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diff --git a/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb b/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb new file mode 100755 index 00000000..cb41afc6 --- /dev/null +++ b/Applied_Physics-I_by_I_A_Shaikh/Chapter2_.ipynb @@ -0,0 +1,853 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:be03421cc765abd4c9572b7c61bb823243fbea415c12e649bb60ed73fc4375e6" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2: Semiconductor Physics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.1,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ro=1.72*10**-8 #resistivity of Cu\n", + "s=1/ro #conductivity of Cu\n", + "n=10.41*10**28 #no of electron per unit volume\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "u=s/(n*e)\n", + "\n", + "print\"mobility of electron in Cu =\",\"{0:.3e}\".format(u),\"m^2/volt-sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "mobility of electron in Cu = 3.491e-03 m^2/volt-sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.2,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=63.5 #atomic weight\n", + "u=43.3 #mobility of electron\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**23 #Avogadro's number\n", + "d=8.96 #density\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "n=1*Ad\n", + "\n", + "ro=1/(n*e*u)\n", + "\n", + "print\"Resistivity of Cu =\",\"{0:.3e}\".format(ro),\"ohm-cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Cu = 1.699e-06 ohm-cm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.3,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "e=1.6*10**-19 #charge on electron\n", + "ne=2.5*10**19 #density of carriers\n", + "nh=ne #for intrinsic semiconductor\n", + "ue=0.39 #mobility of electron\n", + "uh=0.19 #mobility of hole\n", + "\n", + "s=ne*e*ue+nh*e*uh #conductivity of Ge\n", + "\n", + "ro=1.0/s #resistivity of Ge\n", + "\n", + "print\"Resistivity of Ge =\",round(ro,4),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of Ge = 0.431 ohm-m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.5,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Eg=1.2 #energy gap\n", + "T1=600 #temperature\n", + "T2=300 #temperature\n", + "\n", + "#since ue>>uh for intrinsic semiconductor\n", + "\n", + "#s=ni*e*ue\n", + "\n", + "K=8.62*10**-5 #Boltzman constant\n", + "\n", + "s=1l\n", + "\n", + "s1=s*exp((-Eg)/(2*K*T1))\n", + "\n", + "s2=s*exp((-Eg)/(2*K*T2))\n", + "\n", + "m=(s1/s2)\n", + "\n", + "print'Ratio between conductivity =',\"{0:.3e}\".format(m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Ratio between conductivity = 1.092e+05\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.6,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "c=5*10**28 #concentration of Si atoms\n", + "e=1.6*10**-19 #charge on electron\n", + "u=0.048 #mobility of hole\n", + "s=4.4*10**-4 #conductivity of Si\n", + "\n", + "#since millionth Si atom is replaced by an indium atom\n", + "\n", + "n=c*10**-6\n", + "\n", + "sp=u*e*n #conductivity of resultant\n", + "\n", + "print\"conductivity =\",(sp),\"mho/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "conductivity = 384.0 mho/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21.7,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "m=28.1 #atomic weight of Si\n", + "e=1.6*10**-19 #charge on electron\n", + "N=6.02*10**26 #Avogadro's number\n", + "d=2.4*10**3 #density of Si\n", + "p=0.25 #resistivity\n", + "\n", + "#no. of Si atom/m**3\n", + "\n", + "Ad=N*d/m #Atomic density\n", + "\n", + "#impurity level is 0.01 ppm i.e. 1 atom in every 10**8 atoms of Si\n", + "\n", + "n=Ad/10**8 #no of impurity atoms\n", + "\n", + "#since each impurity produce 1 hole\n", + "\n", + "nh=n\n", + "\n", + "print\"1) hole concentration =\",round(n,4),\"holes/m^3\"\n", + "\n", + "up=1/(e*p*nh)\n", + "\n", + "print\"2) mobility =\",round(up,4),\"m^2/volt.sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) hole concentration = 5.14163701068e+20 holes/m^3\n", + "2) mobility = 0.0486 m^2/volt.sec\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.1,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=27 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 3.938e-10\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.2,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "m=0.012 #energy level(Ef-E)\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "p1=1-p\n", + "\n", + "print\"probability of an energy level not being occupied by an electron=\",round(p1,4)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an energy level not being occupied by an electron= 0.614\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.3,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "t=20 #temp in degree \n", + "T=t+273 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=1.12 #Energy band gap\n", + "\n", + "#For intrensic semiconductor (Ec-Ev)=Eg/2\n", + "\n", + "#let (Ec-Ev)=m\n", + "\n", + "m=Eg/2\n", + "\n", + "a=(m/(K*T))\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "p=1.0/(1+exp(a))\n", + "\n", + "\n", + "print\"probability of an electron being thermally excited to conduction band=\",\"{0:.3e}\".format(p)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probability of an electron being thermally excited to conduction band= 2.348e-10\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22.4,Page number 2-51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "Eg=2.1 #Energy band gap\n", + "\n", + "#probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n", + "\n", + "m=K*T\n", + "\n", + "#for f(E)=0.99\n", + "\n", + "p1=0.99\n", + "\n", + "b=1.0-(1.0/p1)\n", + "\n", + "a=math.log(b) #a=(E-2.1)/m\n", + "\n", + "E=2.1+m*a\n", + "\n", + "print\"1) Energy for which probability is 