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-{
- "metadata": {
- "name": "",
- "signature": "sha256:a97623c1294ef4fbd99f1423addadcfc2341e13ca402c26d0b2a69dd71e1782a"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Conducting materials"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.1, Page number 231"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#Variable declaration\n",
- "m=9.1*10**-31; #mass of the electron in kg\n",
- "n=2.533*10**28; #concentration of electrons per m^3\n",
- "e=1.6*10**-19;\n",
- "tow_r=3.1*10**-14; #relaxation time in sec\n",
- "\n",
- "#Calculation\n",
- "rho=m/(n*(e**2*tow_r));\n",
- "\n",
- "#Result\n",
- "print(\"electrical resistivity in ohm metre is\",rho);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('electrical resistivity in ohm metre is', 4.526937967219795e-08)\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.2, Page number 231"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "s=3.75*10**3; #slope\n",
- "k=1.38*10**-23;\n",
- "\n",
- "#Calculation\n",
- "Eg=2*k*s;\n",
- "Eg=Eg/(1.6*10**-19); #converting J to eV\n",
- "Eg=math.ceil(Eg*10**3)/10**3; #rounding off to 3 decimals\n",
- "\n",
- "#Result\n",
- "print(\"band gap of semiconductor in eV is\",Eg);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('band gap of semiconductor in eV is', 0.647)\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.3, Page number 231"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "T=989; #temperature in C\n",
- "k=1.38*10**-23;\n",
- "#let E-EF be E\n",
- "E=0.5; #occupied level of electron in eV\n",
- "\n",
- "#Calculation\n",
- "T=T+273; #temperature in K\n",
- "E=E*1.6*10**-19; #converting eV to J\n",
- "#let fermi=dirac distribution function f(E) be f\n",
- "f=1/(1+math.exp(E/(k*T)));\n",
- "f=math.ceil(f*10**3)/10**3; #rounding off to 3 decimals\n",
- "\n",
- "#Result\n",
- "print(\"probability of occupation of electrons is\",f);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('probability of occupation of electrons is', 0.011)\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.4, Page number 232"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "mew_e=0.0035; #mobility of electrons in m^2/Vs\n",
- "E=0.5; #electric field strength in V/m\n",
- "\n",
- "#Calculation\n",
- "vd=mew_e*E;\n",
- "vd=vd*10**3;\n",
- "\n",
- "#Result\n",
- "print(\"drift velocity of free electrons in m/sec is\",vd,\"*10**-3\");\n",
- "\n",
- "#answer given in the book is wrong"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('drift velocity of free electrons in m/sec is', 1.75, '*10**-3')\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.5, Page number 232"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "A=6.022*10**23; #avagadro number\n",
- "e=1.6*10**-19;\n",
- "rho=1.73*10**-8; #resistivity of Cu in ohm metre\n",
- "w=63.5; #atomic weight \n",
- "d=8.92*10**3; #density in kg/m^3\n",
- "\n",
- "#Calculation\n",
- "d=d*10**3;\n",
- "sigma=1/rho;\n",
- "sigmaa=sigma/10**7;\n",
- "sigmaa=math.ceil(sigmaa*10**3)/10**3; #rounding off to 3 decimals\n",
- "n=(d*A)/w;\n",
- "mew=sigma/(n*e); #mobility of electrons\n",
- "mew=mew*10**3;\n",
- "mew=math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n",
- "\n",
- "#Result\n",
- "print(\"electrical conductivity in ohm-1 m-1\",sigmaa,\"*10**7\");\n",
- "print(\"concentration of carriers per m^3\",n);\n",
- "print(\"mobility of electrons in m^2/Vsec is\",mew,\"*10**-3\");"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('electrical conductivity in ohm-1 m-1', 5.781, '*10**7')\n",
- "('concentration of carriers per m^3', 8.459250393700786e+28)\n",
- "('mobility of electrons in m^2/Vsec is', 4.2708, '*10**-3')\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.6, Page number 232"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "n=18.1*10**28; #concentration of electrons per m^3\n",
- "h=6.62*10**-34; #planck constant in Js\n",
- "me=9.1*10**-31; #mass of electron in kg\n",
- "\n",
- "#Calculation\n",
- "X=h**2/(8*me);\n",
- "E_F0=X*(((3*n)/math.pi)**(2/3));\n",
- "E_F0=E_F0/(1.6*10**-19); #converting J to eV\n",
- "\n",
- "#Result\n",
- "print(\"Fermi energy in eV is\",E_F0);\n",
- "\n",
