deposition was 5 mm away from the final drop of the array. The print process occurred with a nominal stage velocity of 100 mm/s. As the last array drop and the experimental deposition were on separate lines of the printing raster scan, the time between the final drop of the array and the experimental drop was approximately 200 ms. The X–Y stage then moved the resonator directly in the viewing area of the downward-looking camera system and imaged the deposited drop, saving the microscope image for later use. As a pair of examples, Fig. 4 shows the first drop deposited in a 51 drop experiment, and Fig. 5 shows the camera image taken after the 51st drop was deposited. After each drop was deposited, the hot air tool was turned on for 5–10 s in order to quickly dry the droplet. The resonator was then allowed 3–5 mins to return to thermal equilibrium before continuing with the next drop and repeating the process while adjusting the printing position of the droplet. The process for a single drop can be seen in the PLL frequency present in Fig. 6, and a set of 12 subsequent drops in Fig. 7. The added mass due to the drop solids content that did not evaporate during the drying stage is spread out in a “spot.” In this experiment, the deposited drop forms an approximately 55–65 μm diameter spot on the resonator. This spot size could potentially be further reduced by a change in the nozzle diameter, printing parameters (such as back-pressure, inkjet drive voltages, and pulse shaping), ink formulation changes, or potentially a change to another type of inkjet printing. The device to be characterized in this work is a Kyocera CX3225 16 MHz bulk-mode resonator with a corresponding active area with dimensions of 1 mm × 1 mm. Locating the region of highest sensitivity within this area with an accuracy of ±50 μm was desired, so the averaging effect of the 55–65 μm spot size was considered acceptable. In the event this was not acceptable, another inkjet nozzle system would have to be considered, or the rheology of the jetted fluid could be tuned in order to change the spot size on the substrate.

Fig. 4
Fig. 4
Fig. 5
Fig. 5
Fig. 6
Fig. 6
Fig. 7
Fig. 7

One consideration that is based on the design and behavior of the device to be evaluated is that the deposition of previous droplets in a sequence might change the sensitivity of the device to subsequent drops. In order to be sure that this is not the case, it is advisable to estimate the effect of each droplet on the sensitivity of the sensor. The CX3225 device shares some characteristics with quartz crystal microbalance devices—therefore, the Sauerbrey equation can be used to recover a rough estimate of the average sensitivity across the device. For other geometries or types of device some estimate of sensitivity and effective mass should exist in order to ascertain whether previous mass depositions will result in significant deviation in the sensitivity of subsequent ones.

### Validation of the Proposed Approach for a Bulk Resonator.

As noted previously, the Sauerbrey equation can be considered as a starting point for the validation of the approach adopted herein [17,25]. This equation stipulates that for a change in mass Δm, the corresponding frequency shift can be written as
$Δf≈−2f02ΔmAρqμq=CfΔm$
(2)
Here, Cf is the average sensitivity across the device, Δf is the resulting frequency shift, f0 is the resonant crystal frequency in Hertz, Δm is the mass change, A is the piezoelectrically active area, ρq is the density of quartz in g/cm3, and μq is the shear modulus in dyn/cm2 (for AT-cut quartz). Letting $K=Aρqμq$, the differential mass sensitivity is approximately
$S0=ΔfΔm≈−2f02K$
(3)
In order to determine the impact of additional drops on the mass sensitivity, let fi be the natural frequency after the addition of i drops. Then
$Δf1=Δf0ΔmΔm=−2f02KΔmf1=Δf1+f0Δf2=Δf1ΔmΔm=−2f12KΔmf2=Δf2+f1etc…$

This calculation was performed for the parameter values shown in Table 1. The results can be seen in Fig. 8. It appears from the plot that the trend is linear, but it is not (as the equations suggest). However, it is close to linear in the region and parameter space plotted. Nonlinear behavior of the model becomes more evident (see Fig. 9) if drop number or mass is significantly increased, but such changes also push outside the range of applicability of the Sauerbrey model. Another limitation to note is that the Sauerbrey model is only valid for masses covering the entire electrode surface, so this iterated model can be considered to be a spatially averaged model. A third limitation of the Sauerbrey model derivation is that a key assumption that the material added has a similar stiffness and composition to the resonator material itself, which is not the case when depositing inkjet ink, so the results should only be taken as an approximation. Despite the noted limitations, the results indicate that over 200 inkjet drops, the resulting change in the differential sensitivity measurement would be ≤0.125%, which is relatively small compared to our resolution in frequency measurement and small compared to normal variations in inkjet drop volume (up to 5%) and will not make a significant difference for the sensitivity estimation accuracy.

Fig. 8
Fig. 8
Fig. 9
Fig. 9
Table 1

Parameters used for iteration of the Sauerbrey equation

ParameterValueUnits
Δm6000pg
f016MHz
A0.010cm2
ρq2.648g/cm3
μq2.947 × 1011dyn/cm2
ParameterValueUnits
Δm6000pg
f016MHz
A0.010cm2
ρq2.648g/cm3
μq2.947 × 1011dyn/cm2

## Results and Discussion

To compute the drop-to-drop frequency shift, 10 s of PLL output frequency data at the beginning and end of each drop response (as in Fig. 6) were used. The frequency over the 10 s was averaged, and the drop frequency shift was computed as Δfi = fi − fi1. In order to correlate the ith drop with its position, the drops were identified by a user using a matlab script to sequentially specify drop locations on the final image. The individual sequential images, taken after each deposition step, were used to determine the order of droplet deposition, which need not be in a strict pattern.

