The spin-Seebeck effect mediated thermoelectric energy conversion can provide efficient alternative to traditional thermoelectrics for waste heat recovery. To achieve this goal, efficient spin to charge conversion using earth-abundant materials is essential. Proximity induced Rashba effect arises from the charge potential mediated by structural inversion asymmetry, which has been reported in Si thin films and can be manipulated by controlling the thickness of Rashba layer. We demonstrate a giant Rashba spin-Seebeck effect in NiFe/p-Si (polycrystalline) bilayer thin films. The bilayer thin film specimens have p-Si layer thickness of 5 nm, 25 nm and 100 nm while keeping the NiFe layer thickness at 25 nm. The Rashba spin Seebeck coefficient has been estimated to be 0.266 μV/K for 100 nm p-Si, and increases by an order of magnitude to 2.11 μV/K for 5 nm p-Si. The measured spin-Seebeck coefficient in 5 nm p-Si specimen is one of the largest coefficient ever reported. The measured voltage of 100.3 µV is one of the largest reported spin-Seebeck voltage, with smallest area of ~160 X 10 µm2 used in any spin-Seebeck measurement. This scientific and technological breakthrough using earth abundant elements brings the spin mediated thermoelectric energy conversion for waste heat recovery closer to reality.
Spintronics is an analogue to electronics where spin of the electron rather than its charge is functionally controlled for devices. The generation and detection of spin current without ferromagnetic or exotic/scarce materials are two the biggest challenges for spintronics devices. In this study, we report a solution to the two problems of spin current generation and detection in Si. Using non-local measurement, we experimentally demonstrate the generation of helical dissipationless spin current using spin-Hall effect. Contrary to the theoretical prediction, we observe the spin-Hall effect in both n-doped and p-doped Si. The helical spin current is attributed to the site-inversion asymmetry of the diamond cubic lattice of Si and structure inversion asymmetry in MgO/Si bilayer. The spin to charge conversion in Si is insignificant due to weak spin-orbit coupling. For the efficient detection of spin current, we report spin to charge conversion at the MgO (1nm)/Si (2 µm) (p-doped and n-doped) thin film interface due to Rashba spin-orbit coupling. We detected the spin current at a distance of >100 µm, which is an order of magnitude larger than the longest spin diffusion length measured using spin injection techniques. The existence of spin current in Si is verified from coercivity reduction in Co/Pd multilayer due to spin-orbit torque generated by spin current from Si.
The development of spintronics and spin-caloritronics devices need efficient generation, detection and manipulation of spin current. The thermal spin current from spin-Seebeck effect has been reported to be more energy efficient than the electrical spin injection methods. But, spin detection has been the one of the bottlenecks since metals with large spin-orbit coupling is an essential requirement. In this work, we report an efficient thermal generation and interfacial detection of spin current. We measured a spin-Seebeck effect in Ni80Fe20 (25 nm)/p-Si (50 nm) (polycrystalline) bilayers without heavy metal spin detector. The p-Si, having the centosymmetric crystal structure, has insignificant intrinsic spin-orbit coupling leading to negligible spin-charge conversion. We report a giant inverse spin-Hall effect, essential for detection of spin-Seebeck effect, in the Ni80Fe20/p-Si bilayer structure, which originates from Rashba spin orbit coupling due to structure inversion asymmetry at the interface. In addition, the thermal spin pumping in p-Si leads to spin current from p-Si to Ni80Fe20 layer due to thermal spin galvanic effect and spin-Hall effect causing spin-orbit torques. The thermal spin-orbit torques leads to collapse of magnetic hysteresis of 25 nm thick Ni80Fe20 layer. The thermal spin-orbit torques can be used for efficient magnetic switching for memory applications. These scientific breakthroughs may give impetus to the silicon spintronics and spin-caloritronics devices.
