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diff --git a/Engineering_Physics_by_Rajendran/Chapter18.ipynb b/Engineering_Physics_by_Rajendran/Chapter18.ipynb new file mode 100755 index 00000000..25c14fca --- /dev/null +++ b/Engineering_Physics_by_Rajendran/Chapter18.ipynb @@ -0,0 +1,582 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:b2d7b45e6d7157611952afeb132c76e4391a2a303ceb4704e095dc42c36f50c3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "18: Transport properties of semiconductors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.1, Page number 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=300; #temperature(K)\n",
+ "mew_e=0.4; #electron mobility(m**2/Vs)\n",
+ "mew_h=0.2; #hole mobility(m**2/Vs)\n",
+ "Eg=0.7; #band gap(eV)\n",
+ "m0=9.1*10**-31; #mass of electron(kg)\n",
+ "mestar=0.55*m0; #electron effective mass(kg)\n",
+ "mhstar=0.37*m0; #hole effective mass(kg)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "h=6.626*10**-34; #planck's constant\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(2*math.pi*k*T/(h**2))**(3/2);\n",
+ "Eg=Eg*e; #band gap(J)\n",
+ "b=-Eg/(k*T); \n",
+ "ni=2*a*((mhstar*mestar)**(3/4))*math.exp(b); #intrinsic concentration(per m**3)\n",
+ "sigma=ni*e*(mew_e+mew_h); #intrinsic conductivity(per ohm m)\n",
+ "rho=1/sigma; #intrinsic resistivity(ohm m)\n",
+ "\n",
+ "#Result\n",
+ "print \"intrinsic concentration is\",round(ni/10**13,3),\"*10**13 per m**3\"\n",
+ "print \"intrinsic conductivity is\",round(sigma*10**6,3),\"*10**-6 per ohm m\"\n",
+ "print \"intrinsic resistivity is\",round(rho/10**6,2),\"*10**6 ohm m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "intrinsic concentration is 1.352 *10**13 per m**3\n",
+ "intrinsic conductivity is 1.298 *10**-6 per ohm m\n",
+ "intrinsic resistivity is 0.77 *10**6 ohm m\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.2, Page number 26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=300; #temperature(K)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "Nd=10**16; #donor concentration(per cm**3)\n",
+ "ni=1.45*10**10; #intrinsic concentration(per cm**3)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "Efd_Efi=k*T*math.log(Nd/ni); #fermi energy(J)\n",
+ "Efd_Efi=Efd_Efi/e; #fermi energy(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"fermi energy is\",round(Efd_Efi,3),\"eV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "fermi energy is 0.348 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.3, Page number 27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "mew_e=1.35; #electron mobility(m**2/Vs)\n",
+ "mew_h=0.45; #hole mobility(m**2/Vs)\n",
+ "ni=1.45*10**13; #intrinsic concentration(per m**3)\n",
+ "NSi=5*10**28; #atomic concentration(per m**3)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "LbyA=1; #Si crystal(cm**3)\n",
+ "\n",
+ "#Calculation\n",
+ "sigmai=ni*e*(mew_e+mew_h); #intrinsic conductivity(per ohm m)\n",
+ "rho=1/sigmai; #intrinsic resistivity(ohm m)\n",
+ "LbyA=LbyA*10**2; #Si crystal(m**3)\n",
+ "R1=rho*LbyA; #resistance(ohm)\n",
+ "Nd=NSi/10**9; #donor concentration(per m**3)\n",
+ "p=(ni**2)/Nd; #hole concentration(per m**3)\n",
+ "sigma=Nd*e*mew_e; #conductivity(per ohm m)\n",
+ "R2=(1/sigma)*100; #resistance(ohm) \n",
+ "\n",
+ "#Result\n",
+ "print \"resistance of 1cm**3 pure Si crystal is\",round(R1/10**7,2),\"*10**7 ohm\"\n",
+ "print \"resistance when crystal is doped with arsenic is\",round(R2,2),\"ohm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resistance of 1cm**3 pure Si crystal is 2.39 *10**7 ohm\n",
+ "resistance when crystal is doped with arsenic is 9.26 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.4, Page number 28"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=300; #temperature(K)\n",
+ "rho=2.12; #resistivity(ohm m)\n",
+ "mew_e=0.36; #electron mobility(m**2/Vs)\n",
+ "mew_h=0.17; #hole mobility(m**2/Vs)\n",
+ "mestar=0.5*m0; #electron effective mass(kg)\n",
+ "mhstar=0.37*m0; #hole effective mass(kg)\n",
+ "m0=9.1*10**-31; #mass of electron(kg)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "h=6.626*10**-34; #planck's constant\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=1/rho; #conductivity(per ohm m)\n",
+ "ni=sigma/(e*(mew_e+mew_h)); #intrinsic concentration(per m**3)\n",
+ "a=(2*math.pi*k*T/(h**2))**(3/2);\n",
+ "NC=2*a*(mestar**(3/2));\n",
+ "NV=2*a*(mhstar**(3/2));\n",
+ "b=(NC*NV)**(1/2);\n",
+ "Eg=2*k*T*math.log(b/ni); #energy gap of semiconductor(J)\n",
