Elastic flexure of bilayered beams subject to strain differentials

2000 ◽  
Vol 15 (12) ◽  
pp. 2780-2788 ◽  
Author(s):  
T-J. Chuang ◽  
S. Lee
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Residual Stresses ◽  
Ultrathin Films ◽  
Analytical Method ◽  
Si Substrate ◽  
Representative Case

The residual stresses present in a thin film and the curvature formed at its substrate during deposition have been a great concern to electrochemists and process engineers. Here a new hybrid analytical method is presented to reanalyze the flexural problem subjected to a strain differential in the general case. It was shown that the present solutions for ultrathin films agree with Stoney's equation. Moreover, single or dual neutral axes resulted, depending on materials and thickness ratios between the film and the substrate. Quantitative differences with others in the solutions of deformed curvature and residual stress are discussed in a representative case of GaAs top coat/Si substrate wafers.

Residual Stresses for In-Situ Deposition of Thin-Film High-Temperature Superconductors

1994 ◽  
Vol 116 (4) ◽  
pp. 249-257 ◽  
Author(s):  
P. E. Phelan ◽  
M. N. Ghasemi Nejhad
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Residual Stresses ◽  
High Temperature Superconductors ◽  
Oxygen Stoichiometry ◽  
Chemical Shrinkage ◽  
In Situ Deposition ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

Residual stresses are caused by nonuniform thermal expansion and chemical shrinkage taking place during processing. For thin-film high-temperature superconductors, residual stresses result because of the thermal expansion mismatch between the film and substrate, and the introduction of oxygen into the film after in-situ deposition, which makes the unit cell dimensions change (chemical shrinkage) as the oxygen stoichiometry changes. Since both the reliability of the film—especially the bond between the film and substrate—and the film critical temperature are functions of the state of stress, it is important to understand how the residual stresses vary with processing conditions. Here, a three-dimensional residual stress analysis is carried out based on laminate theory, which assumes the lateral dimensions of the entire system to be much larger than its thickness. The normal residual stress components in the film, and the peeling stress at the film/substrate interface, are calculated. The results demonstrate the crucial role that chemical shrinkage plays in the formulation of residual stresses. A large portion of the stresses arises from the initial change of the unit cell dimensions due to changes in the film oxygen stoichiometry. Therefore, the processing temperature, and especially the initial oxygen pressure in the deposition chamber, are the key variables that impact the residual stresses.

RESIDUAL STRESSES IN OBLIQUE INCIDENCE DEPOSITED ALUMINA THIN FILM

2014 ◽  
Vol 21 (02) ◽  
pp. 1450024 ◽  
Author(s):  
LIJUN HE ◽  
CHUAN LI ◽  
XINGZHAO LIU
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Residual Stresses ◽  
Film Thickness ◽  
Substrate Temperature ◽  
Deposition Rate ◽  
Growth Parameters ◽  
Testing Temperature ◽  
Alumina Thin Film ◽  
Inclined Angle

Residual stresses of alumina thin film deposited on silicon substrate by using electron beam evaporation with oblique angle deposition (OAD) method are studied. The growth parameters that affect the residual stresses of alumina thin film, such as the substrate temperature, the deposition rate, the film thickness, the inclined angle, and the testing temperature are discussed. The results show that the tensile stress value decreases with the increasing substrate temperature, and the compressive stress value increases with the increasing substrate temperature at various inclined angles. Along with the deposition rate increasing, the residual stress value decreases at various inclined angles. With the increasing film thickness, the residual stress value decreases at various inclined angles. With the increasing testing temperature, the residual stress value increases at various inclined angles. While the alumina thin film residual stress value is small at high inclined angle. By choosing the appropriate film preparation parameters, the alumina thin film residual stress is effectively controlled.