Spin current experiences minimal dephasing and scattering in Si due to small spin-orbit coupling and spin-lattice interactions is the primary source of spin relaxation. We hypothesize that if the specimen dimension is of the same order as the spin diffusion length then spin polarization will lead to non-equilibrium spin accumulation and emergent phase transition. In n-Si, spin diffusion length has been reported up to 6 μm. The spin accumulation in Si will modify the thermal transport behavior of Si, which can be detected with thermal characterization. In this study, we report observation of spin-Hall effect and emergent antiferromagnetic phase transition behavior using magneto-electro-thermal transport characterization. The freestanding Pd (1 nm)/ Ni80Fe20 (75 nm)/ MgO (1 nm)/ n-Si (2 µm) thin film specimen exhibits a magnetic field dependent thermal transport and spin-Hall magnetoresistance behavior attributed to Rashba effect. An emergent phase transition is discovered using self-heating 3 method, which shows a diverging behavior at 270 K as a function of temperature similar to a second order phase transition. We propose that spin-Hall effect leads to the spin accumulation and resulting emergent antiferromagnetic phase transition. We propose that the length scale for Rashba effect can be equal to the spin diffusion length and two-dimensional electron gas is not essential for it. The emergent antiferromagnetic phase transition is attributed to the site inversion asymmetry in diamond cubic Si lattice.
The entanglement of the charge, spin and orbital degrees of freedom can give rise to emergent behavior especially in thin films, surfaces and interfaces. Often, materials that exhibit those properties require large spin orbit coupling. We hypothesize that the emergent behavior can also occur due to spin, electron and phonon interactions in widely studied simple materials such as Si. That is, large intrinsic spin-orbit coupling is not an essential requirement for emergent behavior. The central hypothesis is that when one of the specimen dimensions is of the same order (or smaller) as the spin diffusion length, then non-equilibrium spin accumulation due to spin injection or spin-Hall effect (SHE) will lead to emergent phase transformations in the non-ferromagnetic semiconductors. In this experimental work, we report spin mediated emergent antiferromagnetism and metal insulator transition in a Pd (1 nm)/Ni81Fe19 (25 nm)/MgO (1 nm)/p-Si (~400 nm) thin film specimen. The spin-Hall effect in p-Si, observed through Rashba spin-orbit coupling mediated spin-Hall magnetoresistance behavior, is proposed to cause the spin accumulation and resulting emergent behavior. The phase transition is discovered from the diverging behavior in longitudinal third harmonic voltage, which is related to the thermal conductivity and heat capacity.
In Si, spin-phonon interaction is the primary spin relaxation mechanism. At low temperatures, the absence of spin-phonon relaxation will lead to enhanced spin accumulation. Spin accumulation may change the electro-thermal transport within the material, and thus may serve as an investigative tool for characterizing spin-mediated behavior. Here we present the first experimental proof of spin accumulation induced electro-thermal transport behavior in a Pd (1 nm)/Ni80Fe20 (25 nm)/MgO (1 nm)/p-Si (2 µm) specimen. The spin accumulation originates from the spin-Hall effect. The spin accumulation changes the phononic thermal transport in p-Si causing the observed magneto-electro-thermal transport behavior. We also observe the inverted switching behavior in magnetoresistance measurement at low temperatures in contrast to magnetic characterization, which is attributed to the canted spin states in p-Si due to spin accumulation. The spin accumulation is elucidated by current dependent anomalous Hall resistance measurement, which shows a decrease as the electric current is increased. This result may open a new paradigm in the field of spin-mediated transport behavior in semiconductor and semiconductor spintronics.
For decades silicon has been the workhorse material for electronic devices, and the semiconductor industry has mastered exquisite control of its electronic properties. With this history of development, and due to its relatively slow spin relaxation, Si is also anticipated to be the principal material for the next generation of spintronics devices. A central requirement for spintronics devices is the generation of a pure spin current, with the spin-Hall effect considered to be more efficient for this than other methods such as injection of spin from a ferromagnetic source. P-doped silicon (p-Si) is predicted to exhibit the spin Hall effect, but to date there has been no convincing experimental evidence to confirm this, nor any practical demonstration of its use. In this article we report the interaction and coupling of spin, charge, and heat transport in p-Si. The spin Hall angle in p-Si is 10-4, which leads to insignificant spin-Hall magnetoresistance, complicating the use of traditional Hall bar spintronics characterization. Instead, we use signatures in the magneto thermal transport to reveal the spin Hall effect in p-Si. Specifically, we used well established third harmonic based resistance thermometry methods (3ω method) which is facilitated by the use of free standing experimental set-ups developed using nanofabrication. We observe magneto-thermal transport behavior, which is analogous to spin Hall magnetoresistance and is called spin Hall magneto thermal resistance, or SMTR. Raman spectroscopy measurements and simulations support the conclusion that the spin-phonon interactions are the underlying mechanism for the observed behavior. The spin-phonon interactions, presented in this work, may allow thermal manipulation of spin current, which is essential for energy-efficient spintronics, spin caloritronics and energy conversion applications.
