Silicon Strain Research Articles

Second‐Order Optical Nonlinearity in Silicon Waveguides: Inhomogeneous Stress and Interfaces

The lack of a dipolar second‐order susceptibility (χ(2)) in silicon due to the centrosymmetry of its diamond lattice usually inhibits efficient second‐order nonlinear optical processes in the silicon bulk. Recently, the deposition of stressed silicon nitride layers and the corresponding inhomogeneous strain in silicon lead to the demonstration of second harmonic generation and electro‐optic modulation in strained silicon waveguides. However, the respective impact of the stress/strain gradient and the involved interfaces is not clear. Here, the influence of the stress and the stressing silicon nitride layer using second harmonic generation measurements in transmission is investigated. The results show that the enhancement of the second‐order nonlinearity arises from a constructive superposition of stress‐induced and interface‐related effects. Particularly, the stress gradient in silicon breaks the symmetry of the crystal lattice, while positive fixed charges at the silicon/silicon nitride interface are responsible for a pronounced electric‐field‐induced‐second harmonic (EFISH) contribution. These results demonstrate the impact of external factors for the creation of an effective χ(2) in materials and open new perspectives for the use of second‐order nonlinear optical processes in silicon photonics.

Wet Etch Rate Behavior of Poly-Si in TMAH Solution at Various Ambient Gas Conditions

As the demand for greater speed in semiconductor devices continues, a typical method of increasing charge mobility is to maximise the silicon strain at the depletion region in p-type transistors through the implementation of “Sigma Cavity” structures in the bulk silicon on either side of the gate structure. These structures, when filled, exhibit a uniaxial strain in the depletion region thus, increasing the charge transport speed [1]. The shape of the Sigma Cavity structure is important in maximising the strain in this region, thus strict control of the shape dimensions is imperative to the electrical performance of the device.

High precision two-dimensional strain mapping in semiconductor devices using nanobeam electron diffraction in the transmission electron microscope

A classical method used to characterize the strain in modern semiconductor devices is nanobeam diffraction (NBD) in the transmission electron microscope. One challenge for this method lies in the fact that the smaller the beam becomes, the more difficult it becomes to analyze the resulting diffraction spot pattern. We show that a carefully designed fitting algorithm enables us to reduce the sampling area for the diffraction patterns on the camera chip dramatically (∼1/16) compared to traditional settings without significant loss of precision. The resulting lower magnification of the spot pattern permits the presence of an annular dark field detector, which in turn makes the recording of images for drift correction during NBD acquisition possible. Thus, the reduced sampling size allows acquisition of drift corrected NBD 2D strain maps of up to 3000 pixels while maintaining a precision of better than 0.07%. As an example, we show NBD strain maps of a modern field effect transistor (FET) device. A special filtering feature used in the analysis makes it is possible to measure strain in silicon devices even in the presence of other crystalline materials covering the probed area, which is important for the characterization of the next generation of devices (Fin-FETs).

Using the Effect of Mechanical Stress on Doped Silicon as an Angular Movement Sensor for MOEMS/MEMS Micro Mirrors

The<b> </b>effect of elastic strain of moderate magnitude using high doped silicon substrate can change the conductivity of the substrate. The commonly used metal (strain) gage has a magnitude factor of between 2 ÷ 4 while high doped silicon (strain) gage factor magnitude is between 150 ÷ 200, thus improving the substrate sensitivity considerably. Using those physical attributes allow us to create a MOEMS sensor resolving accuracy issues and saving space in any future MOEMS device design. Those devices will be able to measure any mechanical movement connected to the high doped silicon substrate by converting the physical strain created from the movement stress to current/voltage change in the substrate device. The simplicity of the device is that the device could measure movement without any need to implement an outer sensor to it. By measuring the device's strain change it would feel the movement and convert it to an analog value, thus creating a strain gage built in the MOEMS device surface.

