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Der Artikel stellt eine bahnbrechende MEMS-Plattform zur thermomechanischen Charakterisierung von Nanomaterialien vor, die die entscheidende Notwendigkeit präziser Tests unter gekoppelten thermischen und mechanischen Belastungsbedingungen adressiert. Die Plattform integriert fortschrittliche Features wie einen thermischen Aktuator mit hoher Steifigkeit, unabhängige Joule-Heizelemente und einen kapazitiven Verdrängungssensor, der eine verdrängungskontrollierte Zugprüfung ermöglicht. Der Entwicklungsprozess umfasste die Bewältigung erheblicher Herausforderungen, darunter die Steuerung komplexer transienter Wärmetransferdynamiken und die Gewährleistung einer präzisen thermischen Kalibrierung. Die Leistungsfähigkeit der Plattform wird durch thermomechanische Charakterisierung von Silber-Nanodrähten mittels in situ REM demonstriert und zeigt ihre Fähigkeit, sowohl Temperatur als auch Verdrängung präzise und stabil zu steuern. Die Finite Element Analysis (FEA) liefert wertvolle Einblicke in das thermische und mechanische Verhalten der MEMS-Komponenten, bestätigt die Funktionalität des Geräts und unterstreicht sein Potenzial zur Erforschung größenabhängiger Phänomene in Nanomaterialien. Der Artikel schließt mit der Vision einer zukünftigen Integration der Plattform mit zusätzlichen In-situ-Techniken wie Röntgenmikroskopie, um ihre Anwendungen in der Materialwissenschaft und Nanotechnologie weiter zu verbessern.
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Abstract
Background
Thermomechanical testing of nanomaterials is essential to assess their performance in applications where thermal and mechanical loads occur simultaneously. However, developing a multi-physics testing platform for nanomaterials that integrates temperature control, displacement control, and force sensing remains challenging due to the interference between heating and mechanical testing components.
Objective
This work aims to develop a novel microelectromechanical system-based platform for in situ thermomechanical testing of nanomaterials with displacement control and precise temperature regulation.
Methods
The platform integrates a high-stiffness thermal actuator, Joule heating elements, and a capacitive displacement sensor, along with sample stage heaters featuring thermal insulation and thermal expansion compensation structures. Finite element analysis was used to optimize the design and minimize thermomechanical interference. Heating performance was characterized using Raman spectroscopy and resistance measurements.
Results
Displacement control and precise localized temperature control are achieved, overcoming limitations of transient heat transfer and thermal drift observed in previous systems. Its performance is demonstrated through in situ thermomechanical tensile testing of silver nanowires, showcasing its capability for nanoscale material characterization.
Conclusions
The developed microelectromechanical system platform enables thermomechanical investigation of size-dependent phenomena in nanomaterials, such as phase transitions and temperature-dependent fracture. Its displacement control and localized temperature regulation, combined with in-situ observation, provide a powerful tool for understanding nanoscale deformation and fracture mechanisms.
Diptiman Kundu and Boyu Zhang contributed equally to this work.
R. Bernal is a member of SEM.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Introduction
Thermomechanical testing [1, 2] is essential to understand the behavior of nanomaterials [3, 4] under operating conditions found in practice, where they are often subjected to simultaneous thermal and mechanical loads. At the nanoscale, material properties such as strength, stiffness, ductility, and thermal conductivity can deviate significantly from their bulk counterparts [5, 6], due to surface effects [7], grain boundary structures [8, 9], and quantum confinement [10, 11]. These unique properties are highly sensitive to temperature and stress, making it crucial to study their simultaneous effects. For example, thermomechanical testing provides insights into phenomena like brittle-to-ductile transitions [12], thermal softening [13, 14], and creep, which are critical for designing nanomaterials used in high-temperature environments such as aerospace components, microelectronics, and energy systems. Additionally, nanoscale materials often exhibit size-dependent mechanical behavior, where properties like yield strength and elastic modulus vary with dimensions [15‐17]. Thermomechanical testing enables researchers to characterize these dependencies while accounting for thermal effects, which can influence dislocation motion [18], grain boundary sliding [19], and phase transformations [20]. Moreover, thermomechanical studies are pivotal for predicting the reliability and lifetime of nanomaterials in applications that involve cyclic thermal and mechanical stresses, such as in sensors and energy devices. Without a clear understanding of how these materials respond to thermomechanical loading, it is challenging to optimize their design or predict their failure mechanisms.
