Modeling the Boron-Doping Silicon Beam by a Multilayer Model

The boron-doping silicon beam commonly used in microdevices exhibits a nonuniform material property along its thickness or width because of the gradient of boron concentration induced by diffusion process. The constant of rigidity, one of the most important parameters of microbeam, needs to be accurately calculated and designed in the development of high precise sensors and actuators. Current design methods, mainly depending on the analytical solutions derived under the assumption of a uniform material property or some commercial software for a varied property, are not adequate and time consuming to calculate the constant of rigidity of boron-doping silicon beam. A multilayer model is proposed in this paper to replace the continuous solid model by dividing the beam into separated layers glued together. The finite element lamination method is utilized to acquire the equivalent Young modulus and moment of inertia of cross section of multilayer model. The equivalent values are calculated from double-layer structures to multilayer ones based on the small deformation theory and the material mechanics theory. The proposed method provides an effective method to design the stiffness or frequency of microdevice and its results are validated by COMSOL simulation.

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On Compression of Rubber Elastic Sphere Over a Large Range of Displacements—Part 1: Theoretical Study

Journal of Engineering Materials and Technology ◽

10.1115/1.2903407 ◽

1991 ◽

Vol 113 (3) ◽

pp. 285-291 ◽

Cited By ~ 68

Author(s):

Y. Tatara

Keyword(s):

Contact Surface ◽

Theoretical Study ◽

Large Range ◽

Young Modulus ◽

Small Deformation ◽

Lateral Extension ◽

Elastic Deformations ◽

Elastic Bodies ◽

Simple Compression ◽

Applied Forces

This paper presents one general theory of large elastic deformations of a rubber sphere in simple compression, as the removal of restrictions of the constant Young modulus and small deformation in the prevailing Hertzian theory in contact of elastic bodies. It derives a set of five equations associated with approach, radii of contact surface without and with lateral extension of free surface, the lateral extensive displacement on the contact surface and the position of the contact surface in a very large range of applied forces, on the basis of the Hertz theory (half-space elastic body model) with an extensive term, in consideration of the rubber-elastic nonlinear elasticity, the lateral extension and the symmetry of the deformed shape of the rubber sphere. In Part 2 it is shown that results calculated by the set of the equations fit experimental data for a rubber sphere.

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Electron Energy Analysis of Germanium and Silica Layers on Silicon Substrates

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100114104 ◽

1975 ◽

Vol 33 ◽

pp. 96-97

Author(s):

R. W. Ditchfield ◽

A. G. Cullis

Keyword(s):

Epitaxial Growth ◽

Electron Energy ◽

Silicon Substrates ◽

Secondary Phases ◽

Si Substrates ◽

Transmission Electron ◽

Layer Structures ◽

Si Films ◽

Electron Energy Loss ◽

Growth Centres

An energy analyzing transmission electron microscope of the Möllenstedt type was used to measure the electron energy loss spectra given by various layer structures to a spatial resolution of 100Å. The technique is an important, method of microanalysis and has been used to identify secondary phases in alloys and impurity particles incorporated into epitaxial Si films.Layers Formed by the Epitaxial Growth of Ge on Si Substrates Following studies of the epitaxial growth of Ge on (111) Si substrates by vacuum evaporation, it was important to investigate the possible mixing of these two elements in the grown layers. These layers consisted of separate growth centres which were often triangular and oriented in the same sense, as shown in Fig. 1.

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Computer programs for the calculation of x-ray intensities emitted by elements in multi-layer structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134685 ◽

1990 ◽

Vol 48 (2) ◽

pp. 216-217

Author(s):

G.F. Bastin ◽

H.J.M. Heijligers ◽

J.M. Dijkstra

Keyword(s):

Software Package ◽

Light Element ◽

Matrix Correction ◽

Excellent Performance ◽

Element Analysis ◽

X Ray ◽

Know How ◽

Accurate Knowledge ◽

Layer Structures ◽

Bulk Matrix

For the calculation of X-ray intensities emitted by elements present in multi-layer systems it is vital to have an accurate knowledge of the x-ray ionization vs. mass-depth (ϕ(ρz)) curves as a function of accelerating voltage and atomic number of films and substrate. Once this knowledge is available the way is open to the analysis of thin films in which both the thicknesses as well as the compositions can usually be determined simultaneously.Our bulk matrix correction “PROZA” with its proven excellent performance for a wide variety of applications (e.g., ultra-light element analysis, extremes in accelerating voltage) has been used as the basis for the development of the software package discussed here. The PROZA program is based on our own modifications of the surface-centred Gaussian ϕ(ρz) model, originally introduced by Packwood and Brown. For its extension towards thin film applications it is required to know how the 4 Gaussian parameters α, β, γ and ϕ(o) for each element in each of the films are affected by the film thickness and the presence of other layers and the substrate.

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Intergrowth of modulated structures in high Tc Bi-Sr-Ca-Cu-O superconductors

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173510 ◽

1990 ◽

Vol 48 (4) ◽

pp. 76-77

Author(s):

A.Q. He ◽

G.W. Qiao ◽

J. Zhu ◽

H.Q. Ye

Keyword(s):

Twin Structure ◽

Modulated Structure ◽

High Tc ◽

One Dimensional ◽

Lattice Constants ◽

Superconducting Phases ◽

Modulated Structures ◽

Layer Structures

Since the first discovery of high Tc Bi-Sr-Ca-Cu-O superconductor by Maeda et al, many EM works have been done on it. The results show that the superconducting phases have a type of ordered layer structures similar to that in Y-Ba-Cu-O system formulated in Bi2Sr2Can−1CunO2n+4 (n=1,2,3) (simply called 22(n-1) phase) with lattice constants of a=0.358, b=0.382nm but the length of c being different according to the different value of n in the formulate. Unlike the twin structure observed in the Y-Ba-Cu-O system, there is an incommensurate modulated structure in the superconducting phases of Bi system superconductors. Modulated wavelengths of both 1.3 and 2.7 nm have been observed in the 2212 phase. This communication mainly presents the intergrowth of these two kinds of one-dimensional modulated structures in 2212 phase.

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Investigation of ferroelectrics using conventional and in situ electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170669 ◽

1994 ◽

Vol 52 ◽

pp. 586-587

Author(s):

V. Saikumar ◽

H. M. Chan ◽

M. P. Harmer

Keyword(s):

Nonvolatile Memory ◽

Ferroelectric Materials ◽

Gate Insulator ◽

Sensors And Actuators ◽

In Situ Electron Microscopy ◽

Ferroelectric Domains ◽

Domain Boundaries ◽

Domain Interactions ◽

Memory Applications

In recent years, there has been a growing interest in the application of ferroelectric thin films for nonvolatile memory applications and as a gate insulator in DRAM structures. In addition, bulk ferroelectric materials are also widely used as components in electronic circuits and find numerous applications in sensors and actuators. To a large extent, the performance of ferroelectric materials are governed by the ferroelectric domains (with dimensions in the micron to sub-micron range) and the switching of domains in the presence of an applied field. Conventional TEM studies of ferroelectric domains structures, in conjunction with in-situ studies of the domain interactions can aid in explaining the behavior of ferroelectric materials, while providing some answers to the mechanisms and processes that influence the performance of ferroelectric materials. A few examples from bulk and thin film ferroelectric materials studied using the TEM are discussed below.Figure 1 shows micrographs of ferroelectric domains obtained from undoped and Fe-doped BaTiO3 single crystals. The domain boundaries have been identified as 90° domains with the boundaries parallel to <011>.

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