3D Magnetic Field Sensor Concept for Use in Inertial Measurement Units (IMUs)

We report on the design, fabrication, and characterization of a microfabricated 3D magnetic field sensor that is suitable for co-integration with inertial sensors to form single-chip inertial measurement units. In contrast to classical resonant MEMS magnetometers, which are based on Lorentz force measurement, our sensor uses permanent magnetic materials and piezoresistive detection with silicon strain gauges of nanometric section, leading to low power consumption and high sensitivity for small sensor size. Thin multilayers of CoFe and PtMn as ferro- and antiferromagnetic materials are integrated within the MEMS fabrication process. Sensitivities of 1.09 V/T for x- and y- components of the magnetic field and 0.124 V/T for z- component of the magnetic field were measured, respectively. To be sensitive to magnetic fields along all three spatial directions, two permanent magnetization directions on the same die are required. Implementation of the two magnetization directions was validated by a measured correlation of 99.7% between x- and y- sensitivity axes. Power consumption of the 3D sensor is for polarization with a 100 μA dc current. With resolutions of 100 nT/√Hz for x- and y-component of the magnetic field and 350 nT/√Hz for z- component, the sensor is suitable for precise measurement of earth magnetic field.

Atomic Layer Deposition of Sidewall Spacers: Process, Equipment and Integration Challenges in State-of-the-Art Logic Technologies

Dielectric thin film spacers play a very important role in defining the silicon channel boundary and junction geometries as well as proximity to silicon stressors and strongly affect key transistor electrical characteristics [1]. Another important application of sidewall spacers is in patterning of 3D FinFETs (Field Effect Transistor), where the Sidewall Image Transfer (SIT) technology [2] helps to overcome the limitations of conventional lithography and to improve control of critical dimensions. Sidewall spacers are also used to control critical dimension (CD) by depositing a spacer film inside a feature to achieve a CD shrink. Tolerance for variability of TFin(Fin width) has to be in the sub nm range to significantly reduce variability in FinFET performance. The need for precise scaling of conventional spacers as well as new patterning applications put very stringent requirements on spacer thin film depositions and on control of spacer film properties during subsequent integration processes. The need for greatly improved spacer process step coverage, tighter thickness control, pattern effects and more stringent film properties requirements strongly influenced the transition from Chemical Vapor Deposition (CVD) to Atomic Layer Deposition (ALD) spacers in the industry.This paper discusses the properties of ALD silicon nitride and silicon oxide spacer films from the perspectives of ALD and MLD (Molecular Layer Deposition) techniques, precursor chemistries and compositional stability after subsequent integration steps like implant anneals and spacer sculpting reactive ion etching processes. Advanced imaging techniques like EELS (Electron Energy Loss Spectroscopy) and XPS (X-ray Photoelectron Spectroscopy) techniques have been used to analyze sidewall spacer transformation. Special attention has been paid to the microloading effect - the dependence of thin film deposition rate on pattern density [3]. Microloading data for CVD, MLD and ALD techniques are compared based on a specially designed microloading measurement vehicle. This is especially useful with geometries needing a sub nm tolerance and when patterning endpoint detection schemes are highly dependent on film properties.The effect of ALD deposition parameters on film electrical characteristics like dielectric breakdown and leakage are also delineated. Silicon strain engineering issues related to the implementation of ALD spacers and techniques aimed at varying and controlling an intrinsic stress level in ALD films are also discussed. The findings helped to optimize the existing ALD/MLD processes for conventional epi and source/drain spacers as well for oxide sidewall ALD spacers for SIT fins patterning and CD shrink on 14nm FinFET technology.

Silicon strain gages bonded on stainless steel using glass frit for strain sensor applications

In this paper, a steel pressure sensor using strain gages bonded on a 17–4 PH stainless steel (SS) diaphragm based on glass frit technology is proposed. The strain gages with uniform resistance are obtained by growing an epi-silicon layer on a single crystal silicon wafer using epitaxial deposition technique. The inorganic glass frits are used as the bonding material between the strain gages and the 17–4 PH SS diaphragm. Our results show that the output performances of sensors at a high temperature of 125 °C are almost equal those at room temperature, which indicates that the glass frit bonding is a good method and may lead to a significant advance in the high temperature applicability of silicon strain gage sensors. Finally, the microstructure of the cured organic adhesive and the fired glass frit are compared. It may be concluded that the defects of the cured organic adhesive deteriorate the hysteresis and repeatability errors of the sensors.

