Thermal Expansion Coefficients Of Silicon Research Articles

SOI-based micro-mechanical terahertz detector operating at room-temperature and atmospheric pressure

We present a micro-mechanical terahertz (THz) detector fabricated on a silicon on insulator substrate and operating at room-temperature. The device is based on a U-shaped cantilever of micrometric size, on top of which two aluminum half-wave dipole antennas are deposited. This produces an absorption extending over the ∼2–3.5 THz frequency range. Due to the different thermal expansion coefficients of silicon and aluminum, the absorbed radiation induces a deformation of the cantilever, which is read out optically using a 1.5 μm laser diode. By illuminating the detector with an amplitude modulated, 2.5 THz quantum cascade laser, we obtain, at room-temperature and atmospheric pressure, a responsivity of ∼1.5×108 pm W−1 for the fundamental mechanical bending mode of the cantilever. This yields noise-equivalent-power of 20 nW/Hz at 2.5 THz. Finally, the low mechanical quality factor of the mode grants a broad frequency response of approximately 150 kHz bandwidth, with a thermal response time of ∼ 2.5 μs.

基于晶格动力学的硅单晶热学性质研究(III)——热膨胀系数公式推导及分析

基于晶格动力学的硅单晶热学性质研究(III)——热膨胀系数公式推导及分析

Temperature drift contribution to frequency instability of silicon Fabry – Perot cavities

A contribution of a temperature drift near the silicon thermal expansion coefficient zero point to the fractional frequency instability of a silicon cavity is analysed. The thermal expansion coefficient of silicon is measured by an optical method near the zero point T0 = 123 K. It is shown that the frequency instability due to cavity temperature drifts observed in an experiment does not exceed a thermal noise limit at averaging intervals of up to 20 s.

An experimentally verified model for thermal microactuators including nonlinear material properties, vacuum, and intra-device heat conduction

This paper presents a model and computational method to predict the steady-state performance of thermal flexure microactuators at high input powers and various levels of partial vacuum. The model accounts for nonlinear temperature dependence of material properties, heat loss due to radiation, and intra-device heat transfer by conduction across an air gap. The model is validated by comparing the model predictions with the experimentally measured voltage, current, and displacement at standard conditions, prior to adjusting for partial vacuum. In order to understand the effect of nonlinearities on model reliability, the predictions of six additional hypothetical models are considered where (1) intra-device heat transfer is neglected, (2) radiation is neglected, (3) the thermal conductivity of silicon is assumed to be temperature-independent, (4) the thermal conductivity of air is assumed to be temperature-independent, (5) the electrical resistivity of silicon is assumed to be linear in temperature, and (6) the thermal expansion coefficient of silicon is assumed to be temperature-independent. All factors except radiation were shown to have a significant influence on the device performance especially at high input powers. The experimentally validated full model is then employed to predict the effect of reduced air pressure on the displacement and heat transfer properties of the actuator. This aspect of the study targets applications of thermal actuators in controlled environments such as space applications, actuators used for in situ micropositioning and tensile testing inside electron microscopy chambers, or actuators incorporated into the design of MEMS resonators. It was demonstrated that the maximum actuator displacement is not a linear function of reduced pressure and that it reaches a maximum at a certain partial vacuum level.

Molecular dynamics study of the thermal expansion coefficient of silicon

Due to the growing applications of silicon in nano-scale systems, a molecular dynamics approach is employed to investigate thermal properties of silicon. Since simulation results rely upon interatomic potentials, thermal expansion coefficient (TEC) and lattice constant of bulk silicon have been obtained using different potentials (SW, Tersoff, MEAM, and EDIP) and results indicate that SW has a better agreement with the experimental observations. To investigate effect of size on TEC of silicon nanowires, further simulations are performed using SW potential. To this end, silicon nanowires of different sizes are examined and their TEC is calculated by averaging in different directions ([100], [110], [111], and [112]) and various temperatures. Results show that as the size increases, due to the decrease of the surface effects, TEC approaches its bulk value.

