Moisture Transport Mechanisms Through Thin Films
Moisture ingress into pMUT devices occurs through multiple transport pathways, each with distinct timescales and degradation consequences. Diffusion through the bulk passivation material is the primary pathway in devices with intact passivation layers. Moisture diffuses according to Fick's second law, with the diffusion coefficient D typically ranging from 10⁻¹⁴ to 10⁻¹² cm²/s for PECVD SiO₂ at 25°C. For a 1 micrometer thick SiO₂ passivation layer with D = 10⁻¹³ cm²/s, the characteristic diffusion time to reach the PZT-passivation interface is approximately 10 days (using the scaling relation t ~ L²/D). This is comparable to the intended wear duration of some sub-dermal drug-delivery patches (7–14 days).
Permeation through the passivation layer occurs when water molecules dissolve at the external surface, diffuse through the material, and evaporate at the internal surface. The permeation rate is directly proportional to the water vapor concentration gradient across the film. In a wearable device at 37°C body temperature, the external surface (in contact with sweat) may be saturated with water (relative humidity approaching 100%), while the internal surface (in contact with the PZT) has lower relative humidity if the device is sealed. This creates a driving gradient for continuous moisture permeation.
Defect-assisted transport through pinholes, cracks, and delamination sites dominates in devices with compromised passivation. Water can penetrate through a 1 micrometer pinhole in a time scale of hours to days, depending on the pinhole size and the driving pressure gradient. In sub-dermal applications, the device is in direct contact with interstitial fluid and sweat, which exerts osmotic and hydrostatic pressure on the passivation layer. This pressure can exceed 10–50 mmHg locally, driving rapid moisture ingress through defects.
Grain-boundary and interface transport occurs along the columnar grain boundaries in PECVD films and at the PZT-passivation interface. PECVD SiO₂ films exhibit columnar grain structure with grain diameters of 50–200 nanometers. Water molecules preferentially diffuse along grain boundaries, which have higher defect density and lower energy barriers compared to the grain interior. Similarly, if the PZT-passivation interface has poor adhesion or contains voids, moisture can penetrate laterally along this interface at rates much faster than bulk diffusion. Research using moisture-sensitive fluorescent dyes has demonstrated that moisture can reach the PZT-passivation interface in 3–7 days through grain-boundary pathways, compared to 10–20 days through bulk diffusion, even in nominally intact passivation layers.
Electrochemical Corrosion Mechanisms
Once moisture reaches the PZT film or the electrode-PZT interface, electrochemical corrosion can initiate. This process is fundamentally an electrochemical cell wherein the PZT (or metal electrodes) acts as the anode, the external environment provides the electrolyte, and oxygen dissolved in the moisture provides the cathodic reactant.
Oxygen Reduction Reaction at the Cathode is the primary cathodic process in sub-dermal environments:
O₂ + 2H₂O + 4e⁻ → 4OH⁻ (in neutral to basic pH)
This reaction consumes dissolved oxygen and generates hydroxide ions, which migrate toward the anode (the PZT or metal electrode). The rate of oxygen reduction is limited by oxygen diffusion through the moisture layer and is typically 0.1–1 microampere per cm² under physiological conditions (37°C, neutral pH, low oxygen concentration in interstitial fluid).
Anodic Dissolution of Lead from PZT occurs at the PZT surface:
Pb → Pb²⁺ + 2e⁻
Lead is the most electrochemically active component in PZT. Under physiological conditions (neutral pH, dissolved oxygen), lead oxidation occurs at potentials as low as -0.5 V versus a standard hydrogen electrode (SHE). The PZT film typically floats at potentials determined by the open-circuit potential of the electrode-PZT system, which is typically -0.2 to +0.3 V versus SHE in physiological solution. At these potentials, lead oxidation occurs, albeit slowly.
Once oxidized, lead ions (Pb²⁺) react with hydroxide ions and other anions in the physiological fluid to form insoluble compounds:
Pb²⁺ + 2OH⁻ → Pb(OH)₂ (precipitate)
Pb²⁺ + SO₄²⁻ → PbSO₄ (precipitate, if sulfate is present)
These precipitates form a corrosion product layer on the PZT surface. In early stages (first few days), this layer is thin and porous. However, as corrosion progresses, the layer can become thick (1–5 micrometers) and dense, eventually limiting further oxygen diffusion and slowing the corrosion rate. This is the passivation paradox: corrosion products can actually slow further corrosion by blocking oxygen access to the underlying material.