### Experimental Repeatability.

In order to gain an understanding of the repeatability of the inkjet-based characterization, an experiment was performed with repeated drop depositions at the same position on the resonator. A 16 MHz CX3225 resonator was used for this experiment as well. The experimental procedure consisted of selecting a point and then repeatedly attempting to deposit a drop at the same point (ten times) and then comparing the resulting shift in frequency after each deposition–drying–thermal recovery cycle. Drop locations were estimated and then plotted on a micrograph of the device (Fig. 10). The three tested locations (1, 2, 3) have corresponding frequency shifts per drop as shown in Fig. 11. There is some significant variability in the frequency shift, and there are a number of possible sources of this variability. While variability in the deposited mass is most likely present, there is a considerable drop placement error, which is a limitation of the inkjet nozzle system rather than that of the positioning stage. The drop placement error was characterized with the standard deviation of drop placement error in the X-direction of the stage system being 29.5 μm, 53.3 μm, and 33.6 μm for drop positions 1, 2, and 3, respectively, with the corresponding Y-axis placement error standard deviations being 34.4 μm, 34.75 μm, and 38.8 μm. The camera resolution was 2.62 μm/pixel with an estimated location accuracy of drop centroid identification of ±2 pixels, or ±5.24 μm. Because the drop placement error is relatively large compared to the dimensions of the device and the gradient of the sensitivity is significant as well, the authors hypothesize that the drop placement accuracy is the dominant source of variation in this experiment. However, the variability even in this experiment is sufficiently small to allow for characterization of which areas of the device have relatively high and low sensitivity.

Fig. 10
Fig. 10
Fig. 11
Fig. 11

### Mapping the Sensitivity of a Resonator.

Figure 5 shows the pattern of droplets deposited in a 51 drop experiment with the goal of mapping the spatial sensitivity dependence of the CX3225 resonator. Individual deposition frequency shifts are plotted in a three-dimensional scatter-bar plot aligned with the drop placement image in order to visualize the relative spatial sensitivity of the device, in Fig. 12. The sensitivity is largest in the center of the device's upper electrode, where the drops, which should be of close to uniform mass, produce the largest frequency shift. In the test pattern shown in Fig. 12, a single drop was deposited at each point.

Fig. 12
Fig. 12

The absolute sensitivity can be estimated if the drop mass is known. In this case, the average drop mass is 6100 pg. This drop mass was estimated by the deposition of 1,250,000 drops of ink into a clean glass scintillation vial, the mass of which was measured before deposition and after allowing the solvents in the ink to evaporate, computing the differential mass, and dividing by the number of drops to compute the average drop mass. Therefore, the maximum sensitivity of the device can be estimated to be −534 Hz/6100 pg = −0.0875 Hz/pg, but notably this sensitivity rapidly gets significantly worse (closer to 0 Hz/pg) around the outside of the electrode of the device, with the lowest sensitivity of any drop location estimated to be −0.000111 Hz/pg. The Sauerbrey equation estimated −17.26 pg/Hz or −0.0579 Hz/pg sensitivity over the entire device, using Eq. (3) and the parameters discussed earlier. In certain sensing applications, it may be useful to only functionalize the highest sensitivity portions of the device. Whether or not this improves performance will depend on other factors, such as the means by which the sensor is being exposed to the compound. The effect of drop placement error in the mapping test is significantly mitigated as compared to the repeatability test since the mapping uses the measured position of the drop to map the sensitivity to that point.

## Conclusions

An inkjet method for mapping relative mass sensitivity across a resonant structure was successfully developed and applied to a quartz bulk-mode resonator. This method can be used to validate numerical and analytical models employed in design, and also to decide the most promising areas for the deposition of functional compounds used in sensing, as long as the drops can be generated in an appropriate size for the application. Future improvements to the process could include refined ink formulation and optimization for the task of keeping spot size small but improve drying times (this could potentially remove the hot air tool from the process). In addition, drop-to-drop variations in mass could cause some error, and characterization of this could be helpful in better bounding the experimental error. Finally, the methodology could be aided by additional automation of the drying system, inkjet system, and back-pressure control to make the characterization a turn-key process, allowing for rapid generation of mass sensitivity maps as demonstrated for the Kyocera CX3225 resonator.

## Acknowledgment

This work was supported by the U.S. Department of Homeland Security's Science and Technology Directorate, Office of University Programs, under Award No. 2013-ST-061-ED0001. The authors would also like to acknowledge the support of the Hewlett-Packard Company, which provided the TIPS printing system and nozzles used in this work. A preliminary version of this paper was submitted to the 2016 ASME Dynamic Systems and Control Conference.

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