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Control of the formation of Benard cells in a horizontal rectangular duct heated from below

Kontrolle der Bildung von Benard-Zellen in einem horizontalen, von unten beheizten Rechteck-Kanal

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Abstract

Flows in horizontal chemical vapor deposition (CVD) ducts heated from below play an important role for manufacturing thin semiconductor layers. However, the formation of Benard cells prevents the growth of layers of uniform thickness. The present paper aims at finding conditions for time-mean uniform growth of the layer on the bottom of a rectangular CVD duct of aspect ratio 2 and heated from below. Experimental studies of various side wall temperature distributions were performed to identify conditions appropriate for controlling the Benard cells. It was found that flows in the chaotic state can provide the uniform horizontal temperature distribution preferable for the uniform growth of semiconductor layers.

Zusammenfassung

Strömungen in horizontalen Rohrleitungen, die für die chemische Gasphasenabscheidung (CVD) von unten beheizt werden, spielen eine wichtige Rolle bei der Erzeugung von dünnen Halbleiterschichten. Jedoch verhindert die Entstehung von Benard-Zellen, daß Schichten gleichmäßiger Dichte wachsen. Das Ziel der vorliegenden Arbeit besteht in der Ermittlung der Verhältnisse für ein mittleres zeitlich gleichmäßiges Wachstum der Schicht auf dem Boden einer rechteckigen CVD-Rohrleitung. Um die günstigsten Verhältnisse zu ermitteln, wurden experimentelle Studien mit verschiedenen Temperaturen auf den Seitenwänden der Rohrleitung durchgeführt. Strömungen im chaotischen Zustand können zu einer gleichmäßigen Verteilung der horizontalen Temperaturen und damit zu einem gleichmäßigen Wachstum von Halbleiterschichten führen.

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Abbreviations

a :

horizontal width of duct

b :

height of duct

D e :

hydraulic diameter=2ab/(a+b)

Gr :

Grashof number=gβ(T b−Tt)De 3/ν 2

Pr :

Prandtl number=α/ν

Ra :

Gr×Pr

Re :

Reynolds number =U mDe/ν

T :

time-averaged temperature

t :

fluctuating temperature

(u, v, w):

velocity components inx, y, z direction

(x, y, z):

rectangular coordinates

α :

temperature conductivity of fluid

β :

volumetric expansion coefficient of fluid

ε :

nondimensional temperature (T−T t)/(T b−Tt)

λ :

Lyapunov exponent

ν :

kinematic viscosity of fluid

φ :

stream function

Δτ :

delayed time

τ dev :

developing time

b :

duct bottom wall

f :

fluid

m :

mean throughout the duct

t :

duct top wall

swu :

upper half of the duct side wall

swl :

lower half of the duct side wall

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Authors and Affiliations

  1. Tokyo Institute of Technology, Ohkayama, Meguro-Ru, Tokyo, Japan

    Y. Mori

  2. Department of Mechanical Engineering, University of Electro-Communications, Chofugaoka, Chofu-ku, Tokyo, Japan

    I. Hosokawa & H. Koizumi

Authors
  1. Y. Mori
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  2. I. Hosokawa
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  3. H. Koizumi
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Additional information

Dedicated to Prof. Dr.-Ing. U. Grigull's 80th birthday

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Mori, Y., Hosokawa, I. & Koizumi, H. Control of the formation of Benard cells in a horizontal rectangular duct heated from below. Wärme- und Stoffübertragung 27, 195–200 (1992). https://doi.org/10.1007/BF01589916

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  • DOI: https://doi.org/10.1007/BF01589916

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