Cantilever Temperature Research Articles

Thermal induced deflection in atomic force microscopy cantilevers: analysis & solution

Atomic force microscopy (AFM) cantilevers are commonly made from two material layers: a reflective coating and structural substrate. Although effective, this can result in thermally induced cantilever deflection due to ambient and local temperature changes. While this has been previously documented, key aspects of this common phenomenon have been overlooked. This work explores the impact of thermally induced cantilever deflection when in- and out-of-contact, including the topographic scan artefacts produced. Scanning thermal microscopy probes were employed to provide direct cantilever temperature measurement from Peltier and microheater sources, whilst permitting cantilever deflection to be simultaneously monitored. Optical lever-based measurements of thermal deflection in the AFM were found to vary by up to 250% depending on the reflected laser spot location on the cantilever. This highlights AFM’s inherent inability to correctly measure and account for thermal induced cantilever deflection in its feedback system. This is particularly problematic when scanning a tip in-contact with the surface, when probe behaviour is closer mechanically to that of a bridge than a cantilever regarding thermal bending. In this case, measurements of cantilever deflection and inferred surface topography contained significant artefacts and varied from negative to positive for different optical lever laser locations on the cantilevers. These topographic errors were measured to be up to 600 nm for a small temperature change of 2 K. However, all cantilevers measured showed a point of consistent, complete thermal deflection insensitivity 55% to 60% along their lengths. Positioning the reflected laser at this location, AFM scans exhibited improvements of up-to 97% in thermal topographic artefacts relative to other laser positions.

Controlled heating and alignment platform enhances versatility in colloidal probe fabrication.

A colloidal probe, comprising a colloidal particle attached to an atomic force microscope cantilever, is employed to measure interaction forces between the particle and a surface. It is possible to change or even destroy a particle while attaching it to a cantilever, thus limiting the types of systems to which the colloidal probe technique may be applied. Here, we present the Controlled Heating and Alignment Platform (CHAP) for fabricating colloidal probes without altering the original characteristics of the attached particle. The CHAP applies heat directly to the atomic force microscope chip to rapidly and precisely control the cantilever temperature. It minimizes particle heating and enables control over the viscosity of the thermoplastic adhesive to prevent it from contaminating the particle surface. 3D-printed components made the CHAP compatible with standard optical microscopes and streamlined the fabrication process, while increasing the platform's versatility. To demonstrate the utility of CHAP, we conducted a case study using a thermoplastic wax adhesive to fabricate colloidal probes bearing polystyrene and silica particles between 0.7 and 40 μm in diameter. We characterized the properties and interactions of the adhesive and particles, as well as the properties of the completed probes, to demonstrate the retention of particle features throughout fabrication. Pull-off tests with CHAP's probes measured adhesive force values in the expected ranges and demonstrated that particles were firmly attached to the cantilevers.

Vibration isolation with high thermal conductance for a cryogen-free dilution refrigerator.

We present the design and implementation of a mechanical low-pass filter vibration isolation used to reduce the vibrational noise in a cryogen-free dilution refrigerator operated at 10 mK, intended for scanning probe techniques. We discuss the design guidelines necessary to meet the competing requirements of having a low mechanical stiffness in combination with a high thermal conductance. We demonstrate the effectiveness of our approach by measuring the vibrational noise levels of an ultrasoft mechanical resonator positioned above a superconducting quantum interference device. Starting from a cryostat base temperature of 8 mK, the vibration isolation can be cooled to 10.5 mK, with a cooling power of 113 µW at 100 mK. We use the low vibrations and low temperature to demonstrate an effective cantilever temperature of less than 20 mK. This results in a force sensitivity of less than 500 zN/Hz and an integrated frequency noise as low as 0.4 mHz in a 1 Hz measurement bandwidth.

Cu(OH)₂ and CuO Nanorod Synthesis on Piezoresistive Cantilevers for the Selective Detection of Nitrogen Dioxide.

Self-controlled active oscillating microcantilevers with a piezoresistive readout are very promising sensitive sensors, despite their small surface. In order to increase this surface and consequently their sensitivity, we nanostructured them with copper hydroxide (Cu(OH)2) or with copper oxide (CuO) nanorods. The Cu(OH)2 rods were grown, on a homogeneous copper layer previously evaporated on the top of the cantilever. The CuO nanorods were further obtained by the annealing of the copper hydroxide nanostructures. Then, these copper based nanorods were used to detect several molecules vapors. The results showed no chemical affinity (no formation of a chemical bond) between the CuO cantilevers and the tested molecules. The cantilever with Cu(OH)2 nanorods is selective to nitrogen dioxide (NO2) in presence of humidity. Indeed, among all the tested analytes, copper hydroxide has only an affinity with NO2. Despite the absence of affinity, the cantilevers could even so condensate explosives (1,3,5-trinitro-1,3,5-triazinane (RDX) and pentaerythritol tetranitrate (PETN) on their surface when the cantilever temperature was lower than the explosives source, allowing their detection. We proved that in condensation conditions, the cantilever surface material has no importance and that the nanostructuration is useless because a raw silicon cantilever detects as well as the nanostructured ones.