In this work, we present an experimental study of spin mediated enhanced negative magnetoresistance in Ni80Fe20 (50 nm)/p-Si (350 nm) bilayer. The resistance measurement shows a reduction of ~2.5% for the bilayer specimen as compared to 1.3% for Ni80Fe20 (50 nm) on oxide specimen for an out-of-plane applied magnetic field of 3T. In the Ni80Fe20-only film, the negative magnetoresistance behavior is attributed to anisotropic magnetoresistance. We propose that spin polarization due to spin-Hall effect is the underlying cause of the enhanced negative magnetoresistance observed in the bilayer. Silicon has weak spin orbit coupling so spin Hall magnetoresistance measurement is not feasible. We use V2ω and V3ω measurement as a function of magnetic field and angular rotation of magnetic field in direction normal to electric current to elucidate the spin-Hall effect. The angular rotation of magnetic field shows a sinusoidal behavior for both V2ω and V3ω, which is attributed to the spin phonon interactions resulting from the spin-Hall effect mediated spin polarization. We propose that the spin polarization leads to a decrease in hole-phonon scattering resulting in enhanced negative magnetoresistance.
In this work, we report reversible reduction in coercivity of Co/Pd multilayer thin films under high-density direct current biasing. We carried out in-situ focused magneto optic Kerr effect based hysteresis measurement while the specimen was under DC bias. The experiments show a reversible reduction in coercivity during the application of direct current. We propose this reduction occurs due to the field like spin-orbit torque generated by spin Hall effect. These results are further supported by the anomalous Hall effect measurement, which do not show any change in coercivity. The magneto-optic Kerr measurement probes the surface (penetration depth) whereas anomalous Hall effect is a bulk transport behavior. These complimentary measurements prove that the origin of spin-orbit torques in ferromagnetic metal/ heavy metal multilayer thin films is spin-Hall effect. .
In this work, we present a MEMS-based in-situ TEM experimental setup for high-temperature uniaxial tensile behavior of nanocrystalline thin films. This setup utilizes self-heating (Ohmic) to raise the temperature of thin films while applying uniaxial tensile loading using electro-thermal actuators. Self-heating is achieved by passing a high-density direct current through the specimen. We carried out a qualitative uniaxial tensile experiment on a 75 nm platinum thin film at 360 K. Temperature is estimated using COMSOL modeling. In this qualitative experiment, we observed initial grain growth followed by formation of edge serrations. We propose that GB sliding coupled with grain growth is the underlying mechanism responsible for the observed behavior. .
In this work, we present the experimental results on the effect of electric current-induced diffusion leading to change in ferromagnetic behavior of Co/Pd multilayer thin films. We applied high-density direct current to a Co/Pd multilayer specimen in ambient conditions. We observed an almost 8.8 times change in coercivity and improved squarness of the thin films using magneto-optic Kerr effect measurement. Magnetic force microscope studies further validates an increase in coercivity for the current-treated thin films. We experimentally observe that this change cannot be attributed to only to Joule heating due to electric current. We propose that the underlying mechanism for the observed behavior is electromigration induced diffusion along the grain boundaries and the thin film surface. Surface diffusion of O2 leads to formation of CoO resulting in permanent coercivity change observed in this work. The composition of the specimens is Ta (1nm) / [Co (0.35 nm) / Pd (0.55nm)]20.
In bulk metals, mechanical strain is known not to influence electrical and thermal transport. However, fundamentally different deformation mechanisms and strain localization at the grain boundaries may influence electron or phonon scattering in nanocrystalline materials. To investigate this hypothesis, we developed an experimental approach, where we performed thermal and electrical conductivity measurements on 100 nm thick freestanding nanocrystalline aluminum films with average grain size of 50 nm in situ inside a transmission electron microscope (TEM). We present experimental evidence of decrease in thermal conductivity and increase in electrical resistivity as a function of uniaxial tensile strain. In-situ TEM observations suggest that grain rotation induced by grain boundary diffusion, and not dislocation-based plasticity, is the dominant deformation mechanism in these thin films. We propose that diffusion causes rise in oxygen concentration resulting in increased defects at grain boundaries. Presence of oxygen only at the grain boundaries is confirmed by energy dispersive spectroscopy. Increased defect concentration by mechanical strain at grain boundary causes the change in thermal and charge transport. .