Prototyping of a highly performant and integrated piezoresistive force sensor for microscale applications

In this paper, the prototyping of a new piezoresistive microforce sensor is presented. An original design taking advantage of both the mechanical and bulk piezoresistive properties of silicon is presented, which enables the easy fabrication of a very small, large-range, high-sensitivity with high integration potential sensor. The sensor is made of two silicon strain gauges for which widespread and known microfabrication processes are used. The strain gauges present a high gauge factor which allows a good sensitivity of this force sensor. The dimensions of this sensor are 700 μm in length, 100 μm in width and 12 μm in thickness. These dimensions make its use convenient with many microscale applications, notably its integration in a microgripper. The fabricated sensor is calibrated using an industrial force sensor. The design, microfabrication process and performances of the fabricated piezoresistive force sensor are innovative thanks to its resolution of 100 nN and its measurement range of 2 mN. This force sensor also presents a high signal-to-noise ratio, typically 50 dB when a 2 mN force is applied at the tip of the force sensor.

Intrinsic Embedded Sensors for Polymeric Mechatronics: Flexure and Force Sensing

While polymeric fabrication processes, including recent advances in additive manufacturing, have revolutionized manufacturing, little work has been done on effective sensing elements compatible with and embedded within polymeric structures. In this paper, we describe the development and evaluation of two important sensing modalities for embedding in polymeric mechatronic and robotic mechanisms: multi-axis flexure joint angle sensing utilizing IR phototransistors, and a small (12 mm), three-axis force sensing via embedded silicon strain gages with similar performance characteristics as an equally sized metal element based sensor.

Sensor and Instrumentation for Cable Tension Quantification

A stainless steel based miniature sensor is designed and fabricated for cable tension measurement. The sensor, with a cut out pattern, is only 5mm high, has an external diameter of 4.5mm and is instrumented with four silicon strain gauges. Applied load will elastically deform the sensor geometry and will induce a resistance change in the Si-piezoresistors. Instrumentation is done using commercial components, and comprise two programmable current sources, that operate the Si-gauges in a current driven Wheatstone bridge configuration. A programmable multi-channel instrumentation amplifier interfaces the Wheatstone bridges with a PIC microcontroller and its on-board 12 bit AD converter. The implemented microcontroller and PC software allows remote adaptation of the analog front and facilitates communication and signal visualization. The sensor system can measure axial forces up to 1000N with a resolution better than 1N.

Silicon Strain Gauge Load Cell for Weighting Disdrometer

In this paper, the usability of a compact silicon strain gauge load cell in a weighting disdrometer for measuring the impact load of a falling raindrop is introduced for application in a multi-meteorological sensor. The silicon strain gauge load cell is based on the piezoresistive effect, which has a high linearity output from the momentum of the raindrop and the simplicity of signal processing. The weighting disdrometer shows a high sensitivity of 7.8 mV/g in static load measurement when the diaphragm thickness of the load cell is <TEX>$250{\mu}m$</TEX>.

Global gene expression of rhizobacteria-silicon mediated induced systemic resistance in tomato (Solanum lycopersicum) against Ralstonia solanacearum

Transcriptome analysis of tomato (Solanum lycopersicum) stem tissue was performed to elucidate gene expression analysis in plant treated with silicon and/or rhizobacteria strain Bacillus pumilis following inoculation with Ralstonia solanacearum strain ToUdk2 (race 1,phylotype 1 originated from Thailand). A total of 174 genes were differentially regulated of which 113 were up-regulated and 61 down-regulated functional categorization of the regulated genes revealed that most of the up-regulated genes are more involved in signal transduction, defence, protein synthesis and metabolism, while a large proportion of down regulated genes were more involved in photosynthesis, lipid metabolism. In plant treated with silicon a higher number of defence related genes were regulated than those treated with rhizobacterium B. pumilis. During the simultaneous application of the two elicitors five genes were down regulated, while they were up-regulated when they were applied separately, suggesting that an antagonistic interaction occurred between genes mediated by ethylene-jasmonate and salicylate pathways. Therefore, separate application of each elicitor is recommended as best strategy for the induction of resistance against bacterial wilt in tomato, with silicon being a stronger inducer than rhizobacteria.