Analytical Solution for Rotational Rub-Impact Plate Under Thermal Shock

AbstractThe analysis method is developed to obtain dynamic characteristics of the rotating cantilever plate with thermal shock and tip-rub. Based on the variational principle, equations of motion are derived considering the differences between rubbing forces in the width direction of the plate. The transverse deformation is decomposed into quasi-static deformation of the cantilever plate with thermal shock and dynamic deformation of the rubbing plate under thermal shock. Then deformations are obtained through the calculation of modal characteristics of rotating cantilever plate and temperature distribution function. Special attention is paid to the influence of tip-rub and thermal shock on the plate. The results show that tip-rub has the characteristics of multiple frequency vibrations, and high frequency vibrations are significant. On the contrary, thermal shock shows the low frequency vibrations. The thermal shock makes the rubbing plate gradually change into low frequency vibrations. Because rub-induced vibrations are more complicated than those caused by thermal shock, tip-rub is easier to result in the destruction of the blade. The increasing friction coefficient intensifies vibrations of the rubbing plate. Minimizing friction coefficients can be an effective way to reduce rub-induced damage through reducing the surface roughness between the blade tip and the inner surface of the casing.

Temperature and non-linear response of cantilever-type mechanical oscillators used in atomic force microscopes with interferometric detection

The sensitivity of atomic force microscopes is fundamentally limited by the cantilever temperature, which can be, in principle, determined by measuring its thermal spectrum and applying the equipartition theorem. However, the mechanical response can be affected by the light field inside the cavity of a Fabry-Perot interferometer due to light absorption, radiation pressure, photothermal forces, and laser noise. By evaluating the optomechanical Hamiltonian, we are able to explain the peculiar distance dependence of the mechanical quality factor as well as the appearance of thermal spectra with symmetrical Lorentzian as well as asymmetrical Fano line shapes. Our results can be applied to any type of mechanical oscillator in an interferometer-based detection system.

Multifunctional atomic force microscope cantilevers with Lorentz force actuation and self-heating capability

This paper reports the development of microcantilevers capable of self-heating and Lorentz-force actuation, and demonstrates applications to thermal topography imaging. Electrical current passing through a U-shaped cantilever in the presence of a magnetic field induces a Lorentz force on the cantilever free end, resulting in cantilever actuation. This same current flowing through a resistive heater induces a controllable temperature increase. We present cantilevers designed for large actuation forces for a given cantilever temperature increase. We analyze the designs of two new cantilevers, along with a legacy cantilever design. The cantilevers are designed to have a spring constant of about 1.5 N m−1, a resonant frequency near 100 kHz, and self-heating capability with temperature controllable over the range 25–600 °C. Compared to previous reports on self-heating cantilevers, the Lorentz–thermal cantilevers generate up to seven times as much Lorentz force and two times as much oscillation amplitude. When used for thermal topography imaging, the Lorentz–thermal cantilevers can measure topography with a vertical resolution of 0.2 nm.

Infrared Emission From Heated Microcantilevers

An understanding of the thermal behavior of heated microcantilevers is essential to their use. In this article, we investigated the infrared (IR) emission of two silicon cantilevers with integrated solid-state heaters over the 2500–3000 cm−1 spectral range. Two cantilevers were examined: the first had a heater surface area of 17 × 20 μm and the second had a heater surface area of 170 × 100 μm. We calculated the spectral power emitted by the cantilever based on the Planck function, dielectric function of the doped silicon at elevated temperatures, and cantilever spectral emissivity. Measurements of the cantilever spectral power compared well with predictions. The first cantilever had a radiative power of 4.2 μW at a heating power of 15.7 mW and maximum temperature of 1,150 K, and the second cantilever had a radiative power of 70.1 μW at a heating power of 54.9 mW and maximum temperature of 850 K. The cantilever emissive power depended on the spatial variation in the cantilever temperature and cantilever emissivity. It is also shown how the heated cantilever can be used as an IR source to acquire absorption spectra of polymer films in an IR spectrometer.

Heated atomic force cantilever closed loop temperature control and application to high speed nanotopography imaging

This paper reports closed loop temperature control of a heated atomic force microscope cantilever and its application to thermal topography imaging. Closed loop feedback implemented in analog circuitry maintains cantilever temperature with 1.73°C accuracy and 0.076°C precision at 1MHz bandwidth. The cantilever can respond to changes in temperature set-point within 16.5μs, enabling thermal topography imaging at 500μm/s, which is a 50× increase over previous work. We demonstrate how the cantilever thermal signal can be used in place of the traditional optical tip height sensing in order to image surfaces. The temperature control architecture can be scaled to large arrays of heated cantilevers without loss in bandwidth.

