Quasi-Transient Calculation of Czochralski Growth of Ge Crystals Using the Software Elmer

A numerical scheme was developed to compute the thermal and stress fields of the Czochralski process in a quasi-time dependent mode. The growth velocity was computed from the geometrical changes in melt and crystal due to pulling for every stage, for which the thermal and stress fields were computed by using the open source software Elmer. The method was applied to the Czochralski growth of Ge crystals by inductive heating. From a series of growth experiments, we chose one as a reference to check the validity of the scheme with respect to this Czochralski process. A good agreement both for the shapes of the melt/crystal interface at various time steps and the change in power consumption with process time was observed.

Download Full-text

Numerical Study of the Effect of Magnetic Fields on Melt-Crystal Interface-Deflection in Czochralski Crystal Growth

Heat Transfer: Volume 3 ◽

10.1115/ht2003-47534 ◽

2003 ◽

Cited By ~ 2

Author(s):

Lijun Liu ◽

Koichi Kakimoto

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Numerical Study ◽

Silicon Crystal ◽

Czochralski Growth ◽

Thermal Flow ◽

Interface Shape ◽

Convective Thermal ◽

And Control ◽

Crystal Interface

In order to control the impurity distribution and remove defects in a crystal grown in Czochralski growth for high quality crystals of silicon, it is necessary to study and control the melt-crystal interface shape, which plays an important role in control of the crystal quality. The melt-crystal interface interacts with and is determined by the convective thermal flow of the melt in the crucible. Application of magnetic field in the Czochralski system is an effective tool to control the convective thermal flow in the crucible. Therefore, the shape of the melt-crystal interface can be modified accordingly. Numerical study is performed in this paper to understand the effect of magnetic field on the interface deflection in Czochralski system. Comparisons have been carried out by computations for four arrangements of the magnetic field: without magnetic field, a vertical magnetic field and two types of cusp-shaped magnetic field. The velocity, pressure, thermal and electromagnetic fields are solved with adaptation of the mesh to the iteratively modified interface shape. The multi-block technique is applied to discretize the melt field in the crucible and the solid field of silicon crystal. The unknown shape of the melt-crystal interface is achieved by an iterative procedure. The computation results show that the magnetic fields have obvious effects on both the pattern and strength of the convective flow and the interface shape. Applying magnetic field in the Czochralski system, therefore, is an effective tool to control the quality of bulk crystal in Czochralski growth process.

Download Full-text

TCAD Study of the Raised SiGe Source/Drain in 40nm PMOS

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.645-646.70 ◽

2015 ◽

Vol 645-646 ◽

pp. 70-74 ◽

Cited By ~ 1

Author(s):

Min Zhong ◽

Yu Hang Zhao ◽

Shou Mian Chen ◽

Ming Li ◽

Shao Hai Zeng ◽

...

Keyword(s):

Computer Aided Design ◽

Critical Role ◽

Sige Layer ◽

Strain Engineering ◽

Effect Transistor ◽

Simulation Results ◽

Aided Design ◽

The Relationship ◽

Growth Experiments ◽

Good Agreement

An embedded SiGe layer was applied in the source/drain areas (S/D) of a field-effect transistor to boost the performance in the p channels. Raised SiGe S/D plays a critical role in strain engineering. In this study, the relationship between the SiGe overfilling and the enhancement of channel stress was investigated. Systematic technology computer aided design (TCAD) simulations of the SiGe overfill height in a 40 nm PMOS were performed. The simulation results indicate that a moderate SiGe overfilling induces the highest stress in the channel. Corresponding epitaxial growth experiments were done and the obtained experimental data was in good agreement with the simulation results. The effect of the SiGe overfilling is briefly discussed. The results and conclusions presented within this paper might serve as useful references for the optimization of the embedded SiGe stressor for 40 nm logic technology node and beyond.