Simultaneous Fluorescent and Amperometric Detection Of Catecholamine Release From Neuroendocrine Cells With Transparent Diamond MEAs

Simultaneous Fluorescent and Amperometric Detection Of Catecholamine Release From Neuroendocrine Cells With Transparent Diamond MEAs

Progress in transparent diamond microelectrode arrays

Diamond multi electrode arrays (MEAs) and ultra‐micro electrode array (uMEA) fabricated from boron‐doped nanocrystalline (BNCD) thin‐films, show excellent performances when detecting cell activity in both amperometric and potentiometric applications. Furthermore they are suitable for delivering electrical stimulation to elicit bioelectric events. Results obtained with our previous 9‐channels uMEA for single cells at high spatial resolution, and 16‐channels MEA for multicellular samples, validated the signal quality of diamond MEAs in comparison with competing technologies. The latest progresses are reported in this paper were we describe a new generation of devices with enhanced performances: a 12‐channel uMEA for recordings from a single cell at high spatial resolution, and a 64‐channel MEA to accommodate larger multicellular samples. The technology is based on a 200 μm thin high‐temperature glass with the same thermal expansion coefficient of silicon and a spin‐on seeding method. Preliminary experiments show excellent electrodes activity and a strongly improved transparency.

Fast-response fiber-optic anemometer with temperature self-compensation.

We report a novel fiber-optic anemometer with self-temperature compensation capability based on a Fabry-Pérot interferometer (FPI) formed by a thin silicon film attached to the end face of a single-mode fiber. Guided in the fiber are a visible laser beam from a 635 nm diode laser used to heat the FPI and a white-light in the infrared wavelength range as the signal light to interrogate the optical length of the FPI. Cooling effects on the heated sensor head by wind is converted to a wavelength blueshift of the reflection spectral fringes of the FPI. Self-temperature-compensated measurement of wind speed is achieved by recording the difference in fringe wavelengths when the heating laser is turned on and then off. Large thermal-optic coefficient and thermal expansion coefficient of silicon render a high sensitivity that can also be easily tuned by altering the heating laser power. Furthermore, the large thermal diffusivity and the small mass of the thin silicon film endow a fast sensor response.

PIEZORESITIVE CHARACTERISTICS OF SILICON MICROCRYSTALS AT CRYOGENIC TEMPERATURES

To create strain sensors operating at cryogenic temperatures piezoresistive characteristics of boron doped p-type Si whiskers, mounted on spring elements fabricated of steel, were studied at fixed temperatures 4.2, 77 and 300 K. It was shown that the effect of thermal strain that appears due to the difference between thermal expansion coefficients of silicon and material of the spring element (steel), when the crystals are mounted on the beam, on the piezoresistive characteristics of silicon crystals is very strong, especially at cryogenic temperatures. This fact should be accounted to develop sensors for strain measurements of constructions, fabricated from different materials. P-type Si whiskers with ρ300К =0.010 Ohm×cm with boron concentration near metalinsulator transition (MIT) from the metallic side of MIT with gauge factor GF4.2K =–1020 at the compressive strain are most suitable to create strain sensors for cryogenic temperatures, particularly, for 4.2 K. To create strain sensors for the temperature of liquid nitrogen the most suitable are p-Si whiskers with ρ300К =0.025 Ohm×cm with gauge factor GF77K =263.

Design and Implementation of a Micromechanical Silicon Resonant Accelerometer

The micromechanical silicon resonant accelerometer has attracted considerable attention in the research and development of high-precision MEMS accelerometers because of its output of quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability. Because of the mismatching thermal expansion coefficients of silicon and glass, the micromechanical silicon resonant accelerometer based on the Silicon on Glass (SOG) technique is deeply affected by the temperature during the fabrication, packaging and use processes. The thermal stress caused by temperature changes directly affects the frequency output of the accelerometer. Based on the working principle of the micromechanical resonant accelerometer, a special accelerometer structure that reduces the temperature influence on the accelerometer is designed. The accelerometer can greatly reduce the thermal stress caused by high temperatures in the process of fabrication and packaging. Currently, the closed-loop drive circuit is devised based on a phase-locked loop. The unloaded resonant frequencies of the prototype of the micromechanical silicon resonant accelerometer are approximately 31.4 kHz and 31.5 kHz. The scale factor is 66.24003 Hz/g. The scale factor stability is 14.886 ppm, the scale factor repeatability is 23 ppm, the bias stability is 23 μg, the bias repeatability is 170 μg, and the bias temperature coefficient is 0.0734 Hz/°C.

