{ "cells": [ { "cell_type": "markdown", "id": "ac6ae84e", "metadata": {}, "source": [ "# Croissance de GaAs par épitaxie\n", "\n", "\n", "## 1. Evolution temporelle de la concentration en AsH3 , CA(t) \n", "\n", "Compléter le script Python permettant de tracer les variations de CA en fonction du temps en utilisant la méthode d'Euler . \n", "Le tracé se fera sur le même graphe que celui obtnu pour le tracé de la fonction dont l'expression est obtenue par résolution analytique " ] }, { "cell_type": "code", "execution_count": 3, "id": "6709d557", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "valeur de kd à 750K = 57.0461782053851 s-1\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "#1ère partie : Evolution temporelle de [AsH3]= CA \n", "#Données\n", "CA0= 1 #concentration initiale en AsH3 mol/L\n", "kd1 = 0.01 # constante de vitesse à T = 580K\n", "Ea= 184 # energie d'activation en kJ/mol\n", "R=8.314 #constante des gaz parfaits\n", "\n", "#Calcul de kd à T = 750\n", "#Calcul de kd à T = 750\n", "kd2 = kd1*np.exp((-Ea*1000/R)*(1/750-1/580))\n", "print(\"valeur de kd à 750K =\",kd2,\"s-1\")\n", "\n", "# Détermination de CA(t) à 750 K et tracé\n", "# 1) Méthode D'Euler\n", "\n", "def Fe(C,t):\n", " return (-kd2*C)\n", "def euler(Fe,t0,tf,CA0,p):\n", " h=(tf-t0)/(p-1)\n", " LC = [CA0]\n", " LT = [0]\n", " c=CA0\n", " d=t0\n", " for k in range(p):\n", " c=c+h*Fe(c,d)\n", " d=d+h\n", " LC.append(c)\n", " LT.append(d)\n", " return (LT,LC)\n", "dates,Concentrations = euler(Fe,0,0.1,CA0,10)\n", "\n", "\n", "\n", "# 2) Fonction odeint\n", "from scipy.integrate import odeint\n", "n=200 #nombre de valeurs de la variable t dans l'intervalle retenu\n", "T=np.linspace ( 0, 0.1 ,n)\n", "def F(CA,t):\n", " return (-kd2*CA)\n", "solCA = odeint ( F, [CA0],T)\n", "\n", "# 3) réolution analytique\n", "def CA3(t):\n", " return (CA0*np.exp(-kd2*t))\n", "Y=CA3(T)\n", " \n", "\n", "plt.figure(0)\n", "plt.plot(dates,Concentrations,'xk',label='CA(t) Euler')\n", "plt.plot(T,solCA,'ob',label='CA(t)')\n", "plt.plot(T,Y,'+ r',label='CA(T) analytique')\n", "plt.grid()\n", "plt.legend()\n", "plt.xlabel(\"t(s)\")\n", "plt.ylabel (\"CA(mol/l)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4aab6c89", "metadata": {}, "source": [ "## 2. Epaisseur et taux de croissance \n", "Résoudre le système d'équations différentielles associées aux fonctions CT(t) , CM(t) et e(t) en utilisant la fonction odeint . \n", "Tracer le graphe montrant l'écolution de l'épaisseur au cours du temps . " ] }, { "cell_type": "code", "execution_count": 4, "id": "baee110c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Données\n", "CT0= 0.01 #concentration initiale en Ga(CH3)3 mol/L\n", "CM0=0 #concentration initiale en Ga(CH3) mol/L\n", "k1 = 5e-2 # constante de vitesse à T = 580K\n", "k2 =5e-4 # energie d'activation en kJ/mol\n", "alpha=10**4\n", "mv= 5.3e6 # masse volumique en g/m3\n", "M= 145 #masse molaire de GaAs en g/mol\n", "\n", "#nouvel intervalle de temps\n", "n=200 #nombre de valeurs de la variable t dans l'intervalle retenu\n", "T2=np.linspace ( 0,500 ,n)\n", "\n", "# Système d'équations différentielles\n", "def F2(X,t):\n", " CT,CM,e =X[0],X[1],X[2]\n", " return (-k1*CT,k1*CT-k2*CM,k2*1000*CM/alpha/mv)\n", "\n", "sol=odeint(F2,[CT0,CM0,0],T2)\n", "\n", "CT=sol[:,0]\n", "CM=sol[:,1]\n", "e=sol[:,2]\n", "\n", "\n", "plt.figure(1)\n", "plt.plot(T2,e,'xr',label='épaisseur')\n", "plt.legend()\n", "plt.xlabel(\"t(s)\")\n", "plt.ylabel (\"e(m)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "437e587a", "metadata": {}, "source": [ "## 3.Taux de croissance \n", "\n", "Tracer le graphe montrant l'évolution du taux de croissance en fonction du temps ." ] }, { "cell_type": "code", "execution_count": 5, "id": "b79de7c5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def tau(C):\n", " return (k2*1000*C/alpha/mv)\n", "CM2=[]\n", "for i in range (len(T2)):\n", " CM2.append (CM[i])\n", "Y=[]\n", "for i in range (len(T2)):\n", " Y.append (tau(CM2[i]))\n", "\n", "plt.figure(2)\n", "plt.plot(T2,Y,'xg',label='taux de croissance')\n", "plt.legend()\n", "plt.xlabel(\"t(s)\")\n", "plt.ylabel (\"de/dt\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c0872096", "metadata": {}, "source": [ "## 4. temps pour lequel le taux de croissance est maximal , tmax\n", "\n", "Faire afficher sur le script Python la valeur tmax obtenue à partir de la résolution analytique . \n", "Cette valeur peut être déterminée en utilisant la fonction argmax . \n", "Regarder l'influence du nombre n de valeurs choisi pour la variable t .\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "61627b56", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tmax analytique = 93.03374113107253 s\n", "tmax numerique = 92.96482412060303 s\n" ] } ], "source": [ "# Instant t pour lequel le taux est maximal\n", "#résolution analytique\n", "tmax = (1/(k2-k1))*np.log(k2/k1)\n", "print (\"tmax analytique = \",tmax,\"s\")\n", "\n", "# A partir de la résolution numérique\n", "print (\"tmax numerique =\",T2[np.argmax(Y)],\"s\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "ac8b62c9", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.10" } }, "nbformat": 4, "nbformat_minor": 5 }