Gauge Factor and Stretchability of Silicon-on-Polymer Strain Gauges

Strain gauges are widely applied to measure mechanical deformation of structures and specimens. While metallic foil gauges usually have a gauge factor slightly over 2, single crystalline silicon demonstrates intrinsic gauge factors as high as 200. Although silicon is an intrinsically stiff and brittle material, flexible and even stretchable strain gauges have been achieved by integrating thin silicon strips on soft and deformable polymer substrates. To achieve a fundamental understanding of the large variance in gauge factor and stretchability of reported flexible/stretchable silicon-on-polymer strain gauges, finite element and analytically models are established to reveal the effects of the length of the silicon strip, and the thickness and modulus of the polymer substrate. Analytical results for two limiting cases, i.e., infinitely thick substrate and infinitely long strip, have found good agreement with FEM results. We have discovered that strains in silicon resistor can vary by orders of magnitude with different substrate materials whereas strip length or substrate thickness only affects the strain level mildly. While the average strain in silicon reflects the gauge factor, the maximum strain in silicon governs the stretchability of the system. The tradeoff between gauge factor and stretchability of silicon-on-polymer strain gauges has been proposed and discussed.

Dependence of Peierls stress on lattice strains in silicon

Several non-Schmid effects of plasticity in Si are discussed in this article. The contribution of shear strain applied in the direction of the Burgers vector and normal to it in the glide plane, and of strain applied normal to the glide plane to defining the Peierls stress are analyzed. The analysis is performed using a combination of atomistic simulations and the Peierls–Nabarro model based on generalized stacking faults. It is shown that a shear strain acting in the direction of the Burgers vector decreases the Peierls stress and the effect is due to the reduction of the shear modulus. Bonding across the glide plane has the most important contribution to the Peierls stress, but the elastic non-linearity of the surrounding material contributes to reducing the instability threshold. A shear strain acting perpendicular to the Burgers vector has no effect on the Peierls stress. A compressive strain normal to the glide plane reduces the Peierls stress for shuffle dislocations and has a weak increasing effect on the critical stress of glide-set dislocations.

Lattice strain of hydrogen-implanted silicon: Correlation between X-ray scattering analysis and ab-initio simulations

Hydrogen implanted silicon has been studied using high resolution X-ray scattering. Strain induced by implantation has been measured as a function of implantation dose. The dependence of strain with implanted dose shows different regimes starting from linear to quadratic and saturation. The observed strain is consistent with ab-initio and elasticity calculations. Strain rate changes can be associated to the predominant location of hydrogen in bond center location.

Ab initiostudy of the effects of pressure and strain on electron-phonon coupling in IV and III-V semiconductors

In this work, we examine the pressure and biaxial tensile strain dependence of the intervalley electron–phonon matrix elements in the lowest conduction band of GaAs, GaP, Si and Ge within the density functional perturbation theory. We study both individual transitions and average deformation potential values which can be used as parameters in transport simulations. In the case of a hydrostatic pressure, we draw the general conclusion that the hydrostatic pressure dependence of the intervalley electron–phonon matrix elements can be safely neglected in the interpretation of most commonly studied phenomena. In contrast, the case of a biaxial strain in silicon shows that strain-dependence should be taken into account in calculations of the intervalley electron–phonon matrix elements.

Analytical models for the thermal strain and stress induced by annular through-silicon-via (TSV)

Accurate analytical models for the strain and stress in silicon induced by annular Through-silicon-via (TSV) are proposed. Finite element method (FEM) is used for the model verification. It is shown that errors for the strain and stress models are respectively less than 6.6% and 6.8% for various metal and dielectric materials. Based on the analytical model of stress, keep-out-zones (KOZs) are also evaluated for pMOS and nMOS, as the stress is parallel and perpendicular to transistor channel. Annular TSVs with various materials induce KOZs of less than 6.6μm. W exhibits the best thermo-mechanical performance with KOZ=0.