Among small scale testing techniques, microelectromechanical systems (MEMS) have revolutionized the mechanical characterization of nanoscale materials by offering unprecedented precision and control [21‐26]. These devices are uniquely suited for studying the intricate mechanical behaviors of nanostructures [27‐30], such as yielding [31, 32], necking [33, 34], phase transitions [35, 36], and brittle-to-ductile transitions [37‐40], often under controlled environmental conditions. MEMS-based testing platforms [41] integrate actuators and sensors [42‐44] into compact designs, enabling high-resolution measurements of stress–strain relationships and providing insight into phenomena that are difficult to capture using traditional testing methods. Recent advances in MEMS technology have demonstrated the potential of these systems to characterize a wide range of nanostructures, such as nanowires, nanotubes [17], and polymer fibers, with unparalleled precision. Tensile testing using MEMS platforms has been highlighted as one of the most effective methods to capture the elasticity, plasticity, and fracture properties of nanostructures. MEMS stages can achieve nanometer-level displacement resolution and nano-Newton force sensitivity, allowing researchers to study fundamental size-dependent mechanical behaviors and deformation mechanisms of nanostructures [45‐48]. Such advancements have positioned MEMS as a critical tool for nanoscale mechanical characterization, enabling investigations that bridge atomistic computational models and experimental observations. However, MEMS platforms that can simultaneously achieve precise mechanical testing under controlled temperature management are still in its embryonic stages.
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Over the years, various MEMS platforms have been developed to address specific challenges in nanoscale tensile testing, each of which contributed valuable insights into the mechanical behavior of nanostructures under different conditions. A notable MEMS platform [49] introduced true displacement control, incorporating a thermal actuator [50] and an electrostatic feedback mechanism. This feedback control was critical to maintaining equilibrium at the sensor, preventing dynamic failure during load drops caused by yielding or necking. The design proved to be highly effective in capturing softening events in materials, significantly enhancing the resolution of stress–strain curves. This capability was validated through tensile testing of silver nanowires, where the system’s precision allowed detailed analysis of nanoscale material behavior. Advancement in MEMS design [51, 52] expanded the experimental scope by integrating an on-chip heater [53, 54], which enabled tensile testing of nanostructures at elevated temperatures. By employing multiphysics simulations, predictions of temperature distributions were obtained, which were experimentally validated via Raman spectroscopy. The platform enabled studies on temperature-dependent properties, such as the brittle-to ductile transition in silicon nanowires [37]. Relying solely on electrostatic actuation typically limits devices to force-controlled experiments, which precludes displacement-controlled testing, essential for capturing post-peak responses and mechanical instabilities. However, when integrated with active feedback control, electrostatic actuation can enable true displacement control [55].
Building upon these advancements and addressing the limitations of previous developments, we here present a novel MEMS platform specifically designed for in situ electron microscopy and X-ray measurements under thermomechanical loading. The MEMS device achieves simultaneous displacement control, precise load sensing, and localized temperature management. This is accomplished by integrating advanced design features that enable accurate and reliable control of both mechanical and thermal conditions, which mitigate issues associated with transient heat transfer and thermal drift. The design incorporates high-stiffness thermal actuators, Joule heaters, a capacitive displacement sensor, and an electrostatic actuator for feedback control. One of the major challenges faced during development was managing the complex transient heat transfer dynamics inherent to the SOIMUMPS [56] microfabricated structure. Silicon-on-Insulator (SOI) technology features a thin silicon device layer separated from the bulk silicon substrate by a buried silicon dioxide (SiO₂) layer. Heat conduction in this multilayer structure is inherently anisotropic, influenced by the contrasting thermal properties of the device layer, the buried oxide, and the substrate. The SiO₂ layer, in particular, acts as a thermal barrier, impeding heat dissipation from the device layer and leading to localized temperature increases. This necessitates precise thermal calibration to maintain stability and ensure accurate temperature control. Additionally, ensuring that temperature gradients did not interfere with the mechanical performance of the thermal actuator posed another challenge. We overcame these challenges using actuation protocols, based on meticulous calibrations, which enabled preventing thermal drift or mechanical instabilities that could affect the accuracy of the test results. The integration of the MEMS elements demanded a thorough understanding. This paper presents the design, calibration, and validation of the new MEMS system. To demonstrate the system capabilities, in situ SEM thermomechanical characterizations on silver nanowires [57] using the developed system are presented.
Design of the MEMS-based Thermomechanical Testing Device
The schematics of the in-situ SEM setup and an optical image of the MEMS device are shown in Fig. 1. The setup consists of two printed circuit boards (PCBs). The bottom PCB, fixed on the customized SEM stage, includes a voltage regulator, capacitive readout chip for force sensing, voltage amplifiers for temperature and displacement control and electrical connectors (Fig. 1b). The top PCB, which has the MEMS device wire-bonded to it, is connected to the bottom PCB using standard 2.54 mm pin connectors, enabling fast sample changes. The MEMS device (Fig. 1c) consists of a thermal actuator (TA), two sets of Joule heating folded beams (sample stage heaters), a differential capacitive force sensor, and an electrostatic actuator. All the above components are structurally connected to a central shuttle, for integrated performance of the MEMS. The V-shaped thermal actuator, consisting of 10 pairs of long inclined beams with a high structural stiffness, provides controlled displacement at the left end of the specimen. Heater 1, located on the thermal actuator side, consists of smaller folded beams and operates in tandem with the thermal actuator. The primary function of Heater 1 is applying controlled heating to one side of the sample stage while ensuring minimal mechanical and thermal interference between the thermal actuator and heaters. To ensure that, a specially designed U-shaped grip structure is introduced at the junction between the thermal actuator and Heater 1. Heater 2, located on the force sensor side, consists of longer folded beams with relatively lower structural stiffness. Its primary function is to provide localized heating while working alongside the force sensing element. The force is determined by converting the measured shuttle displacement into force using the structural stiffness. The displacement sensing mechanism relies on a comb-driven differential capacitive sensor, which consists of two fixed combs and a central shuttle. The shuttle is connected to the substrate with folded beams, whose stiffness was designed to achieve a desired force sensitivity [21].