Residual Stress Analysis of A Multi-Layer Thin Film Structure by Destructive (Curvature) and Non-Destructive (X-Ray) Methods

1989 ◽  
Vol 153 ◽  
Author(s):  
P.C. Chen ◽  
Yoshiki Oshida
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Residual Stresses ◽  
Material System ◽  
Ray Method ◽  
X Ray ◽  
Removal Method ◽  
Layer Removal ◽  
Layer Removal Method ◽  
Layer Thin Film

AbstractMulti-layer thin film which has structure of Cu/Cr/K/Cr/Cu prepared by sputtering process was analyzed for interfacial stresses for as-deposited conditions. This structure was also annealed at 150°C, 250°C, and 350°C for around 15 min. in a vacuum and cooled slowly down for stress analyses.Equations derived by Osgood [1] for residual stress estimations for homogeneous material system using layer removal technique (stress relief) is now applied for inhomogeneous system (multilayer structure). The results are compared with the data obtained from x-ray diffraction technique by using sin2Ψ-2θ method, for Cu layer.From the present analyses, the data obatined using layer removal seem to be qualitatively consistent with but not quantitatively in agreement with x-ray method. Data obtained using the layer removal method have some overlaps with those obtained from x-ray technique. However, in details, data from the curvature method present different scattering band from the x-ray method. It is suggested that the layer removal method is more practical to be used to estimate the average residual stress of the multi-layer system not only because the layer removal method estimates the bulk behavior but also when the metal film is thin (e.g., 200A for Cr layer), x-ray technique becomes impractical. By annealing the sputtered structure up to 250°C, the residual stresses, in particularly Cu layer, decreased on both sides in x- and y-directions.From the main results drawn from the present studies, the layer removal sequence for the curvature method shows significant affects on the obtained results of residual stresses. Minimizing influences caused by layer removal sequences as well as removing duration and temperature provides the most accurate results on residual stress measurements.

Stress Relaxation of a Patterned Microstructure on a Diaphragm

2002 ◽  
Vol 17 (7) ◽  
pp. 1795-1802 ◽  
Author(s):  
D. W. Zheng ◽  
X. H. Wang ◽  
K. Shyu ◽  
C. Chen ◽  
C-T. Chang ◽  
...  
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Stress Relaxation ◽  
Sequential Analysis ◽  
Green Laser ◽  
Simulation Software ◽  
Substrate Thickness ◽  
Si Substrate ◽  
Written Simulation ◽  
Patterned Microstructure

Stress relaxation of a patterned thin film on diaphragms of different material and thickness was investigated through experimental study and numerical simulation. The diaphragm deflections, caused by relaxation of the residual stress in a patterned thin film residing on top, were measured using a Twyman–Green laser interferometer. The first diaphragm used was a Si3N4(top)/SiO2/Si composite diaphragm and the second a 0.5-μm-thick Si3N4 membrane. Custom-written simulation software, which uses a novel numerical algorithm named Nonlinear Sequential Analysis (N-LISA), was utilized to calculate the stress distribution in the patterned thin film and the diaphragm substrate. Agreement between the model and the experimental results was satisfactory. Simulation of the system balance between a tensile-stressed circular Ti film and a stress-free Si substrate of different thickness clearly shows a transition in the substrate behavior from a pure plate to a pure membrane. Interestingly, the deflection of the Si substrate caused by the residual stress in the Ti film reaches its maximum at a certain substrate thickness where plate and membrane characteristics coexist. This study addresses some basic mechanics issues involved in modern devices dealing with thin diaphragms.

Silicon to Silicon Wafer Bonding at Low Temperature Using Residual Stress Controlled Evaporated Glass Thin Film

2006 ◽  
Vol 510-511 ◽  
pp. 1054-1057
Author(s):  
Joon Shik Park ◽  
Yeon Shik Choi ◽  
Sung Goon Kang
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Low Temperature ◽  
Residual Stresses ◽  
Compressive Stress ◽  
Silicon Wafer ◽  
Wafer Bonding ◽  
Annealing Process ◽  
Thick Glass ◽  
Glass Films

Silicon to silicon wafer bonding at low temperature of 300 °C using residual stress controlled evaporated 2 ㎛ thick Pyrex glass thin film (briefly, glass thin film) on silicon wafer was investigated. It was found that residual stresses of 2 ㎛ thick glass films on silicon wafers were strongly dependent upon moisture contents and annealing processes. Residual stresses of asdeposited glass films with compressive stress of -150 MPa could be changed to more compressive stress of -230 MPa by moisture absorption. However, after annealing process at 200 °C to 400 °C for 30 min, residual stresses were remarkably changed to tensile stresses of about 75 MPa to 130 MPa, respectively. For the reliable wafer bonding process, the evaporated glass thin films should be annealed in the range of 200 °C to 500 °C for 30 min. So, bare silicon to bare silicon and bare silicon to patterned silicon were bonded at 300 °C and 30 V ~ 60 V for 15 min using 2 ㎛ thick glass film with residual stress of 130 MPa which were generated after the annealing process of 400 °C for 30 min. These results could be used for low temperature silicon to silicon wafer bondings for applications of micro sensors, micro actuators and micro fluidics devices.