2-ω and 3-ω temperature measurement of a heated microcantilever

This article describes temperature measurement of a heated atomic force microscope cantilever using the 2ω and 3ω harmonics of the cantilever temperature signal. When the cantilever is periodically heated, large temperature oscillations lead to large changes in the cantilever electrical resistance and also lead to nonconstant temperature coefficient of resistance. We model the cantilever heating to account for these sources of nonlinearity, and compare models with experiment. When the heating voltage amplitude is 17.9 V over the driving frequency range 10 Hz-34 kHz, the cantilever temperature oscillation is between 5 °C and 200 °C. Over this range, the corrected 2ω method predicts cantilever temperature to within 16% and the corrected 3ω method predicts the cantilever temperature within 3%. We show a general method for predicting the periodic cantilever temperature, sources of errors, and corrections for these errors.

A conduction–convection model for self-heating in piezoresistive microcantilever biosensors

Thermal drifting caused by the self-heating in piezoresistive microcantilever biosensors is a major source of inaccuracy. To this use, the present study derives a simple and accurate conduction–convection model to predict the temperature distribution in p-doped piezoresistive microcantilevers because of self-heating. The model is applied to a 4-layer gold-coated piezoresistive silicon dioxide microcantilever biosensor with u-shaped silicon piezoresistor. The analytical results are compared to the numerical results. The effect of convective heat transfer coefficient on temperature profile is also studied. The comparison results show the analytical and numerical results are accurate within 4%. The sensitivity results showed that the resistance change produced by thermal drifting is about five-to-eight times that by the surface stress. Finally, the cantilever temperature profile is found to be strongly affected by the piezoresistor size and the convective heat transfer coefficient.

Improved Nanotopography Sensing via Temperature Control of a Heated Atomic Force Microscope Cantilever

This paper reports thermal nanotopography sensing using a heated atomic force microscope cantilever with a sensitivity as high as 4.68 mV/nm, which is two orders of magnitude higher than previously published results for heated cantilevers. The sensitivity improvement arises from closed-loop control of cantilever temperature during the topography sensing. The cantilever temperature is controlled by maintaining constant electrical resistance, current, power, or voltage across either the entire electrical circuit or individual components of the circuit. We develop a model that links the cantilever heat flow and temperature-dependent cantilever properties to the circuit behavior in order to predict and then optimize the cantilever topography sensitivity. Topography measurements on a 100 nm tall silicon gratings how cantilever sensitivity ranging 0.047 to 4.68 mV/nm, depending on the control scheme. The application of closed loop control yields a topography sensitivity that is 100 times increased over previously published work on heated cantilevers.

Photodriven, Flexural–Torsional Oscillation of Glassy Azobenzene Liquid Crystal Polymer Networks

AbstractCantilevers composed of glassy, photoresponsive liquid crystalline polymer networks (LCNs) are shown to oscillate at high frequency (∼50 Hz) and large amplitude when exposed to light from a 442 nm coherent wave (CW) laser. Added dimensionality to previously reported in‐plane oscillations is enabled by adjusting the orientation of the nematic director to the long axis of the cantilever yielding in‐plane bending accompanied by out‐of‐plane twisting (flexural–torsional oscillation). The fundamental photoresponse of this class of glassy azobenzene liquid crystal polymer networks (azo‐LCN) is further probed by examining the influence of cantilever aspect ratio, laser intensity, and temperature. The frequency of photodirected oscillations is strongly correlated to the length of the cantilever while the amplitude and threshold laser intensity for oscillation is strongly correlated to temperature.

Self-heating in piezoresistive cantilevers

We report experiments and models of self-heating in piezoresistive microcantilevers that show how cantilever measurement resolution depends on the thermal properties of the surrounding fluid. The predicted cantilever temperature rise from a finite difference model is compared with detailed temperature measurements on fabricated devices. Increasing the fluid thermal conductivity allows for lower temperature operation for a given power dissipation, leading to lower force and displacement noise. The force noise in air is 76% greater than in water for the same increase in piezoresistor temperature.