Fig. 1
In situ thermomechanical testing setup. (a) Schematic of the thermomechanical MEMS platform installed inside an SEM chamber; (b) Schematic of customized PCB; (c) Optical image of the MEMS device
A key goal in the MEMS design is to achieve precise displacement control of tested nanomaterials during mechanical characterization. The thermal actuator fulfills this requirement by providing direct displacement, at one end of the sample, through thermal expansion-induced via Joule heating [50]. Heater 1 is connected to the thermal actuator and serves exclusively for displacement control; it does not affect force measurements. In contrast, Heater 2 contributes to the effective stiffness of the force sensor system, working in tandem with the sensor beams. The combined stiffness of the thermal actuator and Heater 1 is 37 kN/m, which is substantially greater than the stiffness of the force sensor system, comprising Heater 2 and the sensor beams, measured at 293 N/m. The tested silver nanowire exhibits an axial stiffness of approximately 400 N/m, closely matching the sensor stiffness but remaining significantly lower than the actuator’s stiffness. This capability is critical in nanoscale testing, where achieving the desired amount of displacement is necessary to study material properties under stable conditions, e.g., tensile strains. An alternative for actuation is the comb-driven actuator, which operates based on electrostatic forces. While the comb-driven actuator provides precise force application, which is a valuable characteristic for force-controlled tests, it encounters challenges in capturing fast nanoscale deformation phenomena, such as deformation localization, rapid crack propagation, and failure during tensile tests. Hence, while both options are useful, the choice depends on the scope of the study.
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In this work we focus on developing protocols and demonstrating the use of thermal actuation when conducting thermomechanical testing by means of sample thermal control using Joule heating folded beams. We note that true displacement control experiments also require feedback control of the displacement of the sample stage on the force sensor side. This is achieved via electrostatic actuation (see Fig. 1c). Such control is independent of the temperature control of the samples during thermomechanical characterization, which is the focus of this work. Therefore, we refer the reader to our previous work, where we reported the implementation of a feedback controller during the testing of nanowires exhibiting softening behavior [49].
Finite Element Analysis of designed MEMS
In this section, we provide a Finite Element Analysis (FEA) of the designed MEMS, to quantify displacement and temperature during nanoscale tensile testing. The analysis addresses both the thermal and mechanical behavior of the system, to illustrate important design considerations we incorporated to achieve performance goals. Temperature-dependent material properties for doped silicon are summarized in Table 1, including governing equations describing Joule heating, heat conduction, and thermal expansion as a function of temperature [58‐61]. These models provide a comprehensive framework for analyzing the coupled thermomechanical performance of the MEMS device.
Table 1
Temperature-Dependent Material Properties for Doped Silicon
In Table 1, the electrical resistivity \(\rho (T)\), thermal conductivity \(k\left(T\right)\), and thermal expansion coefficient \(\alpha (T)\) are expressed as functions of temperature, capturing the non-linear behavior of these properties over a range of operating conditions. The electrical resistivity \(\rho (T)\), increases approximately linearly with temperature, which is critical for predicting Joule heating effects in resistive materials. The thermal conductivity \(k\left(T\right)\), decreases with temperature, reflecting the reduced ability of silicon to conduct heat at higher temperatures due to increased phonon scattering. The thermal expansion coefficient \(\alpha (T)\), incorporates both exponential and linear terms to account for low- and high-temperature effects, enabling accurate predictions of thermal strain. These temperature-dependent relationships are fundamental for understanding the coupled thermal, electrical, and mechanical behaviors in MEMS devices operating under varying thermal conditions.
Coupled Multi-physics Equations
Equation (1) describes the heat transfer process in a resistive material subjected to Joule heating, accounting for both thermal conduction and electrical effects.
