On the Calculation of the Thermal Diffusion Constant from Viscosity Data

Jones, R. Clark; Furry, W. H.

doi:10.1103/physrev.57.547

Cited by 9 publications

(4 citation statements)

References 5 publications

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“…Simplified approximations of a were developed for isotopic gas mixtures, where the collision integrals differ by a factor that depends only on the molecular weights, and with the further assumption that IM~ -Mjl << Mj. The expressions include 115 (Mj-Mi~ kT r [4] 118 \Mj + M~/ where kT* is a function of the intermolecular forces (kT* = 1 for elastic spheres) and (22)(23)(24) a = 1.5 \~/…”

Section: J = __dp [Vxi + Xixjav In (T)]mentioning

confidence: 99%

“…For representative conditions in MOCVD (T| = 50~ Ts = 650~ a = 1, Le = 4), Eq. [24] and [27] yield J/J,~o = 0.81. Thermal diffusion results in a 19% decrease in growth rate.…”

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

“…For representative conditions, when MOCVD growth is kinetically controlled, ofTs = 500~ and for T~ = 50~ a = 1, and Le = 4, Eq. [24] and [31] yield J/J~=o = 0.42.…”

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

“…For MOCVD growth at 650~ a free stream temperature of 50~ Le = 4, and a = 1, Eq. [24] and [30] predict that the partial pressure at the surface is only 67% of the free stream partial pressure.…”

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

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Thermal Diffusion in Metal‐Organic Chemical Vapor Deposition

Holstein

1988

J. Electrochem. Soc.

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The rate of chemical vapor deposition (CVD) can be significantly affected by thermal diffusion. Accurate predictions of growth rate and growth rate uniformity require accurate estimations of thermal diffusion factors. A complete first approximation of thermal diffusion factors, however, can be a complex process. We present a simple expression for estimating thermal diffusion factors for heavy molecules present in dilute concentrations in a light carrier gas, conditions that are usually valid for metal-organic chemical vapor deposition (MOCVD). This simple expression yields approximations within a few percent of those calculated from a complete first approximation. The error for the methyl and ethyl organometallics of aluminum, gallium, and indium in hydrogen or helium is less than 1% at concentrations below 0.1% and less than 4% for concentrations below 0.5%. For hydrides of phosphorus, arsenic, or silicon in hydrogen or helium, the error is less than 3% at concentrations below 1%. Thermal diffusion factors for dilute concentrations of organometallics and hydrides in helium are greater than in hydrogen. Thermal diffusion factors are dependent on temperature, much more so for hydrogen carrier gas than for helium. Simple models are used to demonstrate the influence of thermal diffusion on MOCVD growth rate under both mass-transfer controlled and kinetically controlled growth and on the composition of species incorporated under equilibrium-controlled growth conditions.

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Section: J = __dp [Vxi + Xixjav In (T)]mentioning

confidence: 99%

“…For representative conditions in MOCVD (T| = 50~ Ts = 650~ a = 1, Le = 4), Eq. [24] and [27] yield J/J,~o = 0.81. Thermal diffusion results in a 19% decrease in growth rate.…”

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

“…For representative conditions, when MOCVD growth is kinetically controlled, ofTs = 500~ and for T~ = 50~ a = 1, and Le = 4, Eq. [24] and [31] yield J/J~=o = 0.42.…”

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

Section: J (Ln(~t~)/ Jo:0 = ~(~: 1/ [27]mentioning

confidence: 99%

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Thermal Diffusion in Metal‐Organic Chemical Vapor Deposition

Holstein

1988

J. Electrochem. Soc.

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Das Clusius‐Dickelsche Trennrohr und die physikalisch‐mathematische Theorie seiner Wirkungsweise und Leistungsfähigkeit