- "#answer given in the book is wrong"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('Fermi energy in eV is', 3.762396978021977e-19)\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.7, Page number 233"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "E_F0=5.5; #fermi energy in eV\n",
- "h=6.63*10**-34; #planck constant in Js\n",
- "me=9.1*10**-31; #mass of electron in kg\n",
- "\n",
- "#Calculation\n",
- "E_F0=E_F0*1.6*10**-19; #converting eV to J\n",
- "n=((2*me*E_F0)**(3/2))*((8*math.pi)/(3*h**3));\n",
- "\n",
- "#Result\n",
- "print(\"concentration of free electrons per unit volume of silver per m^3 is\",n);\n",
- "\n",
- "#answer given in the book is wrong\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('concentration of free electrons per unit volume of silver per m^3 is', 4.603965704817037e+52)\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.8, Page number 233"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "Eg=1.07; #energy gap of silicon in eV\n",
- "k=1.38*10**-23;\n",
- "T=298; #temperature in K\n",
- "\n",
- "#Calculation\n",
- "Eg=Eg*1.6*10**-19; #converting eV to J\n",
- "#let the probability of electron f(E) be X\n",
- "#X=1/(1+exp((E-Ef)/(k*T)))\n",
- "#but E=Ec and Ec-Ef=Eg/2\n",
- "X=1/(1+math.exp(Eg/(2*k*T)))\n",
- "\n",
- "#Result\n",
- "print(\"probability of an electron thermally excited is\",X);"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('probability of an electron thermally excited is', 9.122602463573379e-10)\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.9, Page number 234"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "k=1.38*10**-23;\n",
- "m=9.1*10**-31; #mass of the electron in kg\n",
- "vf=0.86*10**6; #fermi velocity in m/sec\n",
- "\n",
- "#Calculation\n",
- "Efj=(m*vf**2)/2;\n",
- "Ef=Efj/(1.6*10**-19); #converting J to eV\n",
- "Ef=math.ceil(Ef*10**3)/10**3; #rounding off to 3 decimals\n",
- "Tf=Efj/k;\n",
- "Tf=Tf/10**4;\n",
- "Tf=math.ceil(Tf*10**4)/10**4; #rounding off to 4 decimals\n",
- "\n",
- "#Result\n",
- "print(\"fermi energy of metal in J is\",Efj);\n",
- "print(\"fermi energy of metal in eV is\",Ef);\n",
- "print(\"fermi temperature in K is\",Tf,\"*10**4\");\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('fermi energy of metal in J is', 3.3651800000000002e-19)\n",
- "('fermi energy of metal in eV is', 2.104)\n",
- "('fermi temperature in K is', 2.4386, '*10**4')\n"
- ]
- }
- ],
- "prompt_number": 24
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.10, Page number 234"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#Variable declaration\n",
- "sigma=5.82*10**7; #electrical conductivity in ohm^-1m^-1\n",
- "K=387; #thermal conductivity of Cu in W/mK\n",
- "T=27; #temperature in C\n",
- "\n",
- "#Calculation\n",
- "T=T+273; #temperature in K\n",
- "L=K/(sigma*T);\n",
- "\n",
- "#Result\n",
- "print(\"lorentz number in W ohm/K^2 is\",L);\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('lorentz number in W ohm/K^2 is', 2.2164948453608246e-08)\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example number 8.11, Page number 235"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- " \n",
- "#importing modules\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "m=9.1*10**-31; #mass of the electron in kg\n",
- "e=1.6*10**-19;\n",
- "k=1.38*10**-23;\n",
- "n=8.49*10**28; #concentration of electrons in Cu per m^3\n",
- "tow_r=2.44*10**-14; #relaxation time in sec\n",
- "T=20; #temperature in C\n",
- "\n",
- "#Calculation\n",
- "T=T+273; #temperature in K\n",
- "sigma=(n*(e**2)*tow_r)/m;\n",
- "sigmaa=sigma/10**7;\n",
- "sigmaa=math.ceil(sigmaa*10**4)/10**4; #rounding off to 4 decimals\n",
- "K=(n*(math.pi**2)*(k**2)*T*tow_r)/(3*m);\n",
- "K=math.ceil(K*100)/100; #rounding off to 2 decimals\n",
- "L=K/(sigma*T);\n",
- "\n",
- "#Result\n",
- "print(\"electrical conductivity in ohm^-1 m^-1 is\",sigmaa,\"*10**7\");\n",
- "print(\"thermal conductivity in W/mK is\",K);\n",
- "print(\"Lorentz number in W ohm/K^2 is\",L);\n",
- "\n",
- "#answer for lorentz number given in the book is wrong\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "('electrical conductivity in ohm^-1 m^-1 is', 5.8277, '*10**7')\n",
- "('thermal conductivity in W/mK is', 417.89)\n",
- "('Lorentz number in W ohm/K^2 is', 2.4473623172034308e-08)\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-08 19:39:29 +0000