Optical multistability in a silicon-core silica-cladding fiber

We fabricate a novel silicon-core silica-cladding optical fiber using high pressure chemical fluid deposition and investigate optical transmission characteristics at the telecommunications wavelength of 1550 nm. High thermo-optic and thermal expansion coefficients of silicon give rise to a thermal phase shift of 6.3 rad/K in a 4 mm-long, 6.9 microm diameter fiber acting as a Fabry-Perot resonator. Using both power and wavelength modulation, we observe all-optical bistability at a low threshold power of 15 mW, featuring intensity transitions of 1.4 dB occurring over <0.1 pm change in wavelength. Threshold powers for higher-order multistable states are predicted. Tristability is experimentally confirmed.

Analysis of Temperature Effects on a Fully-Symmetrical Micromachined Gyroscope

This paper researches on the temperature effects of a fully-symmetrical micromachined gyroscope. The Young’s modulus and thermal expansion coefficient of silicon vary with the environment temperature, which affects the modes’ resonant frequencies of micromachined gyroscopes. The effects of temperature fluctuation on the modes’ resonant frequencies is simulated by the FEM software ANSYS. The simulation results show that the fully-symmetrical gyroscope’s resonance frequencies decrease with the increase of temperature and the decrease degree nearly 0.256Hz/°C, but the two modes’ resonance frequencies matches well. The micromachined gyroscope’s dynamic characteristics are tested. The resonant frequencies and the quality factor are reduced with the increase of temperature and the decrease degree of the fit linear about the resonant frequencies is 0.276 Hz/°C. The test results are in good accordance with the simulation results.

Vacuum-plasma-sprayed silicon coatings for biomedical application

Silicon coating was deposited on titanium alloy substrates by vacuum plasma spraying technology. The morphologies and phase composition of the coatings were analyzed by field-emission scanning electron microscopy and X-ray diffraction. The thermal expansion coefficient of silicon coating was measured to be about 3.70 × 10 −6 K −1. The bond strength of coating was approximately 20.6 MPa. The density, open porosity, roughness and Young's modulus of silicon coating were also measured. The as-sprayed silicon coating was treated by deionized water at 60 °C, 80 °C and 100 °C for a period of time and soaked in simulated body fluids to evaluate its bioactivity. The results showed that the water-treated coating could induce apatite to precipitate on its surface in simulated body fluid, indicating that the bioactivity of silicon coating was improved. The increase of temperature and duration of water treatment had a positive effect on the bioactivity of silicon coatings.

Micromechanical sensor for studying heats of surface reactions, adsorption, and cluster deposition processes

We present a newly designed highly sensitive micromechanical sensor devoted to thermodynamic studies involving supported clusters. The thermally sensitive element of the sensor consists of a micromachined silicon cantilever array, onto which a thin metal film is evaporated. Due to the difference between the thermal expansion coefficients of silicon and the metal employed, thermal bending is observed when heat is exchanged with the cantilever. The sensitivity and the response time of the cantilever are studied as a function of the film material (gold or aluminum) and the thickness of the metal film. With our routinely prepared cantilevers, a minimum power of 120 nW is measurable with a submillisecond response time, corresponding to a limit of detection in the femtojoule range. The high sensitivity of the sensor is demonstrated by measuring the heat exchange which occurs during the deposition of clusters on the cantilever. Experimentally, we illustrate the 1,3-butadiene hydrogenation reaction using a cluster model catalysts created by soft-landing palladium clusters onto the cantilever surface.

A novel temperature-compensating structure for micromechanical bridge resonator

A novel temperature-compensating structure for micromechanical bridge resonators has been developed in this paper. The temperature drift of resonance frequency is compensated by the output voltage of a Si/SiO2 bilayer cantilever temperature sensor, which is integrated in the same chip with the bridge resonator. The mechanism of this kind of temperature sensor resembles that of commercial bimetallic temperature sensors. The deformation of the cantilever measured by a Wheatstone bridge located at the clamped end changes with temperature due to the different thermal expansion coefficients of silicon and silicon dioxide. Both the bridge and the cantilever are of the same thickness and are fabricated simultaneously with the same materials and by an identical process flow. So there are few errors caused by the temperature difference between the temperature sensor and the resonator itself, which occurs during fast temperature changes.