The first term on the left-hand side, \(\rho \left(T\right){C}_{p}\frac{\partial T}{\partial t}\) represents the transient temperature response of the material, where \({C}_{p}\) and \({\rm P}\left(T\right)\) are the specific heat capacity and density, respectively. The second term, \(-\nabla \bullet \left(k\left(T\right)\times \nabla T\right)\), accounts for heat conduction, with \(k\left(T\right)\) as the temperature-dependent thermal conductivity. Under steady-state conditions, the transient term is omitted, simplifying the equation. The right-hand side, J · E, represents the heat generation rate due to electrical current, where J and E are the current density and electric field strength, respectively. This equation links electrical and thermal phenomena, enabling the calculation of temperature distribution in doped silicon during operation, which is crucial for maintaining device reliability and thermal stability. The thermal strain induced in the material is described by Eq. (2). The strain \({\epsilon }_{heat}\), is calculated by integrating the thermal expansion coefficient \(\alpha \left(T\right)\), over the temperature range from the reference temperature \({T}_{ref}\) to the final temperature \({T}_{end}\). This formulation captures the cumulative dimensional changes caused by thermal effects, providing an accurate representation of mechanical strain in MEMS structures. Such calculations are essential for evaluating thermal-induced deformations that may influence the mechanical behavior of precision devices.
Design of the Sample Heaters
As described earlier, the samples are maintained at constant temperature using Joule heating folded beams. The shape of the folded beams is designed to counter the thermal displacements associated with temperature changes in various components of the device, which ensures desired displacement control on the specimen. Figure 2a and 2b show the voltage dependent displacement, indicated by an arrow, of the folded beams used in Heater 1 and Heater 2, respectively. Heater 1 has 4 pairs of folded Joule heating beams whereas, Heater 2 has 2 pairs of folded Joule heating beams. Even though the primary objective of the Joule heating beams is to heat up the sample stage, they also play a crucial role in minimizing any unnecessary loads on the sample caused by thermal expansion of the sample stage.
Fig. 2
Design of the Joule heating folded beams through finite element analysis. (a, b) Multi-physics analysis of structural behavior of folded beams arising from thermal expansion due to Joule heating
Referring to Fig. 1c, two important geometric constraints can be visualized for both heaters. First, the folding direction of the beams, after they originate from the substrate, is away from the sample stage. This design allows the folded beam to drive the sample stage in the opposite direction of the shuttle thermal expansion as it is heated. Second, for the shorter set of folded beams, they are located away from the sample stage, whereas the longer set of beams are near it. The shorter set of folded beams heat up more due to their relatively lower resistance, allowing them to provide higher displacement (thermal loads) compared to the longer beams (Fig. 2). The thermal expansion of the central shuttle gradually increases away from the sample stage; to compensate for this motion, the folded beams are displaced accordingly to avoid any residual stress at the junctions. This also helps in maintaining alignment and preventing mechanical instabilities during heater actuation. Hence, the Joule heating beams achieve the objective of applying temperature control over the sample stage along with the compensation of the thermal expansion of the central shuttle.
The balance between the thermal expansion of the central shuttle and the equivalent displacement generated by Joule heating in the beams is given by.
$$\frac{1}{2}{ L}_{shuttle} \alpha \left(T\right)\Delta T=\frac{{P}_{thermal} \times { L}^{3}}{12 E {I}_{beam}}$$
(3)
The left-hand side of the equation models the thermal expansion of the sample stage as the product of the shuttle length \({L}_{shuttle}\), the thermal expansion coefficient \(\alpha \left(T\right)\), and the temperature rise \(\Delta T\). The right-hand side defines the bending displacement of the beams, which is determined by the thermal force \({P}_{thermal}\), the effective length (inset table in Fig. 2a and b) of the set of folded beams \(L\), Young’s modulus \(E\), and the moment of inertia of the beam \({I}_{beam}\). It is to be noted that \({P}_{thermal}\) is considered as an effective remote force that acts at that end of the folded beams where it connects to the shuttle. This force can be estimated using the structural behavior of the beams when subjected to Joule heating, as shown in Fig. 2. This equation is useful for designing MEMS structures in which thermal expansion effects must be compensated to prevent undesirable deformation, ensuring stability and precise operation. Together, these equations and the temperature-dependent material properties summarized in Table 1 provide a comprehensive framework for modeling the thermal, electrical, and mechanical interactions in doped silicon-based MEMS devices. These relationships enable accurate predictions of device behavior under varying thermal and electrical conditions, which is critical for achieving reliable and efficient performance. Hence, the folded beams of the heaters work in a structurally coupled fashion to compensate for the thermal expansion of the central shuttle.
The FEA analyses summarized in Fig. 3 illustrate temperature gradients, and displacement responses across the sample stage of the MEMS device under various operating conditions. By using FEA with proper boundary conditions, we aimed to verify that the design achieves displacement control without unintended heating effects on the sample, which is needed for nanoscale testing accuracy. It is to be noted that the thermal actuator and Heater 1 are structurally disconnected when the sample stage is heated prior to application of load on the sample. This was achieved by incorporating a U-shaped grip structure, which will be discussed later. The grip structure allows Heater 1 to drive the shuttle to compensate for the thermal expansion, as it is heated, without structural interference from the thermal actuator. Meanwhile, when the thermal actuator is activated, it engages the sample stage and apply tensile force on the sample. In other words, its structural design allows the sample to be locally heated to a prescribed temperature, without any strain being applied on it before mechanical loading.
