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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#7: Band Theory of Solids"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.1, Page number 7.5"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"density of electrons is 5.86 *10**28\n",
"mobility of electrons is 0.725 *10**-2 m**2 V-1 s-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rho_s=10.5*10**3; #density(kg/m**3)\n",
"NA=6.02*10**26; #avagadro number(per k mol)\n",
"MA=107.9; #atomic mass\n",
"sigma=6.8*10**7; #conductance(ohm-1 m-1)\n",
"e=1.6*10**-19; #charge(coulomb)\n",
"\n",
"#Calculation\n",
"n=rho_s*NA/MA; #density of electrons\n",
"mew=sigma/(n*e); #mobility of electrons(m**2/Vs)\n",
"\n",
"#Result\n",
"print \"density of electrons is\",round(n/10**28,2),\"*10**28\"\n",
"print \"mobility of electrons is\",round(mew*10**2,3),\"*10**-2 m**2 V-1 s-1\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.2, Page number 7.6"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mobility of electrons is 0.427 *10**-2 m V-1 s-1\n",
"average time of collision is 2.43 *10**-14 s\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=8.92*10**3; #density(kg/m**3)\n",
"rho=1.73*10**-8; #resistivity of copper(ohm m)\n",
"NA=6.02*10**26; #avagadro number(per k mol)\n",
"Aw=63.5; #atomic weight\n",
"m=9.1*10**-31; #mass(kg)\n",
"e=1.6*10**-19; #charge(coulomb)\n",
"\n",
"#Calculation\n",
"n=d*NA/Aw; #density of electrons\n",
"mew=1/(rho*n*e); #mobility of electrons(m**2/Vs)\n",
"t=m/(n*e**2*rho); #average time of collision(s)\n",
"\n",
"#Result\n",
"print \"mobility of electrons is\",round(mew*10**2,3),\"*10**-2 m V-1 s-1\"\n",
"print \"average time of collision is\",round(t*10**14,2),\"*10**-14 s\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.3, Page number 7.7"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"relaxation time of conduction electrons is 3.97 *10**-14 s\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"P=1.54*10**-8; #resistance(ohm m)\n",
"n=5.8*10**28; #number of electrons(per m**3)\n",
"m=9.108*10**-31; #mass(kg)\n",
"e=1.602*10**-19; #charge(coulomb)\n",
"\n",
"#Calculation\n",
"t=m/(n*e**2*P); #relaxation time of conduction electrons(s) \n",
"\n",
"#Result\n",
"print \"relaxation time of conduction electrons is\",round(t*10**14,2),\"*10**-14 s\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 7.4, Page number 7.8"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"free electron concentration is 1.8088 *10**29 electrons/m**2\n",
"mobility is 1.278 *10**-3 m s-1 V-1\n",
"drift velocity of electrons is 0.23 *10**-3 m s-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"R=0.06; #resistance(ohm)\n",
"I=15; #current(A)\n",
"D=5; #length(m)\n",
"MA=26.98; #atomic mass\n",
"rho_s=2.7*10**3; #density(kg/m**3)\n",
"NA=6.025*10**26; #avagadro number(per k mol)\n",
"e=1.602*10**-19; #charge(coulomb)\n",
"\n",
"#Calculation\n",
"n=3*rho_s*NA/MA; #free electron concentration(electrons/m**2)\n",
"mew=1/(n*e*rho_s*10**-11); #mobility(m s-1 V-1)\n",
"E=I*R/D; #electric field(V/m)\n",
"vd=mew*E; #drift velocity of electrons(m/s)\n",
"\n",
"#Result\n",
"print \"free electron concentration is\",round(n/10**29,4),\"*10**29 electrons/m**2\"\n",
"print \"mobility is\",round(mew*10**3,3),\"*10**-3 m s-1 V-1\"\n",
"print \"drift velocity of electrons is\",round(vd*10**3,2),\"*10**-3 m s-1\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
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},
"nbformat": 4,
"nbformat_minor": 0
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|
