Engineering topics

Ramachandran, P. A.

Publications and source records attributed to Ramachandran, P. A..

9 records

NASA NTRS1989

Semiempirical Model Would Control Czochralski Process

Semiempirical mathematical model proposed for control of growth of single crystals of silicon by Czochralski process. Expresses dependence of pulling rate and shape of liquid/solid interface upon important process variables; radius of growing crystal, temperature of crucible, level of melt, and height of exposed portion of crucible wall. Necessary to control shape of interface in manner consistent with other variables, to maintain radially uniform concentration of dopant, and reduce thermally induced stresses in vicinity of interface. Used to simulate complete growth cycles without requiring excessive computer time consumed by rigorous finite-element modeling.

Dudukovic, M. P.↗

NASA NTRS1989

Gas-Jet Cooling Would Improve Czochralski Process

Controlled cooling by jets of gas improves growth of single crystals of silocon by Czochralski process, according to study. Rate of cooling by jets joins temperature of crucible and pulling rate as input variable of process adjusted to achieve required diameter of crystal and shape of crystal/melt interface. Critical parameters of growing crystal, output variables of Czochralski process controlled via two or all three of input variables. One input variable, usually speed, held constant while other two adjusted to achieve required diameter and interface.

Dudukovic, M. P.↗

NASA NTRS1986

Simulation of jet cooling effects on Czochralski crystal growth

The effects of cooling the crystal side surface by blowing a jet of an inert gas are examined in detail for Czochralski crystal growth. A combined model of the crystal + melt, which incorporates the detailed radiation calculations, the shape of the melt-gas meniscus, predicts the growth rate and the crystal-melt interface shape, is used for this study. The convective heat transfer coefficient for the jet is estimated from the correlation available in the literature. The effect of the jet cooling on the interface shape and the pulling rate is significant. The crystal diameter as well as the interface shape tend to be more stable in the environment of the rapid cooling of the crystal by the jet. The crystal diameter or the interface shape can be easily controlled by adjusting the gas flow rate through the jet. This gives the Czochralski pulling an additional degree of freedom facilitating the control of crystal diameter and interface shape.

Srivastava, R. K.↗

NASA NTRS1986

Czochralski growth of crystals - Simple models for growth rate and interface shape

A simple model for the crystal growth by the Czochralski (CZ) process has been proposed based on semiquantitative arguments. The model provides empirical relationships for the dependence of the pulling rate and the interface shape on the important process variables such as crystal radius, crucible temperature, height of the melt level, and the height of the exposed portion of the crucible wall. The parameters of the model can be evaluated by matching the results obtained from a detailed mathematical model of the CZ process or from extensive experimental data. The model has, therefore, the potential application for determining the best process conditions and for on-line control and optimization of the crystal puller to grow crystals with constant diameter and nearly planar interface.

Srivastava, R. K.↗

NASA NTRS1986

Fluidized-bed reactor modeling for production of silicon by silane pyrolysis

An ideal backmixed reactor model (CSTR) and a fluidized bed bubbling reactor model (FBBR) were developed for silane pyrolysis. Silane decomposition is assumed to occur via two pathways: homogeneous decomposition and heterogeneous chemical vapor deposition (CVD). Both models account for homogeneous and heterogeneous silane decomposition, homogeneous nucleation, coagulation and growth by diffusion of fines, scavenging of fines by large particles, elutriation of fines and CVD growth of large seed particles. At present the models do not account for attrition. The preliminary comparison of the model predictions with experimental results shows reasonable agreement. The CSTR model with no adjustable parameter yields a lower bound on fines formed and upper estimate on production rates. The FBBR model overpredicts the formation of fines but could be matched to experimental data by adjusting the unkown jet emulsion exchange efficients. The models clearly indicate that in order to suppress the formation of fines (smoke) good gas-solid contacting in the grid region must be achieved and the formation of the bubbles suppressed.

Dudukovic, M. P.↗

NASA NTRS1986

Czochralski crystal growth: Modeling study

The modeling study of Czochralski (Cz) crystal growth is reported. The approach was to relate in a quantitative manner, using models based on first priniciples, crystal quality to operating conditions and geometric variables. The finite element method is used for all calculations.

Dudukovic, M. P.↗

NASA NTRS1985

Interface shape in Czochralski grown crystals - Effect of conduction and radiation

A sequential modular computational scheme has been proposed for the calculation of temperature profiles in the melt and crystal including the melt-crystal interface shape and the crystal pulling rate for a fixed crystal radius. The heat transfer in the melt is assumed to occur by conduction only. The shape of melt-gas meniscus, described by Laplace-Young equation, is incorporated in the model and its effects on interface shape and pulling rate are examined. Further, the model incorporates the detailed radiation interaction among the various surfaces in the puller using the Gebhart enclosure theory which accounts for both direct and reflected radiation. The effects of various process parameters on the interface shape and the pulling rate have been investigated. The results of this study indicate that the shape of the melt-gas meniscus has a significant effect on the pulling rate and the interface shape in conformity with earlier studies. Further, it is shown that a simple radiation model (Stefan's model) is inadequate to model the radiation heat exchange in the Czochralski puller apparatus and the detailed Gebhart analysis is necessary for accurate calculation of both the temperature profile in the crystal as well as the interface shape.

Srivastava, R. K.↗

NASA NTRS1985

Simulation of the temperature distribution in crystals grown by Czochralski method

Production of perfect crystals, free of residual strain and dislocations and with prescribed dopant concentration, by the Czochralski method is possible only if the complex, interacting phenomena that affect crystal growth in a Cz-puller are fully understood and quantified. Natural and forced convection in the melt, thermocapillary effect and heat transfer in and around the crystal affect its growth rate, the shape of the crystal-melt interface and the temperature gradients in the crystal. The heat transfer problem in the crystal and between the crystal and all other surfaces present in the crystal pulling apparatus are discussed at length. A simulation and computer algorithm are used, based on the following assumptions: (1) only conduction occurs in the crystal (experimentally determined conductivity as a function of temperature is used), (2) melt temperature and the melt-crystal heat transfer coefficient are available (either as constant values or functions of radial position), (3) pseudo-steady state is achieved with respect to temperature gradients, (4) crystal radius is fixed, and (5) both direct and reflected radiation exchange occurs among all surfaces at various temperatures in the crystal puller enclosure.

Dudokovic, M. P.↗

NASA NTRS1984

Modeling of the silane FBR system

Development of a mathematical model for fluidized bed pyrolysis of silane that relates production rate and product properties (size, size distribution, presence or absence of fines) with bed size and operating conditions (temperature, feed concentration, flow rate, seed size, etc.) and development of user oriented algorithm for the model are considered. A parameter sensitivity study of the model was also developed.

Dudokovic, M. P.↗