Fig. 3
Finite element analysis of the heaters to achieve 300 °C at the sample stage. (a, d) Voltage gradient over the integrated heater structures. (b, e) Temperature gradient over the integrated heater structures due to Joule heating. (c, f) Deformation gradient over the integrated heater structures due to coupled thermal expansion of the folded beams
During the study we found that an important feature of the FE analysis is the choice of boundary conditions. All the Joule heating elements, including Heater 1, Heater 2, and the thermal actuator, are structurally connected to a substrate that acts as a heat sink. In the FEA analysis, we have considered these connections as the boundaries for voltage application, constant temperature (heat sink), and structural fixed. Hence, the substrate efficiently dissipates heat generated by the heating elements. By relying on this heat sink, the overall temperature distribution remains stable, and the temperature of the sample is primarily controlled by the heaters.
Figure 3a and d depict the voltage gradients for Heater 1, and Heater 2, respectively, ranging from −2.5 V to + 2.5 V for Heater 1 and −4 V to + 4 V, for Heater 2. This symmetrical voltage application is critical for maintaining a neutral potential on the central shuttle, preventing current flow through conductive samples. This voltage balancing approach highlights the importance of electrical insulation and symmetry in our design, as it ensures that the sample stage remains isolated from any electrical interference, enhancing measurement accuracy for conductive samples.
Fig. 3b and e display the temperature gradients for Heater 1 and Heater 2, respectively. When both heaters are activated, thermal energy is generated along the Joule heating folded beams, creating a gradient with a maximum of 246 °C for Heater 1 and 322 °C for Heater 2 at the prescribed voltages. This gradient is necessary to achieve the thermal expansion needed for precise tensile control. The applied voltages were determined from experimental calibrations to achieve a sample temperature of 300 °C. Simulations indicate that the shuttle maintains a uniform temperature distribution. To validate this, we measured the heater temperature using Raman spectroscopy under vacuum conditions. Although minor radiative heat losses may occur, their impact is negligible due to the continuous power input to the heaters. Furthermore, resistance-based temperature measurements, detailed in Section “Temperature Control and Calibration,” corroborate the accuracy of our thermal estimations.
Figure 3c and f display the displacement gradients corresponding to the thermal expansion of the heaters. These displacement maps are color-coded to show the relative movement across the device, with a positive or negative gradient indicating motion direction. The green areas on the central shuttle in both figures indicate a relative displacement within −10 nm at the sample stage (negative sign corresponds to closing of the sample stage gap). This outcome is crucial, as it ensures that no additional tensile or compressive forces are unintentionally applied to the sample due to thermal expansion. For nanoscale testing, maintaining this displacement stability at the sample stage is challenging but critical, as any unintended force could lead to inaccurate measurements of material properties. This ability to independently control the thermal and mechanical effects avoids additional requirements for complex control during the thermal–mechanical test.
To illustrate the coupled behavior of the thermal actuator and the heaters, the FEA predicted temperature gradient is shown in Fig. 4a. Heat generation by the thermal actuator influences the temperature gradient across the heaters, potentially impacting their performance. For example, when Heater 1 operates independently, a 5 V potential difference applied to it heats up the sample stage to 240 °C. However, when the thermal actuator is actuated, the sample stage temperature increases. At a displacement of approximately 1.4 µm with a 6 V actuation voltage (Fig. 4c), the sample stage temperature rises by 50 °C. Figure 4b highlights the importance of Heater 1 functioning independently while heating the sample stage. The stand-alone heater folded beams were able to compensate for the thermal expansion (Fig. 3c). Without a structural discontinuity between Heater 1 and the high-stiffness thermal actuator, heating the sample stage could lead to a reduction in the sample stage gap up to 100 nm. To address these challenges, special structural designs and detailed experimental calibrations were developed, as described in subsequent sections.
Fig. 4
Finite element analysis depicting the coupled performance of thermal actuator and sample heaters. (a) Temperature gradient over the MEMS depicting the heating effect of the thermal actuator on the sample stage while performing alongside the heaters. (b) Performance of Heater 1 when it is structurally bonded with the thermal actuator. (c) Displacement of the sample stage with 6 V actuation voltage and 5 V heater voltage
For the designed MEMS architecture, achieving precise temperature control is essential for the accurate performance of the thermal actuator, the heaters, and the displacement sensor. Moreover, the ability to maintain precise temperature control is essential for testing nanomaterials, as these materials often exhibit size-dependent properties that are sensitive to temperature variations. For example, thermal expansion, thermal conductivity, and phase transitions can be influenced by even minute changes in temperature. Moreover, nanomaterials often have high surface-to-volume ratios, which make them more susceptible to surface energy effects that are also sensitive to temperature. Therefore, ensuring that temperature is maintained within a narrow range throughout testing is critical to obtaining mechanistic insights that accurately reflect the true nanomaterial mechanical and thermal properties. By combining Raman calibration, Joule heating, dynamic resistance measurement, and real-time voltage adjustment, we established a protocol to precisely control temperature throughout testing. We next report some examples of the robust temperature control being achieved.