0.99=\",(E),\"eV\"\n", + "\n", + "#for f(E)=0.01\n", + "\n", + "p2=0.01\n", + "\n", + "b2=1-1.0/p2\n", + "\n", + "a1=math.log(b2) #a=(E-2.1)/m\n", + "\n", + "E1=2.1+m*a1\n", + "\n", + "print\"2)Energy for which probability is 0.01=\",(E1),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "math domain error", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m<ipython-input-4-0fb7e85ec399>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 17\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mp1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mb\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m#a=(E-2.1)/m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 21\u001b[0m \u001b[0mE\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2.1\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mValueError\u001b[0m: math domain error" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.1,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "ni=2.4*10**19 #density of intrensic semiconductor\n", + "n=4.4*10**28 #no atom in Ge crystal\n", + "Nd=n/10**6 #density\n", + "Na=Nd\n", + "e=1.6*10**-19 #charge on electron\n", + "T=300 #temerature at N.T.P.\n", + "K=1.38*10**-23 #Boltzman constant\n", + "\n", + "Vo=(K*T/e)*log(Na*Nd/(ni**2))\n", + "\n", + "print\"Potential barrier for Ge =\",round(Vo,4),\"Volts\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Potential barrier for Ge = 0.3888 Volts\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.2,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.6 #magnetic field\n", + "d=5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "Nd=10**21 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "Vh=(B*J*d)/(Nd*e) #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",\"{0:.3e}\".format(Vh),\"Volts\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 9.375e-03 Volts\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.3,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=6*10**-7 #Hall coefficient\n", + "B=1.5 #magnetic field\n", + "I=200 #current in strip\n", + "W=1*10**-3 #thickness of strip\n", + "\n", + "Vh=Rh*(B*I)/W #due to Hall effect\n", + "\n", + "print\"Hall voltage =\",(Vh),\"Volt\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 0.18 Volt\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.4,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=2.25*10**-5 #Hall coefficient\n", + "u=0.025 #mobility of hole\n", + "\n", + "r=Rh/u\n", + "\n", + "print\"Resistivity of P type silicon =\",\"{0:.3e}\".format(r),\"ohm-m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of P type silicon = 9.000e-04 ohm-m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.5,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.55 #magnetic field\n", + "d=4.5*10**-3 #distancebetween surface\n", + "J=500 #current density\n", + "n=10**20 #density\n", + "e=1.6*10**-19 #charge on electron\n", + "Rh=1/(n*e) #Hall coefficient\n", + "\n", + "Vh=Rh*B*J*d #Hall voltage\n", + "\n", + "print\"1) Hall voltage =\",round(Vh,4),\"Volts\"\n", + "\n", + "print\"2) Hall coefficient =\",(Rh),\"m^3/C\"\n", + "\n", + "u=0.17 #mobility of electrom\n", + "\n", + "m=math.atan(u*B)\n", + "\n", + "a=m*180/math.pi #conversion randian into degree\n", + "\n", + "print\"3) Hall angle =\",round(a,4),\"degree\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) Hall voltage = 0.0773 Volts\n", + "2) Hall coefficient = 0.0625 m^3/C\n", + "3) Hall angle = 5.3416 degree\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.6,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "Rh=3.66*10**-4 #Hall coefficient\n", + "r=8.93*10**-3 #resistivity \n", + "e=1.6*10**-19 #charge on electron\n", + "\n", + "#Hall coefficient Rh=1/(n*e)\n", + "\n", + "n=1/(Rh*e) #density\n", + "\n", + "print\"1) density(n) =\",round(n,4),\"/m^3\"\n", + "\n", + "u=Rh/r #mobility of electron\n", + "\n", + "print\"2) mobility (u) =\",round(u,4),\"m^2/v-s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1) density(n) = 1.70765027322e+22 /m^3\n", + "2) mobility (u) = 0.041 m^2/v-s\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23.7,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "B=0.2 #magnetic field\n", + "e=1.6*10**-19 #charge on electron\n", + "ue=0.39 #mobility of electron\n", + "l=0.01 #length\n", + "A=0.001*0.001 #cross section area of bar\n", + "V=1*10**-3 #Applied voltage\n", + "d=0.001 #sample of width \n", + "\n", + "r=1/(ue*e) #resistivity\n", + "R=r*l/A #resistance of Ge bar\n", + "\n", + "#using ohm's law\n", + "\n", + "I=V/R\n", + "Rh=r*ue #hall coefficient\n", + "\n", + "#using formulae for hall effect\n", + "\n", + "J=I/A #current density\n", + "Vh=Rh*B*J*d\n", + "\n", + "print\"Hall voltage =\",(Vh)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hall voltage = 7.8e-06\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24.1,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#given data\n", + "\n", + "x1=0.4 #difference between fermi level and conduction band(Ec-Ef)\n", + "T=300 #temp in kelvin\n", + "K=8.62*10**-5 #Boltzman constant in eV\n", + "\n", + "#ne=N*e**(-(Ec-Ef)/(K*T))\n", + "#ne is no of electron in conduction band\n", + "#since concentration of donor electron is doubled\n", + "\n", + "a=2 #ratio of no of electron\n", + "\n", + "#let x2 be the difference between new fermi level and conduction band(Ec-Ef')\n", + "\n", + "x2=-math.log(a)*(K*T)+x1 #arranging equation ne=N*e**(-(Ec-Ef)/(K*T))\n", + "\n", + "print\"Fermi level will be shifted towards conduction band by\",round(x2,4),\"eV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Fermi level will be shifted towards conduction band by 0.3821 eV\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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