Micro-electro-mechanical systems (MEMS) based techniques can outperform conventional materials characterization tools in terms of specimen size and resolution. In addition, multi-functioning as well as access to analytical microscopy is also feasible for complete multi-physics characterization. We present the design and fabrication of a versatile tool that can perform mechanical, electrical and thermal characterization of nanoscale freestanding thin films. The tool is smaller than 3mm x 5mm and is compatible with virtually all types of analytical chambers. This feature allows 'in-situ' studies inside electron microscopes for real time acquisition of composition, microstructure and defect evolution and dynamics data. The unique advantage of such simultaneous acquisition of quantitative and qualitative data can be realized through accurate and quick 'observation-based' modeling of materials behavior. We present preliminary studies on multiphysics, as well as single domain characterization to demonstrate the novel experimental technique. .
Existing models for thermoelastic damping consider geometric size effects only, the focus of this study is on tuning of thermoelastic damping with mechanical strain, which reduces both relaxation rate and thermal conductivity at the nanoscale. We developed a model that accounts for the contribution of tensile force and thermal conductivity in a clamped-clamped configuration nano-resonator. Experimentally measured thermal conductivity is then coupled with the model suggests the existence of a critical length scale (inversion point) below which quality factor increases with increase in thickness and vice versa. The nanoscale strain-thermal conductivity coupling is found to be most effective at and around this inversion point .
We present a quantitative in-situ transmission electron microscope (TEM) study of stress-assisted grain growth in 75 nm thick platinum thin films. We utilized notch-induced stress concentration to observe the microstructural evolution in real time. From quantitative measurements, we find that rapid grain growth occurred above 290 MPa of far field stress and ~0.14% elongation. This value is found to be higher than that required for stable interface motion but lower than the stress required for unstable grain boundary motion. We attribute such grain growth to geometrical incompatibility arising out of crystallographic misorientation in adjoining grains, or in other words, geometrically necessary grain growth.
Pure bulk metals do not exhibit solid–solid phase transformation since they deform and fail far below the required stress levels for phase transformation, which exceeds hundreds of GPa. We propose that for certain grain size, thickness and notch geometry, classical deformation modes can be suppressed to induce phase transformation in pure metal films at stresses few orders of magnitude lower than the theoretical values. For the first time, we present in situ transmission electron diffraction evidence of face-centered cubic (FCC) to hexagonal ω phase transformation in 99.99% pure nanocrystalline aluminum at room temperature and only 2.5 GPa of tensile stress. For 60 nm average grain size, the aluminum films did not show any appreciable diffusion-based processes such as grain growth, rotation and sliding. At the same time, the 200 nm thick specimens are thin enough for the dislocations to escape through the surface. With no active dislocation sources, in situ microscopy did not show any dislocation-based deformation either. Facilitated by the absence of dislocation and diffusion based processes, the uniaxial nature of specimen loading results in phase transformation at stresses two orders of magnitude lower than that predicted for aluminum. We also propose that phase transformation can result in a flaw tolerance in the material.
The trend of miniaturization has highlighted the problems of heat dissipation and electromigration in nanoelectronic device interconnects, but not amorphization. While amorphization is known to be a high pressure and/or temperature phenomenon, we argue that defect density is the key factor, while temperature and pressure are only the means. For nanoscale interconnects carrying modest current density, large vacancy concentrations may be generated without the necessity of high temperature or pressure due to the large fraction of grain boundaries and triple points. To investigate this hypothesis, we performed in situ transmission electron microscope (TEM) experiments on 200 nm thick (80 nm average grain size) aluminum specimens. Electron diffraction patterns indicate partial amorphization at modest current density of about 105 A cm−2, which is too low to trigger electromigration. Since amorphization results in drastic decrease in mechanical ductility as well as electrical and thermal conductivity, further increase in current density to about 7 × 105 A cm−2 resulted in brittle fracture failure. Our molecular dynamics (MD) simulations predict the formation of amorphous regions in response to large mechanical stresses (due to nanoscale grain size) and excess vacancies at the cathode side of the thin films. The findings of this study suggest that amorphization can precede electromigration and thereby play a vital role in the reliability of micro/nanoelectronic devices.