Initial Calibration Using Raman Spectroscopy
Raman is a well-established technique that enables non-invasive temperature measurement by analyzing peak shifts in the spectra. First, the fabricated MEMS device was placed in an environmental chamber with temperature control (Linkam, FTIR600). A Raman system (Horiba LabRam HR800) with a 532 nm laser was used to obtain precise local temperature measurements of the MEMS structure. Using the environmental chamber’s heating stage, the MEMS device was uniformly heated to a target temperature. Once the heating stage stabilized at the set temperature, a Raman spectrum was collected, as shown in Fig. 5b. During this process, Raman peaks at different temperatures were recorded to establish a calibration curve, as shown in Fig. 5c.
Fig. 5
Temperature vs. voltage calibration through Raman spectroscopy for MEMS heaters. (a) Schematic of the vacuum chamber setup for Raman measurement. (b) Raman spectrum of MEMS sample stage at different temperatures. (c) Raman peak position variation with increasing temperature for the thermomechanical MEMS device. (d) Sample stage temperature, heated by Heater 1 and Heater 2, as a function of input voltage
Second, the voltage-temperature response of the MEMS device (Fig. 5d) was calibrated with the setup shown in Fig. 5a. The MEMS device was mounted on a piezo positioning stage within a vacuum chamber. The vacuum chamber was evacuated to 5×10−5 Torr with a turbo pump (Pfeiffer Vacuum) to replicate SEM vacuum conditions. The electrical feedthroughs were used to control the piezo stage and apply voltage inputs to the MEMS device. Heater 1 and Heater 2 were independently heated, and the temperature on each side of the sample stage was measured. To mitigate residual heating effects from prior thermal cycles, we incorporated adequate cooling intervals between calibration experiments. Our results indicate that extended thermal cycling can lead to heat accumulation within the MEMS structure. By allowing sufficient rest periods between tests, we ensured consistent and reproducible voltage–temperature calibration throughout the thermomechanical experiments.
U-shaped Grip to Achieve Thermal Insulation
As discussed earlier, heat generation by the thermal actuator and folded beam heaters can influence each other’s performance. To address this, careful thermal management was implemented to minimize additional heat flow into the shuttle connected to Heater 1. Specifically, we employed the U-shaped grip design shown in Fig. 6a. By reducing the contact area between the shuttles connected to the thermal actuator and Heater 1, through focused ion beam (FIB) manufacturing, direct heat transfer through the suspended MEMS structures of the thermal actuator and Heater 1 was minimized during experiments. This design ensures a stable and controlled thermal environment around the sample, enabling precise and reliable testing conditions. To verify the thermal insulation performance of the grip structure, a series of Raman temperature tests was conducted to evaluate the temperature influence between the thermal actuator and the heaters. During the tests, a constant voltage was applied to the heaters to maintain a temperature of 300 °C. Then, voltage was applied to the thermal actuator, and at each voltage level, Raman measurements were performed to determine the temperatures of the central shuttle near the thermal actuator, Heater 1, and Heater 2, as shown in Fig. 6b. As the temperature of the thermal actuator increased, the sample stage temperature also rose gradually. At approximately 2.5 V, the U-shaped grip engaged, as shown by the bottom right figure in Fig. 6a and marked by the green line in Fig. 6b. No sharp transitions were observed at this point, indicating that the heat flow from the grip structure was minimal.
Fig. 6
U-shaped grip to minimize thermal transport. (a) SEM image of the U-shaped heat insulation grip structure after FIB cutting of wedge tips. (b) Sample stage temperature variation at Heater 1 and Heater 2 as a function of thermal actuator temperature across the grip. The inset shows a schematic of heat transfer through the substrate
However, the grip structure could not entirely maintain the sample stage temperature at 300 °C. Although the thermal actuator, Heater 1, Heater 2, and the load sensor were not directly connected, they rested on the same substrate, which acted as a potential heat sink. When the thermal actuator was energized, it began heating the substrate, which subsequently affected the temperatures of surrounding structures, including the heaters. To account for this effect, a strategy was developed to continuously adjust the heater voltages based on the thermal actuator’s temperature. Since the temperature changes of the thermal actuator and the heat transfer between the thermal actuator and the heaters are dynamic processes, characterizing the temperature using Raman spectroscopy is challenging due to its low temporal resolution. Therefore, a real-time temperature characterization method was implemented to address this issue.
