Detailed Introduction to Crosstalk in Piezoelectric Inkjet Printing
Crosstalk in Piezoelectric Inkjet Printing
Introduction
In piezoelectric inkjet printing, actuation is achieved by deformation of ink channels through piezoelectric elements. Crosstalk refers to the phenomenon whereby the actuation of one channel influences adjacent channels.
Crosstalk effects arising from printhead structures include electrical crosstalk, direct (mechanical) crosstalk, and pressure-induced crosstalk. The latter also occurs through acoustic coupling between ink domains via the ink supply system. In addition, structural resonances within the printhead can be excited. When crosstalk interferes with residual vibrations in the ink domain, significant variations in drop ejection characteristics may occur.
0.1 Electrical Crosstalk
Piezoelectric inkjet printing is fundamentally based on converting an applied electrical driving voltage into mechanical deformation of the ink chamber via piezoelectric elements, generating the pressure required to form droplets at the nozzle. One key differentiator among piezoelectric printheads is the combination of the dominant deformation mode of the piezoelectric actuator and the geometry of the ink channel.
Ideally, only the channel receiving the driving voltage should deform. However, in many cases, neighboring channels also deform. When the electric field extends into adjacent channels, electrical crosstalk occurs. Therefore, the electric field must be confined to a single channel. Other sources of electrical crosstalk—such as parasitic capacitances in the electronic drive circuitry—must also be avoided. With appropriate actuator and driver circuit design, electrical crosstalk can generally be minimized effectively.
0.2 Direct Crosstalk
Shear Mode
In shear-mode actuation, the strong shear deformation component of the piezoelectric material is used to deform the ink chamber walls. An electric field oriented perpendicular to the polarization direction activates the d₁₅ mode, producing shear deformation that displaces the chamber wall.
The shearing mode principle calculates the deformation in the driving direction after applying an electric field between the center and outer electrodes. Two versions used in piezoelectric printheads are shown.
Two shear-mode inkjet designs are illustrated:
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Shared-wall configuration, where the piezoelectric ceramic itself forms the channel wall.
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External actuator configuration, where the actuator forms a separate outer layer covering the channel plate.
In the shared-wall design, the fact that the wall between two adjacent channels participates in deformation leads to significant direct crosstalk. The cross-sectional deformation in neighboring channels can reach approximately 50% of that of the actively driven channel. As a result, pulse counting schemes are required to limit crosstalk, and it becomes impossible to actuate two adjacent channels simultaneously—only one out of every three channels can be driven at a time.
When the actuator is implemented as an external deformable layer, this issue is largely avoided. Only minor electrical crosstalk remains due to a small electric field component parallel to the polarization direction, which causes slight actuator expansion and consequent wall deformation.
Bending Mode
In bending-mode actuation, ink droplets are ejected by bending the chamber wall. In early designs, an external diaphragm with bonded piezoelectric ceramic was used. The electric field is applied along the polarization direction, utilizing both longitudinal and transverse deformation components. Actuators with a single active layer are referred to as single-piezo actuators.
Several bending-mode actuator variants exist:
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Bimorph actuators with two piezo layers (either series or parallel electrode configurations)
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Reinforced bimorphs incorporating a metal shim to enhance mechanical strength
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Monolithic actuators, which integrate the full structure into a single body
In all cases, bending results from differential strain between layers. Since deformation resembles that of externally actuated shear-mode designs, direct crosstalk is generally low. However, soft channel plate materials (e.g., graphite) can still induce some mechanical crosstalk due to bending moments applied to the channel walls.
Push (Impact) Mode
In push-mode actuation, a piezoelectric element pushes directly against the chamber wall to deform the ink chamber. The electric field is applied parallel to the polarization direction, and deformation occurs either parallel or perpendicular to this direction.
A rigid substrate is required to provide reaction force support, which introduces mechanical stress and reduces effective piezoelectric efficiency. To minimize this loss, geometric optimization is employed: at least one dimension perpendicular to the actuator height must be much smaller than the height, limiting substrate-induced constraints.