Jensen

1941

Angewandte Chemie

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V o n P r o j e s s o y D r . H . J E N S E N Mitteilung a u s den I n s t i t u t e n f i i v thporetische P h y s i k I . Einleitung . m Sommer 1938 wurde von Clusius und Dicke3l) eine Methode klviiier & oJT/T. alm \v*n dht klrioeo \\'em CUO u selir geriny seio. '.I) Wddmarw, X. Pllpik 114, W [1939]; Drbye, Ann. Phpik [51 a, 2M [I@]. *I Ifcrtz, Z. Ph.nik 78. 108 [1932]: Oarwich. ebnda 100, IWB [1936l. !Veycn eiued drt.:iib licrtcu Vergleirbv der 'Jhniwrlolge bciui Neon Mi nu1 'MJcIIP 1 111 dcr A i l w i t v*m Cltisias u. Dickrl. 2. pbydk. Clicm.. (Abt.. B) 48.50 [ 19401 t-enviwn. *) Naturwis% PB, 711 [l!140]. I*) Pew'inl. Ui1.t. V. Prof. t.*/tt&s. Zu?loI.z Iiri clrr KorrrMiir : lii7.\vi*t*lipti konl~trw kreits :INI w n i r r i i i es lip* ee\r.nnneu wrr-ivii clkinl eit !~),;B%J. 11) Crolh. S:itunvis. m. 2131 []~:KI]; UrMh 11. Hnrl,ck, rln!nila 2;. W. 1)) Elwii~l:~, iin Em-tAiiw. 'an) Ergrlm. 4. einkt.. Na~ir\\j~~eiircl,;iftcn. R.1. SS. J. Springrr, Hrrlin, in1 Ewrtwilwll. +I) Pllpik. Z. 41, 14 [I!HII]. lkr. niul. I'linic-, iiii Ewlieinr-n. Anpwondfc Chcmfr 64. Jobrg. 1041. N r . a w *l) Der Beitrag dieses T e r m ist im Vergluich zu &::I iibrigen Cliedern der GI. (15) kleinim Verhaltnis a/lO.AT/T au 1, d. h. in aiien l+"ailen au vernachlassigen. *?) Uieser Ausdruck kommt folgendermaoen eustande: Nach der Definition der Viscositatskonstante 9 iibt die innere Reibung auf ein Flachenelement dF, das seiikrecht awn Geschwindigkeitsgefalle steht, die Kraft K = dPq dv/dx am. Auf ein Volurnenelement, das durch ewei parallele Flachenstiicke dF iin Abstand dx begrenzt ist, wirkt. also ais Kraft der Unterschied von dF.q'dv/dx an beiden Begrenzungsflachen, d. 11. rlx.dK/dx = dxdFq dPv/dx'; dxdF ist aber das Volurnen, also ist die resultierende Kraft pro Volumeneinheit gerade q d2v/dxa. Hierbei ist q konstant gehalten (kleine Temperaturdifferenaen), im allgemeinen Fall mu13 man schreiben: Kraft pro Volunieueinheit = d/dx(q dv/dx). 9 Hior miissen wir naturiich auch bei kleineu Temperaturunterschieden die Teriinderlichkeit von p mi6 der Temperatur beriicksichtigen, da nur dadurch iiberhaupt die Zirkulatiansstrbmunr bedin& ist: dweeen kolinen wir dann wieder dt/dT = -o/T d i i g e w a n d t e Chemie 54. Jnliry. 1941. ,Vr. 37/38

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Isotopentrennung durch Thermodiffusion in flüssiger Phase

Alexander

1960

Fortschr. Phys.

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On the Calculation of the Thermal Diffusion Constant from Viscosity Data

Cited by 9 publications

References 5 publications

Thermal Diffusion in Metal‐Organic Chemical Vapor Deposition

Thermal Diffusion in Metal‐Organic Chemical Vapor Deposition

Das Clusius‐Dickelsche Trennrohr und die physikalisch‐mathematische Theorie seiner Wirkungsweise und Leistungsfähigkeit

Isotopentrennung durch Thermodiffusion in flüssiger Phase

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