Etude des écoulements de Poiseuille-Rayleigh-Bénard et leur contrôle LIMSI (UPR 3251, Orsay) : S. Xin LETEM (EA 2546, Marne La Vallée): A. Benzaoui, X. Nicolas FAST (UMR 7608, Orsay): S. Mergui IUSTI (UMR 6595, Château Gombert ): B. Benderradji, C. Abid, M. Médale

Ecoulement de Poiseuille-Rayleigh-Bénard Umax T0 T0+T H Refroidissement des composants électroniques : Améliorer les transferts de chaleur CVD : Dêpot de Vapeur Chimique Obtenir un dépôt uniforme

Diagramme de stabilité linéaire des R// stationnaires (couche infinie) Pr = 0,7 Rouleaux sinueux instationnaires Rouleaux longitudinaux stationnaires Rouleaux sinueux instationnaires Pr = 7 Rouleaux longitudinaux stationnaires

Acquis *Vérification de l’analyse de stabilité linéaire temporelle de Clever et Busse  Développement d’un code spectral ( LETEM + LIMSI) *Observation/Caractérisation de la transition R// - R  Expériences (FAST)  Développement d’un code spatio-temporel 3D ( LETEM + LIMSI)

Mise en évidence du caractère convectif des sinuosités Re=174 ; Ra=6300 Re=174 - Ra=6300 Sans excitation Excitation imposée à l’entrée

Acquis *Vérification de l’analyse de stabilité linéaire temporelle de Clever et Busse  Développement d’un code spectral ( LETEM + LIMSI) *Observation/Caractérisation de la transition R// - R  Expériences (FAST)  Développement d’un code spatio-temporel 3D ( LETEM + LIMSI) En cours, à venir * Influence des sinuosités sur le transfert de masse  Introduction d’un modèle CVD dans le code 3D (LETEM) *Caractérisation de l’instabilité sinueuse – étude de la saturation  Expériences (FAST)  Simulations ( LETEM + LIMSI) * Caractérisation des structures longitudinales  influence du rapport de forme transverse: expériences (FAST) simulations (LETEM)  influence des propriétés du fluide: expériences IUSTI (eau) + FAST (air)

Ecoulement de Poiseuille à Tfroid Modélisation et simulation des dépôts CVD Géométrie et conditions aux limites Tfroid Tfroid=300K Ecoulement de Poiseuille à Tfroid l Sortie Injection d’un gaz porteur neutre (H2) et d’un gaz réactif (SiH4) à P° = 1 atm W°SiH4 = 2% H (1min-8min30) 1- So, the mathematical model to simulate PRB flows in the Boussinesq approximation is the following: 2- The computational domain is a rectangular channel of total length L, width W and heigth H. 3- The channel is cooled from above and heated from below, except upstream where there is a cold entrance of length Le. 4- The vertical lateral walls are adiabatic. 5- Here, A, Ae and B respectively denote the longitudinal, entrance and transversal aspect ratios. -Le Tchaud=900K et 1300K L-Le Tfroid Plaque du bas = substrat chauffé:  Réaction de surface: SiH4(g)→Si(s)+2H2(g)  Dépôt de film mince de silicium Conditions aux limites: - parois verticales latérales: imperméables, adiabatiques, non réactives - parois horizontales (hors substrat) : imperméables, isothermes (froides), non réactives - substrat : imperméable, isotherme (chaud), réactif

Modélisation et simulation des dépôts CVD Conditions aux limites - Entrée: u=uPois(y, z)=profil de Poiseuille analytique ; v=0 ; w=0; T=0; w=1. Sortie: conditions d’Orlanski : F=(u, v, w, T), F/t + U F/x=0; w/x=0; Parois horizontales: u=v=w=0; (non réactives) T=0; w/z=0; Substrat: u=v=w=0; T=1; w/z=Da; Parois verticales: u=v=w=0; T/y=0. w/y=0; (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. R : taux de dépôt du silane (kg/(m2s) Da>1 : réaction contrôlée par la diffusion et le transport de masse Da<1 : réaction contrôlée par la cinétique de la réaction

Modélisation et simulation des dépôts CVD Lois de dépôt du silicium 1ère loi de dépôt : pour SiH4(g) → Si(s)+2H2(g) 0,011<Da1<6,31 [Claasen et al., JCG (1982)] [Chiu et al., NHT-A (2000)] (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. 2ème loi de dépôt : pour un ensemble de réactions produisant du Si 7,4<Da2<40 [Pons et Baillet, Hermès (2002)]

Modélisation et simulation des dépôts CVD Propriétés physiques et conditions opératoires Propriétés physiques du mélange H2+SiH4 - Gaz parfait incompressible avec approximation de Boussinesq : r = P°M/RT = r°(1-b(T-T°)) dans le terme de poussée d’Archimède, r = r° = P°M/RT° sinon. - m, k, Cp, D calculées à T° = (Tfroid+Tchaud)/2 et à P° = 1 atm. Conditions opératoires Tfroid = 300 K 6300 < Ra < 20000 4,9 cm < H < 6,3 cm Tchaud = 900 K ou 1300 K Re = 50 ou 163 e = (Tchaud-Tfroid)/Tfroid = 2 ou 3,33 Pr ≈ 0,66 P = 1 atm Sc ≈ 1,79 W° = 0,02 0,01 < Da < 40 (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small.