Heater Voltage Calibration With Resistance Measurements
To overcome the temporal limitations of the Raman spectroscopy calibration, we leveraged the temperature dependent resistance of the N-doped silicon used in the MEMS. The resistance of the doped silicon is known to change with temperature, which allowed us to build a more precise temperature control mechanism. Using the circuit shown in Fig. 7a, we could measure the resistance of the heaters, using Eq. (4), and deduce the temperature based on the known temperature-resistance characteristics of the doped silicon.
Fig. 7
Temperature calibration of the MEMS heaters through resistance measurements. (a) Schematic of the circuit used to measure resistance in the heaters. (b) Resistance variation of Heater 1 and Heater 2 with increasing voltage. (c) Resistance variation of Heater 1 and Heater 2 with increasing sample stage temperature
At this stage, we transitioned from using a voltage vs. temperature calibration curve to a voltage vs. heater resistance curve, as shown in Fig. 7b. This adjustment was critical, as the resistance of the heaters was more directly correlated with the applied voltage and could be monitored in real time. By combining the voltage vs. heater temperature relationship obtained from Raman measurements with the voltage vs. heater resistance relationship derived from resistance tests, we established a calibration curve for the relationship between temperature and heater resistance, as shown in Fig. 7c.
Using the resistance–temperature calibration curve, we were able to continuously adjust the heater voltages during the experiment and acquire the real-time sample stage temperature, as shown in Fig. 8. The primary goal was to maintain a constant resistance across the heaters, thereby ensuring that the specimen temperature remained stable throughout the test. Since the thermal actuator temperature has a dynamic and nonlinear influence on the sample stage temperature, we performed heater voltage calibrations for two heater temperatures (60 °C and 300 °C) and a thermal actuator loading rate of 2 nm/s as a case study. During the loading cycle, as the thermal actuator strained the sample, the temperature at the sample stage increased. Since the thermal actuator functions as a Joule heating element, a larger applied displacement results in greater heat transfer through the substrate. To compensate for this, we developed calibration voltage curves for the heaters following a two-step approach. First, we monitored the resistance (temperature) changes of the heaters as the thermal actuator operated at a desired displacement rate. Next, we utilized our previously established heater performance curves (Fig. 5d and Fig. 7b) as inverse data feedthroughs to control the real-time temperature of the heaters. The reduction in heater voltages (red curves in Fig. 8) effectively counterbalanced the additional heat generated by the thermal actuator, ensuring that the resistance of the heaters remained constant and the temperature stable. Once the loading cycle was completed and the system transitioned into the unloading phase, the displacement applied by the thermal actuator decreased, resulting in reduced heat generation. During this phase, we gradually increased the heater voltages to compensate for the reduced heat contribution from the thermal actuator.
Fig. 8
Heater voltage calibration during loading–unloading thermal actuation. (a, b) Plots of thermal actuation, with a displacement rate of 2 nm/s, during loading and unloading. Sample stage temperature is maintained, within 300 ± 4 °C, by adjusting the voltages of Heaters 1 and 2 respectively
The MEMS temperature control was validated through the melting of tin microballs and thermomechanical testing of silver nanowires. The heating control and accuracy was confirmed by observing the wrinkled to smooth surface transition when tin microballs were slowly heated. Fusion of two microballs was observed when the melting temperature was reached. Furthermore, thermomechanical testing of silver nanowires revealed a consistent reduction in yield stress. These results confirm the MEMS platform’s reliability for precise thermomechanical testing of nanoscale materials.
In Situ Tin Microball Melting
To confirm accurate control of sample temperature, microballs made of a low-melting-point alloy (Sn/Ag/Cu) were tested. The MEMS sample stage at the location of the microballs were heated until melting occurred. Two tin microballs were dry transferred onto the MEMS shuttles and positioned in contact with each other with a micromanipulator, as shown in Fig. 9a. The MEMS shuttle was then heated to the alloy melting temperature (217 °C) based on the calibration data. When the temperature reached approximately 220 °C, the wrinkled surface morphology of the microballs transitioned to a smooth appearance, indicating the onset of melting (Fig. 9b). Upon further temperature increase, by about 50 °C, the two tin microballs fused into one, as shown in Fig. 9c.
Fig. 9
Controlled melting of tin alloy microballs. (a) Two tin microballs placed side by side on the MEMS shuttle. Wrinkled surfaces are clearly visualized. (b) After reaching a temperature near the melting point, the wrinkled surfaces become smooth. (c) The two microballs fuse upon further temperature increase, an indication of melting
Silver nanowires are promising candidates for next-generation electronics, including flexible electronics, displays, and sensors, due to their high electrical conductivity. These applications may demand high currents and stress; hence, investigation of their thermomechanical properties is needed.