It is well established that stress concentration (or strain gradient) is developed ahead of a crack or flaw, whose magnitude depends upon the extent of crack tip plasticity. Ductile materials exhibit strong grain size effects on deformation mechanisms at the nanoscale, yet very little is known about the size effects on stress concentration or fracture. In this paper, we present a unique experimental setup that directly visualizes crack tip deformation using transmission electron microscopy (TEM) while applying and measuring tension in nanoscale freestanding thin films. In-situ TEM experiments on 100 nm thick aluminum and platinum films show remarkably different behavior even though both the materials have FCC crystal structure. We found that aluminum does not show significant dislocation plasticity at the crack tip. Instead, grain rotation is the primary deformation mechanism. For platinum, very large stress concentration at the notch tip (stress concentration factor ~11) was observed, which decreased remarkably as a function of dislocation-based plasticity.
Classical fracture mechanics as well as modern strain gradient plasticity theories assert the existence of stress concentration (or strain gradient) ahead of a notch tip, albeit somewhat relaxed in ductile materials. In this study, we present experimental evidence of extreme stress homogenization in nanocrystalline metals that result in immeasurable amount of stress concentration at a notch tip. We performed in situ uniaxial tension tests of 80 nm thick (50 nm average grain size) freestanding, single edge notched aluminum specimens inside a transmission electron microscope. The theoretical stress concentration for the given notch geometry was as high as 8, yet electron diffraction patterns unambiguously showed absence of any measurable stress concentration at the notch tip. To identify possible mechanisms behind such an anomaly, we performed molecular dynamics simulations on scaled down samples. Extensive grain rotation driven by grain boundary diffusion, exemplified by an Ashby–Verrall type of grain switching process, was observed at the notch tip to relieve stress concentration. We conclude that in the absence of dislocations, grain realignment or rotation may have played a critical role in accommodating externally applied strain and neutralizes any stress concentration during the process.
We present experimental evidence of anomalously high grain boundary mobility in 3–5 nm grain size platinum films at near room temperature. This mobility can be explained in terms of the localized electromigration stresses of the order of a few GPa that we observed. In the absence of conventional deformation mechanisms, the stress is relaxed through rapid grain growth up to a grain size of 40 nm. For larger grain sizes, grain boundary mobility is reduced as the stresses are relaxed by grain rotation and dislocation-based deformation mechanisms.
We demonstrate a microelectromechanical-system-based setup for fatigue studies on 200-nm-thick freestanding aluminum specimens in situ inside the transmission electron microscope. The specimens did not show any sign of fatigue damage even at 1.2 ×106 cycles under nominal stresses about 80% of the static ultimate strength. We show direct evidence to propose that the conventional theory of fatigue crack nucleation through slip bands does not work for nanoscale freestanding thin films, which gives rise to the anomalous fatigue insensitivity.
Titanium nitride is a very brittle and flaw sensitive ceramic material at temperatures below 750 °C. In this study, we present experimental evidence of room temperature dislocation-based plasticity in the material as well as insensitivity to flaws in form of single edge notches. We performed in-situ fracture experiments inside the transmission electron microscope on 150–300 nm thick, 5 μ wide freestanding films fabricated from titanium nitride/titanium multi-layers with titanium nitride as the notched and titanium as un-notched layers. The calculated stress concentration factor for the 800 nm to 1.5 μ long notches were greater than 8, however, the terminal cracks always nucleated at the un-notched edge of the specimens and not at the notch tip. To explain such remarkable flaw tolerance, we observe motion of dislocations (pre-existing and nucleated away from the notch) towards the notch tip. We suggest that the room temperature dislocation activities are facilitated by the residual stresses in the multi-layer specimens and the thickness dependence of image forces, which reduces the effective shear modulus to promote dislocation motion. The migration of dislocations towards the notch tip shields it from stress concentration to manifest the flaw tolerance in 150 nm specimens, which is observed real time in the microscope.
The amorphous to crystalline phase transformation process is typically known to take place at very high temperatures and facilitated by very high compressive stresses. In this study, we demonstrate crystallization of amorphous ultra-thin platinum films at room temperature under tensile stresses. Using a micro-electro-mechanical device, we applied up to 3% uniaxial tensile strain in 3–5 nm thick focused ion beam deposited platinum films supported by another 3–5 nm thick amorphous carbon film. The experiments were performed in situ inside a transmission electron microscope to acquire the bright field and selected area diffraction patterns. The platinum films were observed to crystallize irreversibly from an amorphous phase to face-centered cubic nanocrystals with average grain size of about 10 nm. Measurement of crystal spacing from electron diffraction patterns confirms large tensile residual stress in the platinum specimens. We propose that addition of the externally applied stress provides the activation energy needed to nucleate crystallization, while subsequent grain growth takes place through enhanced atomic and vacancy diffusion as an energetically favorable route towards stress relaxation at the nanoscale.
