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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | 4a1f703f1c1808d390ebf80e80659fe161f69fab (patch) | |
| tree | 31b43ae8895599f2d13cf19395d84164463615d9 /Engineering_Physics_by_G._Vijayakumari/Chapter11.ipynb | |
| parent | 9d260e6fae7328d816a514130b691fbd0e9ef81d (diff) | |
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diff --git a/Engineering_Physics_by_G._Vijayakumari/Chapter11.ipynb b/Engineering_Physics_by_G._Vijayakumari/Chapter11.ipynb new file mode 100644 index 00000000..a7245a22 --- /dev/null +++ b/Engineering_Physics_by_G._Vijayakumari/Chapter11.ipynb @@ -0,0 +1,613 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#11: Extrinsic Semiconductors"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.1, Page number 307"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Before adding boron atoms,the semiconductor is an intrinsic semiconductor\n",
+ "conductivity before adding boron atoms is 2.016 ohm^-1 m^-1\n",
+ "After adding boron atoms,the semiconductor becomes a P-type semiconductor\n",
+ "conductivity after adding boron atoms is 1.44 *10**4 ohm^-1 m^-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=2.1*10**19; #intrinsic charge carriers(m^-3)\n",
+ "me=0.4; #electron mobility(m^2 V^-1 s^-1)\n",
+ "mh=0.2; #hole mobility(m^2 V^-1 s^-1)\n",
+ "d=4.5*10**23; #density of boron(m^-3)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "C=ni*e*(me+mh); #conductivity before adding boron atoms(ohm^-1 m^-1)\n",
+ "c=d*e*mh; #conductivity after adding boron atoms(ohm^-1 m^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"Before adding boron atoms,the semiconductor is an intrinsic semiconductor\"\n",
+ "print \"conductivity before adding boron atoms is\",C,\"ohm^-1 m^-1\"\n",
+ "print \"After adding boron atoms,the semiconductor becomes a P-type semiconductor\"\n",
+ "print \"conductivity after adding boron atoms is\",c/10**4,\"*10**4 ohm^-1 m^-1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.2, Page number 307"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "DensiTy of electrons in n-type silicon is 1.4423 *10**24 electrons/m^3\n",
+ "DensiTy of holes in n-type silicon is 1.56 *10**8 holes/m^3\n",
+ "DensiTy of holes in p-type silicon is 3.75e+24 holes/m^3\n",
+ "DensiTy of electrons in p-type silicon is 6.0 *10**7 electrons/m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=1.5*10**16; #intrinsic charge carriers(m^-3)\n",
+ "me=1300*10**-4; #electron mobility(m^2 V^-1 s^-1)\n",
+ "mh=500*10**-4; #hole mobility(m^2 V^-1 s^-1)\n",
+ "c=3*10**4; #conductivity of n-tpye silicon(ohm^-1 m^-1)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "ne=c/(e*me); #DensiTy of electrons in n-type silicon(electrons/m^3)\n",
+ "nh=ni**2/ne; #Density of holes in n-type silicon(holes/m^3)\n",
+ "Ne=c/(e*mh); #Density of holes in p-type silicon(holes/m^3)\n",
+ "Nh=ni**2/Ne; #Density of electrons in p-type silicon(holes/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"DensiTy of electrons in n-type silicon is\",round(ne/10**24,4),\"*10**24 electrons/m^3\"\n",
+ "print \"DensiTy of holes in n-type silicon is\",nh/10**8,\"*10**8 holes/m^3\"\n",
+ "print \"DensiTy of holes in p-type silicon is\",Ne,\"holes/m^3\"\n",
+ "print \"DensiTy of electrons in p-type silicon is\",Nh/10**7,\"*10**7 electrons/m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.3, Page number 308"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The electron concentration is 2.0 *10**9 electrons/m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=2*10**16; #intrinsic charge carriers(m^-3)\n",
+ "Na=5*10**23; #density of acceptor concentration of silicon with arsenic(atoms)\n",
+ "Nd=3*10**23; #density of donor concentration of silicon with arsenic(atoms)\n",
+ "\n",
+ "#Calculation\n",
+ "nh=Na-Nd; #density of hole(m^-3)\n",
+ "ne=ni**2/nh; #The electron concentration(electrons/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The electron concentration is\",ne/10**9,\"*10**9 electrons/m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.4, Page number 309"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The position of fermi level is 4.893 *10**-20 J or 0.3058 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=5*10**28; #density of silicon atom(atoms/m^3)\n",
+ "nd=2.5*10**7; #donor concentration in 1 atom per si atom\n",
+ "T=300; #Temperature(K)\n",
+ "Eg=1.1*1.6*10**-19; #Eg for silicon(eV)\n",
