{
"metadata": {
"name": "",
"signature": "sha256:1a361e48153d58a5820c879429a5bbafe3e6e3df7d99a198492b082874550ac1"
},
"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",
"\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",
"\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",
"\n",
"#Variable declaration\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",
"\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",
"\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",
"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",
"\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",
"\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",
"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": {}
}
]
}