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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 8: Semiconductor Physics"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.1, Page number 229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ratio of density of electrons is 0.227\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=2.5*10**19; #concentration(per m**3)\n",
+ "d=4.4*10**28; #density(per m**3)\n",
+ "n=4*10**8; #number of Ge atoms\n",
+ "\n",
+ "#Calculation\n",
+ "Na=d/n; #density of acceptor atoms\n",
+ "np=ni**2/Na; \n",
+ "npbyni=np/ni; #ratio of density of electrons\n",
+ "\n",
+ "#Result\n",
+ "print \"ratio of density of electrons is\",round(npbyni,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.2, Page number 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hole concentration is 1.44e+16 holes/m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "ni=2.4*10**19; #concentration(per m**3)\n",
+ "d=4*10**28; #density(per m**3)\n",
+ "n=10**6; #number of Ge atoms\n",
+ "\n",
+ "#Calculation\n",
+ "Nd=d/n; #density of acceptor atoms\n",
+ "np=ni**2/Nd; #hole concentration(holes/m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"hole concentration is\",np,\"holes/m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.3, Page number 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "density of holes and electrons is 3.352 *10**19 per m**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "me=9.1*10**-31; #mass of electron(kg)\n",
+ "kb=1.38*10**-23; #boltzmann constant\n",
+ "T=300; #temperature(K)\n",
+ "h=6.62*10**-34; #planck's constant\n",
+ "Eg=0.7; #band gap(eV)\n",
+ "e=1.6*10**-19; #charge(c)\n",
+ "\n",
+ "#Calculation\n",
+ "x=2*math.pi*me*kb*T/(h**2); \n",
+ "n=2*(x**(3/2))*math.exp(-Eg*e/(2*kb*T)); #density of holes and electrons(per m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"density of holes and electrons is\",round(n/10**19,3),\"*10**19 per m**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.4, Page number 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position of Fermi level is 0.35 eV\n",
+ "answer in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "kb=1.38*10**-23; #boltzmann constant\n",
+ "T=300; #temperature(K)\n",
+ "m=6;\n",
+ "Eg=0.7; #band gap(eV)\n",
+ "\n",
+ "#Calculation\n",
+ "x=3*kb*T*math.log(m)/4;\n",
+ "EF=(Eg/2)+x; #position of Fermi level(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"position of Fermi level is\",EF,\"eV\"\n",
+ "print \"answer in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.5, Page number 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position of Fermi level is 0.33 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T1=300; #temperature(K)\n",
+ "T2=330; #temperature(K)\n",
+ "E=0.3; #band gap(eV)\n",
+ "\n",
+ "#Calculation\n",
+ "Ec_Ef=T2*E/T1; #position of Fermi level(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"position of Fermi level is\",Ec_Ef,\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.6, Page number 239"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall coefficient is 3.045 *10**-4 m**3/C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=2.05*10**22; #charge carrier density\n",
+ "e=1.602*10**-19; #charge of electron\n",
+ "\n",
+ "#Calculation\n",
+ "RH=1/(n*e); #hall coefficient(m**3/C)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall coefficient is\",round(RH*10**4,3),\"*10**-4 m**3/C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.7, Page number 239"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall coefficient is -0.125 *10**-9 m**3/C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=5*10**28; #charge carrier density\n",
+ "e=1.6*10**-19; #charge of electron\n",
+ "\n",
+ "#Calculation\n",
+ "RH=-1/(n*e); #hall coefficient(m**3/C)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall coefficient is\",round(RH*10**9,3),\"*10**-9 m**3/C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.8, Page number 240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall coefficient is -0.245 *10**-9 m**3/C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=4.28*10**-10; #side(m)\n",
+ "e=1.6*10**-19; #charge of electron\n",
+ "\n",
+ "#Calculation\n",
+ "n=2/(a**3);\n",
+ "RH=-1/(n*e); #hall coefficient(m**3/C)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall coefficient is\",round(RH*10**9,3),\"*10**-9 m**3/C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.9, Page number 240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall coefficient is 2.7 *10**-4 m**3/C\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "rho=9*10**-3; #resistivity(ohm m)\n",
+ "mew=0.03; #mobility(m**2/Vs)\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=1/rho;\n",
+ "RH=mew/sigma; #hall coefficient(m**3/C)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall coefficient is\",RH*10**4,\"*10**-4 m**3/C\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.10, Page number 240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "density of charge carrier is 1.73611 *10**22 per m**3\n",
+ "mobility is 0.04 m**2/Vs\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "rho=9*10**-3; #resistivity(ohm m)\n",
+ "RH=3.6*10**-4; #hall coefficient(m**3/C)\n",
+ "e=1.6*10**-19; #charge of electron\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=1/rho;\n",
+ "rho=1/RH; \n",
+ "n=rho/e; #density of charge carrier(per m**3)\n",
+ "mew=sigma*RH; #mobility(m**2/Vs)\n",
+ "\n",
+ "#Result\n",
+ "print \"density of charge carrier is\",round(n/10**22,5),\"*10**22 per m**3\"\n",
+ "print \"mobility is\",mew,\"m**2/Vs\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.11, Page number 241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "charge carrier concentration is 6.25e+22 m**-3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron\n",
+ "z=0.3*10**-3; #thickness(m)\n",
+ "VH=1*10**-3; #hall voltage(V)\n",
+ "Ix=10*10**-3; #current(A)\n",
+ "Bz=0.3; #magnetic field(T)\n",
+ "\n",
+ "#Calculation\n",
+ "n=Ix*Bz/(VH*z*e); #charge carrier concentration(m**-3)\n",
+ "\n",
+ "#Result\n",
+ "print \"charge carrier concentration is\",n,\"m**-3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8.12, Page number 241"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hall angle is 1.0704 degrees\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "rho=0.00912; #resistivity(ohm m)\n",
+ "RH=3.55*10**-4; #hall coefficient(m**3/C)\n",
+ "B=0.48; #flux density(Wb/m**2)\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=1/rho;\n",
+ "theta_H=math.atan(sigma*B*RH); #hall angle(radian)\n",
+ "theta_H=theta_H*180/math.pi; #hall angle(degrees)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall angle is\",round(theta_H,4),\"degrees\""
+ ]
+ }
+ ],
+ "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": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2025-03-03 14:18:33 +0000