+ "kb=1.38*10**-23; #Boltzmann's Constant(m^2 Kg s^-2 k^-1)\n",
+ "m=9.11*10**-31; #mass of electon(kg)\n",
+ "h=6.625*10**-34; #plank's constant(m^2 Kg/sec)\n",
+ "\n",
+ "#Calculation\n",
+ "Nd=d/nd; #The donor concentration(atoms/m^3)\n",
+ "Ef=(Eg/2)+(kb*T*(math.log(Nd/(2*((2*math.pi*m*kb*T)/h**2)**(3/2))))); #The position of fermi level at 300K(J)\n",
+ "\n",
+ "#Result\n",
+ "print \"The position of fermi level is\",round(Ef*10**20,3),\"*10**-20 J or\",round(Ef/(1.6*10**-19),4),\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.5, Page number 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The density of the intrinsic crystal for p-type is 1.302 *10**21 m^-3\n",
+ "The minor carrier concentration for p-type is 1.728e+11 electrons/m^3\n",
+ "The density of the intrinsic crystal for n-type is 4.6296 *10**20 m^-3\n",
+ "The minor carrier concentration for n-type is 4.86e+11 holes/m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=1.5*10**16; #intrinsic charge carriers(m^-3)\n",
+ "r1=10*10**-2; #resistivity of p-type silicon(ohm m)\n",
+ "r2=10*10**-2; #resistivity of n-type silicon(ohm m)\n",
+ "me=1350*10**-4; #The mobility of the charge carrier(m^2 V^-1 s^-1)\n",
+ "mh=480*10**-4; #The hole charge carrier(m^2 V^-1 s^-1)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "Na=1/(r1*e*mh); #The density of the intrinsic crystal for p-type(m^-3)\n",
+ "ne=ni**2/Na; #The minor carrier concentration for p-type(electrons/m^3)\n",
+ "Nd=1/(r2*e*me); #The density of the intrinsic crystal for n-type(m^-3)\n",
+ "nh=ni**2/Nd; #The minor carrier concentration for n-type(electrons/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of the intrinsic crystal for p-type is\",round(Na/10**21,3),\"*10**21 m^-3\"\n",
+ "print \"The minor carrier concentration for p-type is\",ne,\"electrons/m^3\"\n",
+ "print \"The density of the intrinsic crystal for n-type is\",round(Nd/10**20,4),\"*10**20 m^-3\"\n",
+ "print \"The minor carrier concentration for n-type is\",nh,\"holes/m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.6, Page number 315"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The electron mobility is 0.14 m^2 V^-1 s^-1\n",
+ "The charge carrier density is 5e+21 electrons/m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "c=112; #conductivity of a n-type silicon specimen(ohm^-1 m^-1)\n",
+ "RH=1.25*10**-3; #Hall coefficient of a n-type silicon specimen(m^3 C^-1)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "me=c*RH; #electron mobility(m^2 V^-1 s^-1)\n",
+ "ne=c/(me*e); #The charge carrier density(electrons/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The electron mobility is\",me,\"m^2 V^-1 s^-1\"\n",
+ "print \"The charge carrier density is\",ne,\"electrons/m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.7, Page number 315"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Hall coefficient of semiconductor is 3.7e-06 C^-1 m^3\n",
+ "The density of the charge carrier is 1.689 *10**24 electrons/m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=12*10**-3; #length of semi conductor crystal(m)\n",
+ "b=1*10**-3; #breadth of semi conductor crystal(m)\n",
+ "t=1*10**-3; #thickness of semi conductor crystal(m)\n",
+ "I=20*10**-3; #current(A)\n",
+ "Vh=37*10**-6; #voltage measured across the width(V)\n",
+ "B=0.5; #magnetic flux density(Wb/m^2)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "RH=Vh*t/(I*B); #Hall coefficient of semiconductor(C^-1 m^3)\n",
+ "ne=1/(RH*e); #The density of the charge carrier(electrons/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"Hall coefficient of semiconductor is\",RH,\"C^-1 m^3\"\n",
+ "print \"The density of the charge carrier is\",round(ne/10**24,3),\"*10**24 electrons/m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.8, Page number 315"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Hall coefficient of silicon plate is 3.66 *10**-4 m^3 C^-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=100*10**-3; #length of silicon plate(m)\n",
+ "b=10*10**-3; #breadth of silicon plate(m)\n",
+ "t=1*10**-3; #thickness of silicon plate(m)\n",
+ "I=10**-2; #current(A)\n",
+ "Vh=1.83*10**-3; #voltage measured across the width(V)\n",
+ "B=0.5; #magnetic flux density(Wb/m^2)\n",
+ "\n",
+ "#Calculation\n",