For example, a 500 μm-high PZT actuator mounted on a 1 mm AlOx substrate and bonded to a channel block with 75 channels/inch resolution exhibits significant crosstalk. Reaction forces transmitted through the substrate deform neighboring inactive channels, causing deformation opposite to that required for droplet ejection. This results in nearly 50% direct crosstalk, reducing drop velocity when adjacent channels are activated.
A front view of a collision-mode channel structure and the calculated deformation of the channel structure (chromatic light → dark is 13nm → -27nm) is shown in the first example, a, where the deformation is magnified 2000 times. The reaction force of the substrate is directed to adjacent elements, causing adjacent channels to produce an opposite deformation. In the second example b, the estimated deformation of a 220μm wide channel in graphite covered with a 10μm polyimide foil is shown. The chromaticity now corresponds to a displacement range of 0–60nm. The reaction force of the substrate is directed to the channel walls, which eliminates direct crosstalk. In the third example, c, the calculated deformation of the 220μm wide channel in graphite is magnified 1000 times. The pressure in the middle channel is 1 bar, which results in a displacement of approximately 2nm/bar of the foil in the driving direction.
Mitigation of Direct Crosstalk
Direct crosstalk can be suppressed by redirecting reaction forces into other parts of the printhead structure—most effectively into the channel walls. For a 220 μm-wide channel, doubling the actuator resolution allows half of the actuators to serve as structural supports, forming a force ring around each active channel.
Foil stiffness plays a critical role. A 25 μm tantalum foil has stiffness comparable to a 500 μm PZT actuator, resulting in ~10% residual crosstalk. In contrast, a 10 μm polyimide foil significantly reduces stiffness, eliminating direct crosstalk. In this case, actuator-driven displacement reaches ~40 nm in the active channel while remaining below 1 nm in adjacent channels.
0.3 Pressure-Induced Crosstalk
Channel actuation generates pressure waves with amplitudes of 1–2 bar, which deform the structure, particularly when soft channel materials such as graphite are used. Pressure-induced crosstalk occurs when a positive pressure in the active channel causes deformation across all channels.
Channel deformation consists of:
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Elongation
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Bending
Elongation reduces pressure and drop velocity across all channels. The magnitude depends on foil stiffness and channel wall stiffness. A 25 μm tantalum foil has stiffness comparable to channel walls and actuators, leading to substantial deformation. With a 10 μm polyimide foil, deformation is localized, but adjacent channels still experience ~10% deformation, significantly reducing drop velocity.
Bending stiffness of the channel wall is also critical. While bending can partially compensate for elongation effects, simultaneous activation of multiple channels can still result in cumulative drop velocity losses of several meters per second. Extremely stiff channel materials (e.g., silicon) are required to suppress this effect.
Another mitigation mechanism arises from the fact that pressure-induced crosstalk shares the same dynamics as pressure waves: meniscus motion in inactive channels occurs in the opposite direction to that in active channels. This counter-motion explains reduced drop velocities when multiple channels fire simultaneously.
The simulation was performed using an acoustic model, which took into account the acoustoelastic interaction added to the deformation of the printhead structure in the finite element simulation. The deformation ΔAi of the cross-section of all channels can be written as the sum of all contributions to deformation obtained by adjacent channels from direct crosstalk αij and pressure-induced crosstalk βij:
ΔA_i / A_0 = ∑ ( α_ij V_j + β_ij p_j )
Using the formula in the above figure as the input and output for the acoustic part, it simulates wave propagation in narrow channels, and the motion of the semi-liquid surface in many channels can then be calculated.
