• 대한수학회지
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• 제35권3호
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• pp.637-658
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• 1998

One-dimensional diffusion processes are characterized by Feller's data of canonical scales and speed measures and, if we apply the theory of spectral functions of strings developed by M. G. Krein, Feller's data are determined by paris of spectral characteristic functions so that theses pairs may be considered as invariants of diffusions under the homeomorphic change of state spaces. We show by examples how these invariants are useful in the study of one-dimensional diffusion processes.

• 한국전기전자재료학회논문지
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• 제28권11호
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• pp.683-689
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• 2015

For the formation of $N^+$ doping, the antimony ions are mainly used for the fabrication of a BJT (bipolar junction transistor), CMOS (complementary metal oxide semiconductor), FET (field effect transistor) and BiCMOS (bipolar and complementary metal oxide semiconductor) process integration. Antimony is a heavy element and has relatively a low diffusion coefficient in silicon. Therefore, antimony is preferred as a candidate of ultra shallow junction for n type doping instead of arsenic implantation. Three-dimensional (3D) profiles of antimony are also compared one another from different tilt angles and incident energies under same dimensional conditions. The diffusion effect of antimony showed ORD (oxygen retarded diffusion) after thermal oxidation process. The interfacial effect of a $SiO_2/Si$ is influenced antimony diffusion and showed segregation effects during the oxidation process. The surface sputtering effect of antimony must be considered due to its heavy mass in the case of low energy and high dose conditions. The range of antimony implanted in amorphous and crystalline silicon are compared each other and its data and profiles also showed and explained after thermal annealing under inert $N_2$ gas and dry oxidation.

• 대한기계학회논문집B
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• 제23권8호
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• pp.997-1009
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• 1999

Silica particle formation and growth process including chemical reaction, coagulation and sintering was studied in a counterflow diffusion flame burner. The counterflow geometry provides a one dimensional flow field, along the stagnation point streamline, which greatly simplifies interpretation of the particle growth characteristics. $SiCl_4$ has been used as the source of silicon in hydrogen/oxygen/argon flames. The temperature profiles obtained by calculation showed a good agreement with experiment data. Using one and two dimensional sectional method, aerosol dynamics equation in a flame was solved, and these two results were compared. The two dimensional section method can consider sintering effect and growth of primary particle during synthesis, thus it showed evolution of morphology of non-spherical particles (aggregates) using surface fractal dimension. The effects of flame temperature and chemical loading on particle dynamics were studied. Geometric mean diameter based on surface area and total number concentration followed the trend of experiment results, especially, the change of diameters showed the sintering effect in high temperature environment.

• 대한전자공학회논문지
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• 제23권6호
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• pp.929-935
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• 1986

In this paper, we describe the physical modelling and numerical aspects of a program called PRECISE(Program for Efficient Calculation of Impurity Profile in Semiconductor by Elimination) which calcualtes a two-dimensional impurity profile in silicon due to diffusion and ion implantation steps. The PRECISE enables rapid prediction of the two-dimensional impurity profile near the mask edge-or the bird's beak during the local oxidation process. This has been developed by modifying the existing one-dimentional simulator, DIFSIM(DIFfusion SIMulator to include models for arsenic diffusion and emitter dip effect which were found out to agree fairly well with the xperimental data.

• 전자공학회논문지A
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• 제32A권8호
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• pp.107-118
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• 1995

Three-dimensional simulator for thermal oxidation process is developed. The simulator is consisted by two individual module, one is analytic-model module and the other is numerical-model module. The analytic-model which uses simple complementary-error function guarantees fast calculation in prediction of multi-dimensional oxidation process. The numerical-model which is based on boundary element method (BEM), has a good accuracy and suitable for various process conditions. The results of this study show that oxide growth is retarded at the corner of hole structure and enhanced at the corner of island structure. These effects are reson of different distribution of oxidant diffusion and mask stress. The utility of models and simulator developed in this study is demonstrated by using it to predict not only traditional shape of LOCOS but also process effects in small geometry.