Simulation de dépôts CVD en présence de rouleaux longitudinaux Ra=104 - Re=150 - B=20 - Da2=8,4 - Tc=900K - H=5,6 cm y Champ de température T dans le plan horizontal médian (x,y) écoulement x y (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. écoulement x Vitesse de dépôt Vd du silicium sur la plaque inférieure [µm/min]

Vitesse de dépôt moyenne en temps: Simulations de dépôt en présence de rouleaux longitudinaux et sinueux Ra=10000 - Re=150 - B=10 - Da2=8,4 - Tc=900K - H=5,6 cm (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. Vitesse de dépôt moyenne en temps: [µm/min]

Ra=10000 - Re=150 - B=20 - Da2=8,4 - Tc=900K - H=5,6 cm (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small.

Vitesse de dépôt moyenne Simulations de dépôt en présence de rouleaux longitudinaux et sinueux Ra=10000 - Re=150 - B=10 - Da1=0,012 - Tc=900K - H=5,6 cm (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. Vitesse de dépôt moyenne 8×10-4 Vd (µm/min) 8×10-4 Vd (µm/min) 7,97×10-4 7,85×10-4

Expériences menées au FAST : Pr = 0.7 Excitation à fréquence imposée à l’entrée Canal d’air 3m Re=174 ; Ra=9000 Saturation Taux de croissance spatiale et amplitudes de saturation des structures sinueuses, en fonction de la fréquence d’excitation (comparaison expériences/calculs) Dimensions: H × l × L = 1,45×variable×200 cm3 A=L/H=110 B=l/H = 1 à 10.8 Perturbation sinusoïdale transverse

Perspectives : -CVD: effets non Boussinesq - confronter les résultats obtenus sur le comportement des structures longitudinales pour 2 fluides différents (eau à l’IUSTI, air au FAST) - étudier l’influence du rapport de forme transverse sur les structures d’écoulements (longueur d’établissement des rouleaux longitudinaux, nombre d’onde transverse) - continuer l’étude du comportement de l’instabilité sinueuse dans les domaines d’amplification linéaire et non linéaire. (forme de la perturbation imposée, comportement des structures saturées, influence des parois latérales sur les amplitudes de saturation)

Analyse de la réponse des structures sinueuses à des excitations sinusoïdales de différentes fréquences Ra=6300 - Re=162 - Pr=0,7 - A=250 - B=10 Taux de croissance spatiale k et amplitudes de saturation A de la composante transversale de la vitesse des modes fondamentaux des structures sinueuses, en fonction de la fréquence d’excitation (comparaison entre expériences et calculs numériques); (2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small. Longueur Lg pour atteindre l’amplitude de saturation de la vitesse transversale des rouleaux sinueux R et estimation de l’amplitude du déplacement ds=As/(2f) des R en fonction de la fréquence d’excitation. Champs de température dans le plan horizontal médian pour des écoulements pleinement développés de structures sinueuses pour différentes fréquences d’excitations sinusoïdales à l’entrée du canal.

(2min-4min) 1- So, we were lead to develop a special code to solve the incompressible Navier-Stokes equations because we are interested in PRB flows for Chemical Vapor Deposition applications (CVD applications). More precisely, we are interested in the flows in the cold wall rectangular thermal reactors at atmospheric pressure. 2- Indeed, the CVD reactors are used to make thin and if possible, uniform films of cristaline materials by pyrolisis on a heated substrate from a vapor phase. 3- However, the shape of the film depending on the flow structure, it’s very important to control the flow patterns in the reactors to get uniform films. 4- But, in the rectangular CVD reactors at atmospheric pressure, the flow configuration is the PRB flow configuration. Therefore, there can be many thermoconvective flow patterns in the rectangular reactor depending on the flow parameters. There can be transversal thermoconvective rolls, steady longitudinal rolls (which are the most usual pattern in the rectangular CVD reactor), wavy or snaking rolls, and many other patterns. 5- The wavy rolls are a bit special because they result from a convective instability of the longitudinal rolls. That means that the longitudinal rolls must be permanently excited, by a mechanical excitation for instance, to make the wavy rolls appear. 6- We are particularly interested in controling the wavy roll patterns because they are liable to produce much more uniform CVD deposition than the longitudinal rolls in rectangular CVD reactors at atmospheric pressure. 7- However, to obtain these flows, long channels are needed because their space growth rate is small.