Here we investigate silver nanowires synthesized on a silicon substrate by means of chemical vapor deposition (CVD). To prevent silver oxidation, a 20-nm gold layer was deposited on their surface via physical vapor deposition (PVD). The nanowires were transferred onto a MEMS device using a dry transfer technique. A probe station integrated with a micro-manipulator (the Micromanipulator Company) was used to precisely pick up individual silver nanowires and position them on the MEMS device. To ensure stability and secure attachment during testing, the nanowires were fixed onto the movable shuttle using platinum (Pt) deposition. Tensile tests were subsequently conducted on the silver nanowires in situ SEM (ThermoFisher, Scios 2).
Using the newly developed in-situ SEM thermomechanical testing platform, quasi-static uniaxial tensile tests were performed on silver nanowires (Fig. 10) at low temperature (60 °C), high temperature (300 °C), and near their melting point (∼950 °C). Before each tensile test, a pre-calibrated voltage was applied to the heater to raise the sample temperature, allowing it to stabilize for 10 minutes. Two Pt fiducial markers were deposited near the sample for digital image correlation (DIC). During the test, the thermal actuator voltage gradually increased to maintain a loading rate of 2 nm/s. The voltage applied to the heaters was adjusted according to the calibration to maintain a constant temperature. The deformation of the silver nanowire throughout the tensile and failure processes was recorded using SEM imaging. As shown in Fig. 10a, the stress-strain behavior at 60 °C and 300 °C was very similar. The modulus and yield strength of the silver nanowires were approximately 80 GPa and 1 GPa, respectively. Notably, the silver nanowires did not exhibit significant changes in the early plastic regime, as temperature increased from 60 °C to 300 °C, other than a slight increase in ductility. In contrast, tensile tests conducted at ~950 °C, near the melting point of silver, exhibited a distinct behavior with a significant drop in yield strength and necking. Slight differences in the measured elastic modulus may result from uncertainty in determining the nanowire’s cross-sectional dimensions. At this temperature, the Young’s modulus almost remained unchanged, but the yield strength decreased from 1 GPa to 0.6 GPa, followed by an extended plastic deformation up to 2.7%. To reach 950 °C, localized Joule heating was applied directly to the nanowire by introducing a potential difference across its ends, supplementing the external sample heater. This localized approach confines the thermal exposure to the nanowire, thereby preventing significant heating of surrounding Pt or Si components that could otherwise lead to changes in physical properties (e.g., plastic deformation) or undesired chemical reactions. Because of the unknown resistivity of the silver nanowire, Pt bonding, and contact to the MEMS shuttle, we report an estimated temperature. The experimental protocol allowed the temperature of the silver nanowire to be controlled from room temperature to near its melting point. We also accounted for potential asymmetries introduced during fabrication, particularly those arising from FIB-cut edges (Fig. 6a), and implemented measures to minimize their impact. Experimental observations show that while transverse deflections can induce minor shear stresses due to bending, these are over an order of magnitude smaller than the axial tensile stresses applied to the nanowires.
Fig. 10
Tensile testing of silver nanowires using the new MEMS. (a) Stress–strain curves at three temperatures. (b) SEM image of a fractured nanowire at 300o C. (c) Silver nanowire melting through Joule heating
This work presents a novel MEMS-based thermomechanical in-situ characterization platform designed to address the critical need for precise testing of nanomaterials under coupled thermal and mechanical loading conditions. The MEMS device features a high-stiffness thermal actuator, independent Joule heating elements, and a capacitive displacement sensor, enabling displacement-controlled tensile testing. Through systematic calibration and experimental validation, the platform achieves accurate and stable control of both temperature and displacement, overcoming challenges such as substrate heating and transient heat transfer that complicate nanoscale testing. The MEMS device leverages several key innovations, including Joule heating folded beam that allow precise heating with zero structural thermal expansion, and a FIB-fabricated U-shaped grip that ensures thermal isolation and the structural integrity of the sample during experiments. Finite Element Analysis provides insights and quantification of thermal and mechanical behaviors across the MEMS components, while experimental measurements reveal agreement with the FEA predictions, and validate the device functionality. A comprehensive characterization of the MEMS platform, including temperature and mechanical calibration, together with the establishment of a protocol for thermal management, during loading and unloading phases, provides a robust method for experimental investigation of nanomaterials. The measured temperature-dependent mechanical behavior of silver nanowires underscores the critical role of thermal and surface effects in determining their deformation and failure mechanisms. These findings demonstrate the capability of the MEMS platform to explore such phenomena in detail.
The novel MEMS platform is envisioned as an important tool for the thermomechanical investigating of size-dependent phenomena in nanomaterials, such as phase and brittle-to-ductile transitions, thermal softening effects, and temperature dependent fracture in low dimensional materials. Its ability to combine displacement control with localized temperature management makes it an invaluable tool for advancing the understanding of nanoscale deformation mechanisms. Future work will focus on integrating the platform with additional in situ techniques, such as X-ray microscopy, to further enhance its capabilities and broaden its applications to material science and nanotechnology.
Declarations
Competing Interest
All authors declare that they have no conflicts of interest.
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