• JSTS:Journal of Semiconductor Technology and Science
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• 제16권4호
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• pp.497-505
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• 2016

The two-dimensional (2D) Discrete Cosine Transform (DCT) is used widely in image and video processing systems. The perception of human visualization permits us to design approximate rather than exact DCT. In this paper, we propose a digital implementation of 16-point approximate 2D DCT architecture based on one-dimensional (1D) DCT and Modified Gate Diffusion Input (MGDI) technique. The 8-point 1D Approximate DCT architecture requires only 12 additions for realization in digital VLSI. Additions can be performed using the proposed 8 transistor (8T) MGDI Full Adder which reduces 2 transistors than the existing 10 transistor (10T) MGDI Full Adder. The Approximate MGDI 2D DCT using 8T MGDI Full adders is simulated in Tanner SPICE for $0.18{\mu}m$ CMOS process technology at 100MHZ.The simulation result shows that 13.9% of area and 15.08 % of power is reduced in the 8-point approximate 2D DCT, 10.63 % of area and 15.48% of power is reduced in case of 16-point approximate 2D DCT using 8 Transistor MGDI Full Adder than 10 Transistor MGDI Full Adder. The proposed architecture enhances results in terms of hardware complexity, regularity and modularity with a little compromise in accuracy.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1995년도 추계학술대회 논문집
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• pp.48-51
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• 1995

We have developed the three dimensional mesh generator for three dimensional process simulation using the FEM(Finite Element Method). Tetrahedron element construct the presented three dimensional mesh, which is suitable for the simulation of three dimensional behavior of the LOCOS. The simulation of thermal oxidation is one of the problem in scale downed semiconductor processes. As three dimensional simulators use the huge size of the memory, we use the efficient method that generates the new nodes inside the growing oxide and removes the nodes nearby the SiO2/Si interface in silicon. The resented three dimensional mesh generator was designed to be used in various process simulations, for instance thermal oxidation, silicidation, nitridation, ion implantation, diffusion, and so on.

• 한국환경과학회지
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• 제1권1호
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• pp.35-43
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• 1992

Handling the emergency problems such as Chemobyl accident require real time prediction of pollutants dispersion. One-point real time sounding at pollutant source and simple model including turbulent-radiation process are very important to predict dispersion at real time. The stability categories obtained by one-dimensional numerical model (including PBL dynamics and radiative process) are good agreement with observational data (Golder, 1972). Therefore, the meteorological parameters (thermal, moisture and momentum fluxes; sensible and latent heat; Monin-Obukhov length and bulk Richardson number; vertical diffusion coefficient and TKE; mixing height) calculated by this model will be useful to understand the structure of stable boundary layer and to handling the emergency problems such as dangerous gasses accident. Especially, this simple model has strong merit for practical dispersion models which require turbulence process but does not takes long time to real predictions. According to the results of this model, the urban area has stronger vertical dispersion and weaker horizontal dispersion than rural area during daytime in summer season. The maximum stability class of urban area and rural area are "A" and "B" at 14 LST, respectively. After 20 LST, both urban and rural area have weak vertical dispersion, but they have strong horizontal dispersion. Generally, the urban area have larger radius of horizontal dispersion than rural area. Considering the resolution and time consuming problems of three dimensional grid model, one-dimensional model with one-point real sounding have strong merit for practical dispersion model.al dispersion model.

• Bulletin of the Korean Chemical Society
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• 제8권2호
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• pp.83-88
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• 1987

The Smoluchowski equations with a linear and a parabolic potentials in one-dimensional case are solved for the reflecting boundary condition. Analytic expressions for the long-time behaviors of the remaining probabilities are obtained. These results, together with the previous result for a step potential, show the dependence of the desorption process on the form of potential. The effect of the radiation boundary condition is also investigated for three types of potentials.

• Water Engineering Research
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• 제2권3호
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• pp.187-196
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• 2001

An approximate analytical solution of a nonlinear hydro-thermo coupled diffusion equation is derived using the dimensionless form of the equation and transformation method. To derive an analytical solution, it is drastically assumed that the product of first order derivatives in the non-dimensionalized governing equation has little influence on the solution of heat and moisture behavior problem. The validity of this drastic assumption is demonstrated. Some numerical simulation is performed to investigate the applicability of a derived approximate analytical solution. The results show a good agreement between analytical and numerical solutions. The proposed solution may provide a useful tool in the verification process of the numerical models. Also, the solution can be used for the analysis of one-dimensional coupled heat and moisture movements in unsaturated porous media.