{ "metadata": { "name": "", "signature": "sha256:0a8e4e4ffe1102aa0e8d709fa097c42aa3e09b9945c321059b30f1ddc8f4e107" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "16: Electron theory of solids" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 16.1, Page number 10" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "sigma=5.87*10**7; #electrical conductivity of Cu(per ohm m)\n", "K=390; #thermal conductivity(W/mK)\n", "T=20+273; #temperature(K)\n", "\n", "#Calculation\n", "L=K/(sigma*T); #Lorentz number(W ohm/K**2)\n", "\n", "#Result\n", "print \"Lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Lorentz number is 2.2676 *10**-8 W ohm/K**2\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 16.2, Page number 11" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "tow_r=10**-14; #relaxation time(s)\n", "T=300; #temperature(K)\n", "kB=1.38*10**-23; #boltzmann constant\n", "e=1.6*10**-19; #charge of electron(c)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "n=6*10**28; #electron concentration(per m**3)\n", "\n", "#Calculation\t\n", "sigma=n*e**2*tow_r/m; #electrical conductivity(per ohm m)\n", "K=n*math.pi**2*kB**2*T*tow_r/(3*m); #thermal conductivity(W/mK)\n", "L=K/(sigma*T); #Lorentz number(W ohm/K**2)\n", "\n", "#Result\n", "print \"electrical conductivity is\",round(sigma/10**7,4),\"*10**7 per ohm m\"\n", "print \"thermal conductivity is\",round(K,4),\"W/mK\"\n", "print \"Lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "electrical conductivity is 1.6879 *10**7 per ohm m\n", "thermal conductivity is 123.9275 W/mK\n", "Lorentz number is 2.4474 *10**-8 W ohm/K**2\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 16.3, Page number 11" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "tow_r=10**-14; #relaxation time(s)\n", "rho=8900; #density of Cu(kg/m**3)\n", "aw=63.5; #atomic weight of Cu\n", "N=6.022*10**23; #avagadro constant\n", "f=1*10**3; #number of free electrons per atom\n", "e=1.6*10**-19; #charge of electron(c)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "\n", "#Calculation\t\n", "n=N*rho*f/aw; #electron concentration(per m**3)\n", "sigma=n*e**2*tow_r/m; #electrical conductivity(per ohm m)\n", "\n", "#Result\n", "print \"electrical conductivity is\",round(sigma/10**7,3),\"*10**7 per ohm m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "electrical conductivity is 2.374 *10**7 per ohm m\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 16.4, Page number 12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "rho=1.54*10**-8; #resistivity(ohm m)\n", "EF=5.5; #fermi energy(eV)\n", "e=1.6*10**-19; #charge of electron(c)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "E=100;\n", "n=5.8*10**28; #electron concentration(per m**3)\n", "\n", "#Calculation\t\n", "tow_r=m/(rho*n*e**2); #relaxation time(s)\n", "mew=e*tow_r/m; #mobility of electrons(m**2/Vs)\n", "v=e*tow_r*E/m; #drift velocity(m/s)\n", "EF=EF*e; #fermi energy(J)\n", "vF=math.sqrt(2*EF/m); #fermi velocity(m/s)\n", "lamda=vF*tow_r; #mean free path(m)\n", "\n", "#Result\n", "print \"relaxation time is\",round(tow_r*10**14,2),\"*10**-14 s\"\n", "print \"mobility of electrons is\",round(mew*10**3,3),\"*10**-3 m**2/Vs\"\n", "print \"drift velocity is\",round(v,4),\"m/s\"\n", "print \"fermi velocity is\",round(vF/10**6,2),\"*10**6 m/s\"\n", "print \"mean free path is\",round(lamda*10**8,2),\"*10**-8 m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "relaxation time is 3.98 *10**-14 s\n", "mobility of electrons is 6.997 *10**-3 m**2/Vs\n", "drift velocity is 0.6997 m/s\n", "fermi velocity is 1.39 *10**6 m/s\n", "mean free path is 5.53 *10**-8 m\n" ] } ], "prompt_number": 15 } ], "metadata": {} } ] }