Download Full-text

Effect of the pulling, crystal and crucible rotation rate on the thermal stress and the melt–crystal interface in the Czochralski growth of germanium crystals

CrystEngComm ◽

10.1039/d1ce00455g ◽

2021 ◽

Vol 23 (39) ◽

pp. 6967-6976

Author(s):

Mahboobeh Saadatirad ◽

Mohammad Hossein Tavakoli ◽

Hossein Khodamoradi ◽

Seyedeh Razieh Masharian

Keyword(s):

Thermal Stress ◽

Rotation Rate ◽

Czochralski Growth ◽

Interface Shape ◽

Crucible Rotation ◽

Crystal Interface

The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.

Download Full-text

Prediction of the melt/crystal interface geometry in liquid encapsulated Czochralski growth of InP bulk crystals

Journal of Crystal Growth ◽

10.1016/s0022-0248(02)02238-8 ◽

2003 ◽

Vol 250 (1-2) ◽

pp. 189-194 ◽

Cited By ~ 9

Author(s):

E.N. Bystrova ◽

V.V. Kalaev ◽

O.V. Smirnova ◽

E.V. Yakovlev ◽

Yu.N. Makarov

Keyword(s):

Czochralski Growth ◽

Bulk Crystals ◽

Crystal Interface ◽

Interface Geometry

Download Full-text

The Effect of Hydrogen on the Kinetics of Solid Phase Epitaxy in Amorphous Silicon

MRS Proceedings ◽

10.1557/proc-205-45 ◽

1990 ◽

Vol 205 ◽

Cited By ~ 9

Author(s):

J. A. Roth ◽

G. L. Olson ◽

D. C. Jacobson ◽

J. M. Poate ◽

C. Kirschbaum

Keyword(s):

Growth Rate ◽

Solid Phase ◽

Intrinsic Value ◽

Amorphous Layer ◽

Inert Gas ◽

Solid Phase Epitaxy ◽

Depth Profiles ◽

Kinetics Of ◽

Crystal Interface ◽

Good Agreement

AbstractThis paper discusses the intrusion of H into a-Si layers during solid phase epitaxy and the effect of this H on the growth kinetics. We show that during annealing in the presence of water vapor, H is continuously generated at the oxidizing a-Si surface and diffuses into the amorphous layer, where it causes a reduction in the epitaxial growth rate. The measured variation of growth rate with the depth of the amorphous/crystal interface is correlated with the concentration of H at the interface. The diffusion coefficient for H in a-Si is determined by comparing measured depth profiles with calculated values. Hydrogen intrusion is observed even in layers annealed in vacuum and in inert gas ambients. Thin (<;5000 Åthick) a-Si layers are especially susceptible to this effect, but we show that in spite of the presence of H the activation energy for SPE derived earlier from thin-layer data is in good agreement with the intrinsic value obtained from thick, hydrogen-free layers.

Download Full-text

Impact of force function formulations on the numerical simulation of centre-based models

10.1101/2020.03.16.993246 ◽

2020 ◽

Author(s):

Sonja Mathias ◽

Adrien Coulier ◽

Anass Bouchnita ◽

Andreas Hellander

Keyword(s):

Cell Division ◽

Open Source Software ◽

Computational Study ◽

Population Level ◽

Biological Behaviour ◽

Cancer Modelling ◽

Software Implementations ◽

Cell Trajectories ◽

Cell Centre ◽

Good Agreement

AbstractCentre-based, or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeler to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a growing monolayer. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

Download Full-text

New Optimisation Procedure for Outlet Angle of a Hawt Turbine Blade Element

Wind Engineering ◽

10.1260/0309524001495594 ◽

2000 ◽

Vol 24 (3) ◽

pp. 241-245 ◽

Cited By ~ 2

Author(s):

Nzumbe-Mesape Ntoko

Keyword(s):

Turbine Blade ◽

Relative Velocity ◽

Numerical Scheme ◽

Blade Angle ◽

Impulse Turbine ◽

Outlet Angle ◽

Velocity Coefficient ◽

Optimisation Procedure ◽

Good Agreement ◽

Blade Element

A new expression is developed for the optimum outlet blade angle of a HAWT turbine blade element using impulse turbine theory. A simple numerical scheme is then given for calculating the blade angle using a modified expression for the relative velocity coefficient. Numerical results are presented which are in good agreement with optimum values.