Thin film components of conventional and flexible solid-state devices experience mechanical strain during fabrication and operation. At the bulk scale, small values of strain do not affect thermal conductivity, but this may not true for grain sizes comparable with the electron and phonon mean free paths and for higher volume fraction of grain boundaries. To investigate this hypothesis, thermal and electrical conductivity of nominally 125-nm-thick aluminum films (average grain size 50 nm) were measured as functions of tensile thermo-mechanical strain, using a modified version of the 3-ω technique. Experimental results show pronounced strain–thermal conductivity coupling, with ∼50% reduction in thermal conductivity at ∼0.25% strain. The analysis shows that mechanical strain decreases the mean free path of the thermal conduction electrons, primarily through enhanced scattering at the moving grain boundaries. This conclusion is supported by similar effects of mechanical loading observed on the electrical conduction in the nanoscale aluminum specimens.
To visualize the fracture mechanisms in nanoscale thin films while measuring their fracture properties, we developed an experimental setup to carry out the experiments in-situ in the transmission electron microscope. The setup includes a 3 mm × 5 mm micro-electro-mechanical testing chip with actuators and sensors to measure fracture toughness of notched specimens. Fracture experiments were performed on about 125 nm thick free-standing aluminum thin film specimens with average grain size of about 50 nm. The specimens fractured at uniform far field stress of 470 MPa with stress intensity factor of 0.8–1.1 MPa m1/2. Commonly cited deformation mechanisms, such as dislocation-based plasticity and grain boundary sliding processes were not observed even at the notch tip, where the calculated stress considering the concentration factor exceeded 4 GPa. We propose that for grain sizes below 50 nm, dislocation motion confined at grain boundaries and grain rotation emerge to be significant processes in thin film deformation.
Fracture of Ti/TiN multilayer specimens was studied in situ inside a transmission electron microscope. Fracture toughness for cracks propagating perpendicular to the multilayers is found to be thickness dependent, varying from 1.45 to 2.45 MPa-m0.5 as the specimen thickness increased from 150 to 300 nm. Single-mode crack renucleation was observed in the metals layers, which is anomalous to the continuum-based elastic–plastic multilayer fracture model predictions. This is explained by the ultrafine columnar grain structure in the metal layers.
Thermal relaxation is a key factor in determining the quality factor of micro and nano resonators, which controls the energy dissipation through the coupling of the mechanical and thermal domains. While the literature contains approximate, exact and computational models for quantitative analysis of thermo-elastic coupling, very few techniques are available to ‘tune’ it without changing the material, geometry or operating conditions. In this paper, we develop an analytical model that considers a pre-stress in a flexural resonator to modify the thermal relaxation time and thus increase the quality factor. The effects of length-scale, pre-stress and geometry on the quality factor have been analyzed. The model predicts that significant improvement in terms of dimensionless quality factors is possible by tuning the pre-stress.
To study the effect of stress concentration at the nanoscale, we performed fracture experiments on single edge notched thin film specimens inside the transmission electron microscope. Even at about 4 GPa stress at the notch tip, the specimens failed far away from the notch at places with no apparent stress concentration. The in situ electron microscopy showed evidence of little or no plastic deformation at the notch tip. We propose that the apparent notch insensitivity arises from the breakdown of the classical fracture mechanics at the nanoscale, where materials fail by reaching a uniform rupture stress and not due to stress concentration.
Thermo-elastic damping is the dominant mode of energy loss due to the coupling of thermal and elastic fields in a body vibrating at or near resonant frequency. While the literature contains both exact and numerical schemes to quantify it, no technique is available yet to reduce thermo-elastic damping. We address this issue by introducing a secondary elastic field to derive an exact expression that predicts linear reduction in thermo-elastic damping with respect to frequency. Contrary to the current understanding, introduction of a static axial stress in addition to the flexural stresses is shown to increase quality factor and resonant frequency simultaneously.