Microcantilever with integrated solid-state heater, conductive tip, and Schottky diode

This paper reports a heated atomic force microscope cantilever having a Schottky diode fabricated near the cantilever free end. The forward bias and reverse bias operation of this cantilever offer different current–voltage characteristics, such that the cantilever heating and temperature sensing capabilities are different in forward bias versus reverse bias operation. When 43 V is applied to the cantilever, the cantilever temperature is 677 °C in the forward bias and 786 °C in reverse bias. Thermal runaway for the device occurs at 445 °C, corresponding to forward and reverse bias resistances of 1.2 kΩ and 2.0 kΩ. Below the thermal runaway point, the cantilever temperature coefficient of resistance (TCR) is 943 ppm/°C in the forward bias and 2996 ppm/°C in reverse bias. We characterize cantilever thermomechanical bending, which is a function of bias direction, applied voltage, and actuation frequency. The diode junction at the cantilever free end grants an additional degree of electro-thermal and thermomechanical control compared to other types of heated cantilevers.

Natural advection from a microcantilever heat source

Fluid motion induced by a microcantilever heat source immersed in water is assessed by microscopic particle image velocimetry. Large fluid velocity is observed near the heated cantilever and its magnitude increases with cantilever temperature. Neither Brownian nor thermophoretic motion of the tracer particles can account for these large velocities. Rather, this fluid motion is consistent with buoyancy-driven advection. The observation of natural advection due to a microscopic heat source is important for electronics cooling, performance of thermal sensors, and the thermal processing of small biological samples.

Liquid Operation of Silicon Microcantilever Heaters

This letter reports characterization and calibration of silicon microcantilever heaters for operation in liquid environments. Cantilever thermomechanical noise spectra were measured in air and in water using a commercial atomic force microscope. Cantilever electrical characteristics were measured in air and water. Laser Raman thermometry measured cantilever temperature in air and water, allowing temperature calibration through comparison with electrical characteristics. Cantilever thermal conductance in water was 136-610 W/K, depending upon the cantilever type. The cantilever electrical resistance is an accurate measure of cantilever temperature in both air and water.

Compact cantilever force probe for plasma pressure measurements

A simple, compact cantilever force probe (CFP) has been developed for plasma pressure measurements. It is based on the pull-in phenomenon well known in microelectromechanical-system electrostatic actuators. The probe consists of a thin (25 mum) titanium foil cantilever (38 mm of length and 14 mm of width) and a fixed electrode separated by a 0.75 mm gap. The probe is shielded by brass box and enclosed into boron nitride housing with a 9 mm diameter window for exposing part of cantilever surface to the plasma. When the voltage is applied between the cantilever and the electrode, an attractive electrostatic force is counterbalanced by cantilever restoring spring force. At some threshold (pull-in) voltage the system becomes unstable and the cantilever abruptly pulls toward the fixed electrode until breakdown occurs between them. The threshold voltage is sensitive to an additional externally applied force, while a simple detection of breakdown occurrence can be used to measure that threshold voltage value. The sensitivity to externally applied forces obtained during calibration is 0.28 V/microN (17.8 VPa for pressure). However, the resolution of the measurements is +/-0.014 mN (+/-0.22 Pa) due to the statistical scattering in measured pull-in voltages. The diagnostic temporal resolution is approximately 10 ms, being determined by the dynamics of pull-in process. The probe has been tested in the tokamak ISTTOK edge plasma, and a plasma force of approximately 0.07 mN (plasma pressure approximately 1.1 Pa) has been obtained near the leading edge of the limiter. This value is in a reasonable agreement with the estimations using local plasma parameters measured by electrical probes. The use of the described CFP is limited by a heat flux of Q approximately 10(6) W/m(2) due to uncontrollable rise of the cantilever temperature (DeltaT approximately 20 degrees C) during CFP response time.

Microcantilever actuation via periodic internal heating

This paper reports electrothermal actuation of silicon microcantilevers having integrated resistive heaters. Periodic electrical excitation induced periodic resistive heating in the cantilever, while the cantilever deflection was monitored with a photodetector. Excitation was either at the cantilever resonant frequency, f(0), f(0)/2, or f(0)/3. When the time averaged maximum cantilever temperature was 174 degrees C, the cantilever out-of-plane actuation amplitude was 484 nm near the cantilever resonance frequency of 24.9 kHz. This actuation was sufficiently large to operate the cantilever in intermittent contact mode and scan a calibration grating of height of 20 nm.

Temperature calibration of heated silicon atomic force microscope cantilevers

This article presents calibration techniques for heated silicon atomic force microscope cantilevers and analyzes the accuracy of these techniques. A calibration methodology using Raman thermometry is presented and validated with heat transfer simulations and experimental measurements. Raman thermometry generates a calibration standard against which other techniques can be compared. Theoretical predictions of the cantilever temperature-dependent electrical properties do not by themselves provide accurate cantilever temperature calibration. Isothermal calibration is also insufficient. The temperature calibrations are stable with storage time and number of heating cycles, although an electrical ‘burn-in’ period is required to stabilize the cantilever response. These techniques for precise temperature calibration of heatable silicon cantilevers are required for applications where temperature must be carefully controlled, including surface science measurements and nano-manufacturing.