Therefore, the semi-liquid surface velocity resonates with the channel in all channels, and there is a time delay between the start of the drive in adjacent channels, which has a significant impact on the falling speed, as shown in Figure b.
a. The calculated half-liquid surface velocity as a function of time is obtained at the nozzles of the operating channel and adjacent channels. The figure shows a tenfold increase in the velocity of the half-liquid surface in adjacent channels, clearly indicating that the half-liquid surface is moving in opposite directions. This results in a lower falling velocity when both channels are simultaneously operating.
b. Regarding the effect of the measured falling velocity on the time delay between the reference point and the first adjacent channel, this time delay has a significant impact on pressure-induced crosstalk. The 8mm long pressure channel has a cross-sectional area of 220μm × 120μm, formed in a graphite channel block and covered with a 25μm polyimide foil. The nozzle diameter is 32μm in a 50μm electroformed nickel nozzle plate.
With the time delay coinciding with the half-cycle of channel vibration, the half-cycle of the 8mm long channel with a resonant frequency of 44kHz is 11μs. The movement of the half-liquid surface in adjacent channels will be synchronized with the movement of the half-liquid surface in the operating channel. Then, even higher drop speeds will be caused by crosstalk here. A time delay equal to 1/4 of the channel oscillation period will offset the effect of this crosstalk on the drop speed, which can be used to minimize the error in dot positioning on the paper. In the scanning printing concept, the dot positioning error is proportional to the deviation in the ink droplet velocity.
0.4 Acoustic Crosstalk
Complete reflection of pressure waves within the ink supply or reservoir channels is essential. If reflection is incomplete, pressure waves propagate into neighboring channels, producing acoustic crosstalk throughout the printhead.
The characteristic acoustic impedance Z of a channel depends on its cross-sectional area A and the speed of sound c:
Z = ρc / A
where ρ is ink density, and c depends on channel compliance β.
c = c₀ √( 1 / (1 + ρc₀²β) )
To reduce acoustic crosstalk:
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Supply channels should have much larger cross-sections than pressure channels.
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Alternatively, compliance can be increased by covering supply channels with thin, flexible foils.
As shown in Figure a: One option is to make the acoustic impedance of the supply as low as possible. Since acoustic impedance is inversely proportional to the cross-sectional area of the channel, the supply channel must have a much larger size than the pressure channel. The first step is to avoid using separate supply channels for individual channels, except in the context of a three-dimensional finite element acoustic model in the ink domain, where a large supply is required for all channels.
To reduce acoustic crosstalk, the minimum supply height can be calculated using the model described above. When only one channel is active, a 1mm high supply is sufficient for almost complete reflection. However, when all channels are active, a significant portion of the pressure wave passes through the supply. Only the height difference between the pressure channel and the supply affects the acoustic impedance difference. For a 100μm high channel, the supply height must be kept within 10mm to ensure that the transmitted pressure wave is at least 1% lower than the incoming wave. This is not always possible because the printhead size must be kept within certain limits. Another way to reduce supply impedance is to increase supply compliance. The simplest way to increase supply compliance is to cover the power supply with a thin foil; when the pressure wave reaches the supply, the compliant foil deforms.
For example, a 25 μm polyimide foil over a 1.4 mm gap deflects ~300 nm under a 0.8 bar pressure wave, compensating for pressure displacement and eliminating acoustic pressure.
The effect of compliance is the same as adding an extra volume Vc to the ink supply channel volume Vs. The formula for the extra volume is obtained by considering the compliance determined by the volume compliance ρc² of the liquid in the power supply and the undeformed supply volume Vs:
V_c = β ρ c^2 V_s
Another solution is a restricted inlet acting as a closed boundary. If the inlet length exceeds 10% of the pressure channel length and its cross-section is less than 25% of the channel cross-section, the transmitted pressure can be reduced below 1%. However, Helmholtz-type resonances may occur if the inlet inductance is insufficient.
0.5 Printhead Resonance
Pressure wave generation requires drive frequencies in the tens of kilohertz range. Rapid piezoelectric motion can excite structural resonances, especially when multiple actuators are driven simultaneously.
The image above depicts the reaction of the semi-liquid surface on the actuators of all channels on the other side of the double-sided channel block. The channels on the other side are activated by a sinusoidal drive wave with an amplitude 10% of the normal amplitude of the printhead in embossed mode. The movement speed of the semi-liquid surface within the nozzle in the middle of this printhead is measured using a laser Doppler device.