+ "RH=Vh*t/(I*B); #Hall coefficient of silicon plate(m^3 C^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"Hall coefficient of silicon plate is\",RH*10**4,\"*10**-4 m^3 C^-1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.9, Page number 316"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The negative sign of the Hall coefficient indicates that the nature of the semiconductor is n-type\n",
+ "The density of the charge carrier is 8.503 *10**22 electrons/m^3\n",
+ "The mobility of the charge carrier is 14.7 *10**-3 m^2 V^-1 s^-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=7.35*10**-5; #Hall coefficient of silicon specimen(m^3 C^-1)\n",
+ "rh=-7.35*10**-5; #Hall coefficient of silicon specimen(m^3 C^-1)\n",
+ "c=200; #conductivity(ohm^-1 m^-1)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "ne=1/(RH*e); #The density of the charge carrier(electrons/m^3)\n",
+ "me=c*RH; #The mobility of the charge carrier(m^2 V^-1 s^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"The negative sign of the Hall coefficient indicates that the nature of the semiconductor is n-type\"\n",
+ "print \"The density of the charge carrier is\",round(ne/10**22,3),\"*10**22 electrons/m^3\"\n",
+ "print \"The mobility of the charge carrier is\",me*10**3,\"*10**-3 m^2 V^-1 s^-1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.10, Page number 316"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The density of the charge carrier is 1.7728 *10**22 electrons/m^3\n",
+ "The mobility of the charge carrier is 0.06346 m^2 V^-1 s^-1\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=4.16*10**-4; #Hall coefficient of n-type semiconductor(m^3 C^-1)\n",
+ "c=180; #conductivity(ohm^-1 m^-1)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "x=1.18; #correction factor for RH\n",
+ "\n",
+ "#Calculation\n",
+ "ne=x/(RH*e); #The density of the charge carrier(electrons/m^3)\n",
+ "me=c/(ne*e); #The mobility of the charge carrier(m^2 V^-1 s^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of the charge carrier is\",round(ne/10**22,4),\"*10**22 electrons/m^3\"\n",
+ "print \"The mobility of the charge carrier is\",round(me,5),\"m^2 V^-1 s^-1\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.11, Page number 317"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The hall coefficient measured by the probes is 1.75 mV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "l=1*10**-3; #length of rectangular plane sheet of doped silicon(m)\n",
+ "b=1*10**-3; #breadth of semi rectangular plane sheet of doped silicon(m)\n",
+ "t=0.5*10**-3; #thickness of rectangular plane sheet of doped silicon(m)\n",
+ "RH=1.25*10**-3; #Hall coefficient of the material(m^3 C^-1)\n",
+ "I=1*10**-3; #current(A)\n",
+ "B=0.7; #magnetic flux density(Wb/m^2)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "Vh=RH*I*B/t; #The hall coefficient measured by the probes(mV)\n",
+ "\n",
+ "#Result\n",
+ "print \"The hall coefficient measured by the probes is\",Vh*10**3,\"mV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.12, Page number 317"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The density of the charge carrier is 1.70765 *10**22 m^-3\n",
+ "The mobility is 0.04099 m^2 V^-1 s^-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=3.66*10**-4; #Hall coefficient of a doped silicon(m^3 C^-1)\n",
+ "r=8.93*10**-3; #The resistivity(ohm m)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "n=1/(RH*e); #The density of the charge carrier(m^-3)\n",
+ "me=RH/r; #The mobility(m^2 V^-1 s^-1)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of the charge carrier is\",round(n/10**22,5),\"*10**22 m^-3\"\n",
+ "print \"The mobility is\",round(me,5),\"m^2 V^-1 s^-1\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 11.13, Page number 317"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The current density is 2880.0 A/m^2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=0.0125; #Hall coefficient of a sample n-type semiconductor(m^3 C^-1)\n",
+ "rh=-0.0125; #Hall coefficient of a sample n-type semiconductor(m^3 C^-1)\n",
+ "me=0.36; #electron mobility(m^2 V^-1 s^-1)\n",
+ "EH=100; #electric field(V/m)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "n=1/(RH*e); #The density of the charge carrier(m^-3)\n",
+ "c=n*e*me; #conductivity of n-type semiconductor(ohm^-1 m^-1)\n",
+ "J=c*EH; #The current density(A/m^2)\n",
+ "\n",
+ "#Result\n",
+ "print \"The current density is\",J,\"A/m^2\""
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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