Linear Thermal Expansion Coefficient of Silicon from 293 to 1000 K

As a part of the program to establish a thermal expansion standard, the linear thermal expansion coefficients of single-crystal silicon have been determined in the temperature range 293 to 1000 K using a dilatometer which consists of a heterodyne laser Michelson interferometer and gold versus platinum thermocouple. The relative standard deviation of the measured values from those calculated from the best least-squares fit was 0.21%. The relative expanded uncertainty in the measurement was estimated to be 1.1 to 1.5% in the temperature range, based upon an analysis of thirteen standard uncertainties. The present data are compared with the data previously obtained by similar dilatometers and the standard reference data for the thermal expansion coefficient of silicon, recommended by the Committee on Data for Science and Technology (CODATA). The present data are in good agreement with the most recently reported data but not with the earlier high-temperature data used to evaluate the standard reference data, which suggests a need for the reevaluation of the standard reference data for the thermal expansion coefficient of silicon at temperatures above 600 K.

Development of a Laser Interferometric Dilatometer for Measurements of Thermal Expansion of Solids in the Temperature Range 300 to 1300 K

A laser interferometric dilatometer has been developed for measuring linear thermal expansion coefficients of reference materials for thermal expansion in the temperature range 300 to 1300 K. The dilatometer is based on an optical heterodyne interferometer capable of measuring length change with an uncertainty of 0.6 nm. Linear thermal expansion coefficients of silicon were measured in the temperature range 700 to 1100 K. The performance of the present dilatometer was tested by a comparison between the present data and the data measured with the previous version of the present dilatometer and the data recommended by the Committee on Data for Science and Technology (CODATA). The present data agree well with the recommended values over all the temperature range measured. On the other hand, the present values at lower temperatures are in poor agreement with the previous experimental data. The combined standard uncertainty in the present value at 900 K is estimated to be 1.1×10−8 K−1.

The Thermophysical Properties (Heat Capacity and Thermal Expansion) of Single-Crystal Silicon

Fragmentary investigations of the heat capacity and of the thermal expansion coefficient of single crystals of high-purity silicon are reported. The results of these investigations are compared with the entire body of data on these properties available to date. Generalized equations expressing the heat capacity and thermal expansion coefficient of silicon as functions of temperature are obtained for the temperature ranges of 298–1690 and 100–1400 K, respectively. The Debye temperature of crystalline silicon and the root-mean-square dynamic displacement of atoms from the equilibrium position in its crystal lattice are calculated using the available data on thermal expansion.

Thermomechanical stress in silicon on quartz wafer bonding and Smart Cut® process

ABSTRACTThe thermal stress behavior of silicon/quartz bonded wafer pairs is examined. Sliding, debonding, and cracking are the observed mechanisms of relaxation. When the elastic energy due to the different thermal expansion coefficients of silicon and quartz exceeds the bonding energy, sliding will start and lead to a serrated curve on the curvature-versus-temperature graph. Finally, debonding will occur once the peeling stress exceeds the interface bonding strength. The debonded parts crack due to the overhang structure, and debonding-cracking processes continue during a further temperature increase. The stress behavior of the hydrogen-implantation induced layer splitting process (the so-called “Smart-Cut process”) of silicon/quartz pairs is also monitored in a stress measurement setup. It is observed that Smart-Cut process is a sudden process in agreement with the observations reported in the literature.

A study on thermal-stress-reliability of Si-based PLC substrate

Planar lightwave technology is rapidly advancing and promises excellent performance as economical opto-electro-devices. To confirm its feasibility, it is very important to estimate its mechanical reliability especially against the thermal stresses caused by the difference of the thermal expansion coefficients of Silicon and silica glass. This paper examines the thermal strain and stress distribution on silicon-based Planar-Lightwave-Circuits (PLC) substrates and the stress concentration on silicon terrace structures prepared for mounting active optical devices. Experimental data on the fracture strength of silicon obtained by three-point-bending tests are given. Finally, the thermal-stress-reliability of PLC substrates based on probabilistic analysis is calculated and it is confirmed that the PLC substrate, even its present form, is reliable enough for a new family of optical components.