Zirconium and Titanium Corrosion also occurs, though at slower rates than lead. Zr and Ti are less electrochemically active than lead, and their oxidation products (ZrO₂, TiO₂) are more protective than lead compounds. However, in acidic microenvironments (which can develop locally due to hydrolysis of metal cations), zirconium and titanium can dissolve.
Galvanic Corrosion at Electrode-PZT Interfaces represents a particularly aggressive degradation mechanism. In pMUT devices, the top electrode is typically platinum (Pt) or gold (Au), while the bottom electrode may be platinum or a more reactive metal such as titanium (Ti). If moisture penetrates the passivation layer and reaches the electrode-PZT interface, a galvanic couple forms between the electrode metal and the PZT (which can be considered as a mixed-valence oxide semiconductor). The electrode metal (particularly if it is Ti or another reactive metal) acts as the anode and preferentially corrodes.
Interface Degradation and Structural Consequences
The accumulation of corrosion products and the loss of material from the PZT surface and electrode-PZT interface leads to progressive degradation of device performance. Interfacial resistance increase is one of the earliest detectable changes. As corrosion products accumulate on the PZT surface, they introduce an additional resistive layer between the electrode and the bulk PZT. Electrochemical impedance spectroscopy (EIS) measurements on pMUT devices after 2–4 weeks in physiological solution show an increase in interfacial impedance from 10–50 ohms (fresh devices) to 100–500 ohms (corroded devices), an increase of 5–10×.
Piezoelectric coefficient degradation follows from the loss of polarization in the surface layer of the PZT. The effective d₃₃ coefficient (measured by laser vibrometry or acoustic output testing) decreases by 10–30% after 4 weeks of continuous exposure to physiological solution in commercial pMUT devices. This degradation is not uniform; it is most severe at the electrode-PZT interface and decreases into the bulk of the film. Cross-sectional transmission electron microscopy (TEM) of corroded pMUT devices reveals a 100–500 nm thick surface layer with reduced crystallinity and altered domain structure compared to the bulk PZT.
Mechanical Delamination and Cracking can result from corrosion-induced volume changes. When lead oxidizes to form Pb(OH)₂ or PbSO₄, the molar volume increases by 20–40% compared to the original PbO in the PZT lattice. This volume expansion creates compressive stress at the PZT surface, which can exceed the material's compressive strength locally, leading to microcracking. These cracks provide additional pathways for moisture ingress, accelerating further corrosion in a positive feedback loop.
Electrochemical Migration of Dopants within the PZT film can occur under the electric field generated by the corrosion cell. Dopant ions (such as acceptor dopants used to control the PZT properties) migrate toward the cathode, creating regions of altered composition. This dopant redistribution can reduce the piezoelectric coefficient in affected regions by 15–25%.
Specific Degradation Pathways in Sub-Dermal Wearable Environments
Sub-dermal pMUT devices face a unique combination of stressors that distinguishes them from laboratory test environments. Sweat chemistry varies significantly between individuals and over time. Sweat typically contains 0.5–1% sodium chloride, with additional ions including potassium (K⁺), calcium (Ca²⁺), magnesium (Mg²⁺), and phosphate (PO₄³⁻). The pH of sweat typically ranges from 4.5 to 7.5, with acidic conditions (pH 4.5–5.5) occurring during intense exercise. At acidic pH, the corrosion rate of lead from PZT increases significantly, with corrosion current potentially doubling for each 0.5 unit decrease in pH.
Interstitial fluid in the skin has a pH of approximately 7.2–7.4 and contains proteins (albumin, immunoglobulins), amino acids, glucose, and ions. The presence of proteins can alter corrosion mechanisms; proteins can adsorb on the PZT surface and either inhibit or accelerate corrosion depending on their specific interactions with corrosion products. Albumin, the most abundant plasma protein, can form complexes with lead ions, potentially enhancing lead dissolution by removing dissolved lead ions from equilibrium.