Download Full-text

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Bulletin of Mathematical Biology ◽

10.1007/s11538-020-00810-2 ◽

2020 ◽

Vol 82 (10) ◽

Author(s):

Sonja Mathias ◽

Adrien Coulier ◽

Anass Bouchnita ◽

Andreas Hellander

Keyword(s):

Cell Division ◽

Open Source Software ◽

Computational Study ◽

Population Level ◽

Biological Behaviour ◽

Cancer Modelling ◽

Software Implementations ◽

Cell Trajectories ◽

Cell Centre ◽

Good Agreement

Abstract Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

Download Full-text

A comparative evaluation of functions for partitioning nitrogen and amino acid intake between maintenance and growth in broilers

The Journal of Agricultural Science ◽

10.1017/s0021859607007423 ◽

2007 ◽

Vol 146 (2) ◽

pp. 163-170 ◽

Cited By ~ 10

Author(s):

E. KEBREAB ◽

J. FRANCE ◽

H. DARMANI KUHI ◽

S. LOPEZ

Keyword(s):

Amino Acid ◽

Comparative Evaluation ◽

Crude Protein ◽

Live Weight ◽

N Balance ◽

Straight Line ◽

Amino Acid Intake ◽

The Relationship ◽

Growth Experiments ◽

Good Agreement

SUMMARYThe results from three types of study with broilers, namely nitrogen (N) balance, bioassays and growth experiments, provided the data used herein. Sets of data on N balance and protein accretion (bioassay studies) were used to assess the ability of the monomolecular equation to describe the relationship between (i) N balance and amino acid (AA) intake and (ii) protein accretion and AA intake. The model estimated the levels of isoleucine, lysine, valine, threonine, methionine, total sulphur AAs and tryptophan resulting in zero balance to be 58, 59, 80, 96, 23, 85 and 32 mg/kg live weight (LW)/day, respectively. These estimates show good agreement with those obtained in previous studies. For the growth experiments, four models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine crude protein (CP) intake at maintenance and efficiency of utilization of CP intake for producing gain. They were: a straight line, two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola) and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The estimates of CP requirement for maintenance and efficiency of utilization of CP intake for producing gain varied from 5·4 to 5·9 g/kg LW/day and 0·60 to 0·76, respectively, depending on the models.

Download Full-text

Numerical Analysis for Resistance Calculations of NPL as a Floating Hull for Wave Glider

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.619.38 ◽

2014 ◽

Vol 619 ◽

pp. 38-43 ◽

Cited By ~ 2

Author(s):

Aladdin Elhadad ◽

Wen Yang Duan ◽

Rui Deng ◽

H. Elhanfey

Keyword(s):

Numerical Analysis ◽

Mesh Generation ◽

Numerical Scheme ◽

Water Resistance ◽

Numerical Predictions ◽

Calm Water ◽

Resistance Prediction ◽

Wave Glider ◽

Solution Parameters ◽

Good Agreement

Thewave glideris an autonomous unmanned vehicle (AUV) which uses the power of the ocean to propel itself. The purpose of this study is using the well known slender modelNPLin developing hull in an attempt to design the floating hull ofwave glider.CFDandMaxsurfsoftware are used to present a method focused on mesh generation to predictcalm water resistancefor the hull. Calculations are carried out for Froude numbers in the range of 0.10 to 0.40. Three different mesh sizes are used forCFDto calculate the mesh effects. The results of numerical predictions under the same conditions obtained fromCFDandMaxsurfcalculations are obtained and compared for accuracy of the solution parameters. The comparison shows a good agreement between the results. The method is useful and acceptable and the overall numerical scheme is suitable for resistance prediction.

Download Full-text