Exploring novel characteristics of strain compensated SiGeC nanoscale MOSFET

In the present work a precise but simple empirical model for single gate nanoscale single-layer fully depleted strained-silicon-on-insulator MOSFET is proposed. The threshold voltage is calculated by solving the two-dimensional (2D) Poisson equation under befitting boundary conditions incorporating short-channel effects, the effect of strain, strained-silicon thin film thickness, and gate work function. The proposed empirical model provides results comparable with those obtained from 2D device simulation thereby establishing the extent of accuracy of our present model. The empirical model so developed correctly exhibits that the threshold voltage is reduced with the increase of strain in the silicon thin film. We have investigated, herewith our proposed model, the influences of various device parameters like: strain (with minute amount of carbon and significant amount of Ge), strained-silicon thin-film thickness and gate work function on the threshold voltage. The extent of equivalent Ge content enhances the performance of the proposed MOSFET in terms of better speed because of the carrier mobility enhancement due to addition of carbon atoms.

Stress and Strain in the Sweet Cherry Skin

Rain-cracking of sweet cherry (Prunus avium L.) fruit involves failure of the exocarp caused by excessive stress and strain. The objective of our study was to quantify exocarp strain in developing cherries. The release of linear elastic strain was followed in vivo using a gaping assay, whereas the release of biaxial elastic strain was followed in vitro after excision of small exocarp segments (ESs) that were submerged in silicone oil and strain release quantified by image analysis. When mature sweet cherry fruit were cut (by making two or more deep, longitudinal incisions parallel to the stylar/pedicel axis and on opposing sides of the fruit down to the pit), the incisions rapidly “gaped.” The gaping wounds continued to widen as they progressively released the linear elastic strain in the skin. By 24 hours the combined widths of two gapes represented 8.8% ± 0.1% of the fruit circumference. Increasing the number of cuts from two to 12 increased the cumulative gape widths to 14.9% ± 0.2%. In ES, monitoring the time course of relaxation after excision revealed a rapid release of biaxial strain, having a half-time of ≈2.7 minutes. Relaxation continued, but at a decreasing rate, for up to 48 hours. Across eight cherry cultivars, the biaxial strain in the exocarp at maturity ranged from 18.7% ± 1.9% in ‘Lapins’ to 36.0% ± 1.8% in ‘Katalin’. Elastic strain in the ES was always lower than that measured in an isolated cuticular membrane (CM). Increasing the temperature from 2 to 35 °C increased the rate of strain release and also the total percent strain released at 96 hours. In developing ‘Hedelfinger’ sweet cherry fruit, there was essentially no elastic strain in the exocarp at 45 days after full bloom (DAFB). Thereafter, significant elastic strain developed, reaching a maximum of 47.6% ± 2.5% at 87 DAFB. The effect of exocarp cell turgor on strain in the ES (evidenced by the difference in the reversible strain between ES with and without turgor) was closely and positively related to the relative area growth rate of the skin (r2 = 0.957). Strain release peaked at ≈59 DAFB, and there was no effect of turgor on strain release in mature fruit. Our data demonstrated the following: 1) the exocarp is a viscoelastic material composite; 2) at maturity, plastic and elastic strain components make up 66% and 34% of the total percent strain, respectively; 3) elastic strain in the exocarp increases during Stage III development; and 4) the strain in the exocarp is unaffected by strain in the CM. Thus, the epidermis and hypodermis layers must represent the main, load-bearing structure in sweet cherry fruit with the cuticle making a mechanically insignificant contribution.

Study of shear-stiffened elastomers

This paper presents a novel shear-stiffened elastomer (SSE) fabricated with a mixture of silicone rubber and silicone oil. A total of four SSE samples were fabricated in this study. Their mechanical and rheological properties under both steady-state and dynamic loading conditions were tested with a parallel plate rheometer. The effects of silicone oil composition, strain amplitude and angular frequency were summarized. When raising the angular frequency in the dynamic shear test, the storage modulus of conventional silicone rubber shows a small increasing trend with the frequency. However, if silicone oil is selected to be mixed with silicone rubber, the storage modulus increases dramatically when the frequency and strain are both beyond the critical values.