Bacterial biofilm formation on the device surface is a significant concern in sub-dermal applications. Bacteria in skin flora (such as *Staphylococcus epidermidis* and *Corynebacterium* species) can colonize the device surface within 24–48 hours of implantation. Biofilms create localized microenvironments with pH as low as 3.5–4.5 (due to bacterial acid production) and near-zero oxygen concentration in the biofilm interior. These conditions dramatically accelerate PZT corrosion. Electrochemical measurements on pMUT devices with biofilms show corrosion current densities 10–50× higher than sterile control devices.
Thermal cycling from body temperature variations (diurnal cycles of 35–39°C) and local heating during device operation (which can raise local temperature by 2–5°C due to acoustic energy absorption) accelerates both diffusion and corrosion reactions. The diffusion coefficient for moisture in PECVD SiO₂ approximately doubles for every 10°C increase in temperature. Additionally, thermal cycling induces mechanical stress at interfaces due to thermal expansion mismatch between different materials (PZT, SiO₂, electrodes, substrate), promoting crack formation and delamination.
Mechanical Flexing from body movement creates cyclic strain at the device-skin interface and within the device structure. This mechanical cycling can cause delamination of the passivation layer or initiate crack propagation in brittle passivation materials. Devices worn in high-motion areas (such as joints) experience significantly higher delamination rates than devices worn on relatively immobile areas (such as the forearm).
Current Status of Accelerated Testing and Standardization
A critical gap in the field is the lack of standardized accelerated stress testing for sub-dermal pMUT devices. Different manufacturers and research groups employ different test protocols, making it difficult to compare results or establish design guidelines. Common test approaches include:
- 85°C/85% RH testing: Devices are stored in an environmental chamber at 85°C and 85% relative humidity for 500–1000 hours. This accelerates moisture diffusion (approximately 10–20× acceleration compared to 25°C/50% RH) but does not capture mechanical cycling or realistic physiological chemistry.
- Physiological fluid immersion: Devices are immersed in saline solution (0.9% NaCl) or artificial sweat at 37°C for 1–4 weeks. This captures electrochemical corrosion but not the moisture barrier properties of the passivation layer (since the device is fully immersed rather than in contact with moisture vapor).
- Thermal cycling: Devices are cycled between -10°C and +60°C for 100–500 cycles. This induces mechanical stress but does not accelerate moisture diffusion as effectively as elevated temperature and humidity.
- Combined stress testing: Some research groups combine multiple stressors (elevated temperature, humidity, mechanical cycling, and physiological fluid exposure), but test protocols and duration vary widely.
Established results from literature include: (1) PECVD SiO₂ passivation layers typically fail (allowing moisture penetration) after 2–8 weeks of continuous exposure to 85°C/85% RH or physiological solution; (2) Si₃N₄ provides superior moisture barrier properties but is prone to cracking under mechanical strain; (3) ALD Al₂O₃ offers excellent moisture barrier properties but adhesion to PZT is often poor; and (4) lead loss from PZT surfaces accelerates exponentially with decreasing pH.
Device-specific or emerging observations include: (1) some commercial pMUT devices show unexpected asymmetry in corrosion between the top and bottom electrodes, suggesting differences in electrode material or interface quality that are not disclosed in technical specifications; (2) corrosion rates vary by 2–5× between different commercial products under identical test conditions, indicating significant differences in passivation quality or electrode material; (3) biofilm formation on pMUT surfaces accelerates corrosion by 10–50×, but this has been documented in only a few research studies and is not routinely tested by manufacturers; and (4) the interaction between mechanical strain from acoustic cycling and electrochemical corrosion is incompletely understood—some studies suggest mechanical strain accelerates corrosion, while others report protective effects from strain-induced surface passivation.
The absence of standardized testing metrics represents a significant barrier to device reliability prediction and comparison. Clinical use of sub-dermal pMUT drug-delivery patches requires confidence that devices will maintain acoustic output (and thus therapeutic dose delivery) throughout their intended wear duration (typically 7–14 days). Without standardized accelerated testing, manufacturers cannot reliably predict device lifetime under realistic wearable conditions, and clinicians cannot assess whether acoustic output degradation poses a risk of therapeutic under-dosing.