Thin Film Residual Stress Assessment of MEMS Microphone Using Process Modeling Technology

2011 ◽  
Author(s):  
Han-Jung Wang ◽  
Hung-An Deng ◽  
Shih-Ying Chiang ◽  
Kuo-Ning Chiang
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Residual Stresses ◽  
Process Modeling ◽  
Lattice Mismatch ◽  
Aluminum Film ◽  
Intrinsic Stress ◽  
Element Analysis ◽  
Modeling Technology ◽  
Mems Microphone

The characteristic of MEMS component is affected by different process procedures such as depositing and etching thin films on substrate. These processes might induce residual stresses or deformations in MEMS component, which will reduce its efficiency and quality, and it is very unfavorable in MEMS development. This study develops a methodology that uses Finite Element Analysis (FEA) along with process modeling technology to analyze the residual stress in a MEMS microphone structure. The residual stress of thin film is composed of thermal and intrinsic stress. The thermal stress can be obtained directly in FEA but not for the intrinsic stress, which is a process-dependent material property. The intrinsic stress in multilayered structure is obtained from Stoney’s experiment which measures the curvature on blanket wafer after each process. A comparison of the experimental and simulated results showed that dislocation induced intrinsic stress in aluminum can be rearrangement after first annealing. The lattice mismatch induced intrinsic stress, however, will influence the residual stress of the aluminum film when its thickness is under 1μm. The residual stresses and the deformations in two electrode plates are presented for the process simulation in the MEMS microphone. The polysilicon would buckle and warp downward if it is subjected to compressive stress. However, the polysilicon diaphragm would be flat in the positive intrinsic stress.

Influences of Initial Residual Stresses on Milling Distortion for Thick Aero-Aluminum-Alloy Plate

2011 ◽  
Vol 381 ◽  
pp. 44-47
Author(s):  
Hun Guo ◽  
Dun Wen Zuo ◽  
Guo Xing Tang ◽  
W.M. Gan
Keyword(s):  
Residual Stress ◽  
Aluminum Alloy ◽  
Residual Stresses ◽  
Analytical Method ◽  
Milling Process ◽  
Alloy Plate ◽  
Machining Distortion ◽  
Aluminum Alloy Plate

Formulae of stress re-distribution and distortion by stress releasing during milling process are deduced to Initial Residual Stresses. Theory prediction of milling deformation due to residual stress is finished, and some calculating equation is given for the deformation solution. By means of these researches, the mechanism of the milling deformation due to residual stress is analyzed, the machining distortion caused by residual stress are analyzed and summarized using the analytical method.

Thin Film Critical Residual Stress for Metal Pads on a Ceramic Substrate

1992 ◽  
Vol 36 ◽  
pp. 213-220
Author(s):  
C. C. Goldsmith ◽  
S. M. Kamath ◽  
A. H. Kumar
Keyword(s):  
Thin Film ◽  
Residual Stress ◽  
Stress Intensity ◽  
Residual Stresses ◽  
Deposition Process ◽  
Ceramic Substrates ◽  
Metal Thickness ◽  
Multi Level ◽  
General Defect

AbstractResidual stresses present in thin films evaporated on ceramic substrates, can lead to loss of adhesion of the metal features to the ceramic, or, between metal films in multi-level stacks. If the adhesion is good, ceramic cracking may occur around the metal features. Long term one must avoid stress corrosion cracking in the ceramic. These residual stresses are generated by a variety of causes. In general, defect incorporation during the deposition process and thermal expansion mismatch between thin film and substrate play major roles.In this paper, we describe a method for determining the residual stresses that may be detrimental, or more accurately, the residual stress induced load that may cause reliability problems. This method involves evaporating metal pads or various thicknesses onto the ceramic to the point of failure, and measuring the residual stress loading on the substrate. A direct measure of this loading is the stress intensity factor which takes into account both the residual stress and pad or film thickness. Thus, a critical “load” or stress intensity at which substrate cracking or thin film delamination occurs can be estimated. This approach can be used to select the optimum metal-thickness combination for various substrates.

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