Laser Doppler measurements reveal strong meniscus motion in non-driven channels at frequencies of 35–100 kHz and 130–170 kHz, caused by structural resonances. These effects are analyzed using full 3D finite-element models (e.g., ANSYS), simplified to manage computational complexity.
Thus, the first simplification of the model is to remove all the small parts. It's unlikely these small parts have no effect; secondly, the mesh simplification is accomplished by replacing the small circles with rectangular geometry.
F is the load vector, and m, c, and k are the mass, damping, and stiffness matrices of the structure. The equation for the displacement vector x is:
F=mx¨+cx˙+kx
However, solving this equation using a complete transient analysis of a full printhead model requires a significant amount of computation. Therefore, modal analysis can be initiated simultaneously with modal superposition analysis to obtain the complete transient behavior. It is empirically known that the damping in the printhead structure is much smaller than that in the ink channels. Damping is neglected in the modal analysis of the printhead structure. For a linear system, the form of the free-vibrating harmonics is x = φ i cos （ω i t）, where φ i is the shape of the eigenmode at angular frequency ω i. The equation of motion without load vectors solves for the eigenmodes, reducing the time for each model to:
(-ωᵢ²·m + k)φᵢ = 0
With the frequency range as the standard, the size of the grid elements is maximized. For most applications, only modes with frequencies below 250kHz are expected to affect channel acoustics and droplet formation. The minimum wavelength corresponding to the relevant modes is approximately 1mm, provided that at least 10 elements are needed to capture the shape of the mode, and the maximum element size becomes 100μm. The smallest element is necessary to describe the smallest details, such as a foil with a thickness of 25μm. In modal analysis, the voltage of all electrodes is set to zero. In modal analysis, all resonances within the printhead structure can be identified. Now, we need to calculate which mode is most active. First, the deformation S, which is caused by the electrical load (electric field E applied to the piezoelectric element with a piezoelectric coefficient of d and compliance of s) and the mechanical load T (constraints from the substrate and channel block):
was converted to a purely mechanical load to further reduce the computational effort. The deformation as a sum of mechanical and piezoelectric strains is converted into an elastic stress:
Only the composition of the stresses acting in the drive direction at the top and bottom of the piezoelectric element has a significant effect. These normal components of the elastic stress are multiplied by the surface area to find the load vector F. The displacement x in the printhead structure can be written as
in ξ i modal coordinates, or the effect of each intrinsic mode of deformation of the printhead, under orthogonal conditions:
where f i is defined as after solving the modal coordinates ξ i and eigenmodes φ i, then the transient response of the printhead structure can be expressed as Eq.
to solve the modal superposition analysis. In order to simulate the effect of resonance within the printhead structure regarding pressure waves in the ink channel, a finite element model of the ink domain must be used. Typically, the channel is driven by piezoelectric elements, causing deformation of the cross section. The deformation of the channel walls in the modal and superposition analysis models is now used as a boundary condition. In order to determine which mode contributes to the pressure wave in the channel, the deformation of the channel wall under each model must be used as a boundary condition.
Modal analysis identifies dominant resonant modes. Structural damping is negligible compared to ink-domain damping and is therefore ignored. Transient response is reconstructed using modal superposition.
Only resonances strongly coupled to channel acoustics significantly affect droplet formation, depending on pressure, channel length, and frequency matching.
0.6 Residual Vibrations
High-frequency drop-on-demand printing requires repeated actuation at intervals shorter than 100 μs. If a droplet is ejected before residual acoustic waves decay, the next droplet forms with a non-zero meniscus velocity, causing variations in drop velocity and size at frequencies exceeding 10 kHz.
Velocity peaks correspond to channel resonance frequencies and their subharmonics. Damping is dominated by viscous dissipation at the nozzle. Nozzle area and length strongly influence residual vibration amplitude.
Residual vibrations interact with crosstalk effects at high repetition rates, causing large drop velocity differences between isolated and simultaneously driven channels.