+ "Eg=Eg/e; #energy gap of semiconductor(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"energy gap of semiconductor is\",round(Eg,3),\"eV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "energy gap of semiconductor is 0.727 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.5, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "mew_e=0.39; #electron mobility(m**2/Vs)\n",
+ "mew_h=0.19; #hole mobility(m**2/Vs)\n",
+ "ni=2.4*10**19; #intrinsic concentration(per m**3)\n",
+ "\n",
+ "#Calculation\n",
+ "sigmai=ni*e*(mew_e+mew_h); #conductivity of Ge(per Wm)\n",
+ "\n",
+ "#Result\n",
+ "print \"conductivity of Ge is\",round(sigmai,3),\"per Wm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conductivity of Ge is 2.227 per Wm\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.6, Page number 29"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "EC_EF300=-0.3; #position of fermi level(eV)\n",
+ "T1=300; #temperature(K)\n",
+ "T2=330; #temperature(K)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "EC_EF330=-EC_EF300*T2/T1; #new position of fermi level(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"new position of fermi level is\",EC_EF330,\"eV\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "new position of fermi level is 0.33 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.7, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T1=20; #temperature(C)\n",
+ "T2=40; #temperature(C)\n",
+ "Eg=0.72; #energy gap(eV)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "sigmai20=2; #conductivity(per ohm m)\n",
+ "\n",
+ "#Calculation\n",
+ "T1=T1+273; #temperature(K)\n",
+ "T2=T2+273; #temperature(K)\n",
+ "Eg=Eg*e; #energy gap(J)\n",
+ "a=(T2/T1)**(3/2);\n",
+ "b=Eg/(2*k);\n",
+ "c=(1/T1)-(1/T2);\n",
+ "ni40byni20=a*math.exp(b*c); #ratio of intrinsic concentration\n",
+ "sigmai40=sigmai20*ni40byni20; #conductivity at 40C(per ohm m)\n",
+ "\n",
+ "#Result\n",
+ "print \"conductivity at 40C is\",round(sigmai40,3),\"per ohm m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "conductivity at 40C is 5.487 per ohm m\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.8, Page number 30"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "T=300; #temperature(K)\n",
+ "m0=9.1*10**-31; #mass of electron(kg)\n",
+ "Eg=1.1; #energy gap(eV)\n",
+ "mestar=0.31*m0; #effective mass of electron(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "Eg=Eg*e; #energy gap(J)\n",
+ "a=(2*math.pi*k*T*mestar/(h**2))**(3/2);\n",
+ "b=-Eg/(2*k*T); \n",
+ "ni=2*a*math.exp(b); #intrinsic concentration(per m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"intrinsic concentration is\",round(ni/10**15,4),\"*10**15 per m**3\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "intrinsic concentration is 2.5367 *10**15 per m**3\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.9, Page number 31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=-0.55*10**-10; #hall coefficient(m**3/As)\n",
+ "sigma=5.9*10**7; #conductivity(per ohm m)\n",
+ "\n",
+ "#Calculation\n",
+ "mewd=-RH*sigma; #drift mobility(m**2/Vs)\n",
+ "\n",
+ "#Result\n",
+ "print \"drift mobility is\",round(mewd*10**3,1),\"*10**-3 m**2/Vs\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "drift mobility is 3.2 *10**-3 m**2/Vs\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.10, Page number 31"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "sigma=5.9*10**7; #conductivity(per ohm m)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "mew=3.2*10**-3; #drift velocity(m**2/Vs)\n",
+ "N=6.022*10**23; #avagadro number\n",
+ "ne=8900*10**3; #number of free electrons per atom\n",
+ "w=63.5; #atomic weight of Cu(kg)\n",
+ "\n",
+ "#Calculation\n",
+ "ni=sigma/(e*mew); #intrinsic concentration(per m**3)\n",
+ "n=N*ne/w; #concentration of free electrons(per m**3)\n",
+ "a=ni/n; #average number of electrons\n",
+ "\n",
+ "#Result\n",
+ "print \"intrinsic concentration is\",round(ni/10**29,2),\"*10**29 per m**3\"\n",
+ "print \"concentration of free electrons is\",round(n/10**28,2),\"*10**28 per m**3\"\n",
+ "print \"average number of electrons is\",int(a)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "intrinsic concentration is 1.15 *10**29 per m**3\n",
+ "concentration of free electrons is 8.44 *10**28 per m**3\n",
+ "average number of electrons is 1\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.11, Page number 32"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "RH=3.66*10**-11; #hall coefficient(m**3/As)\n",
+ "sigma=112*10**7; #conductivity(per ohm m)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "n=3*math.pi/(8*RH*e); #concentration of electrons(per m**3)\n",
+ "mew_e=sigma/(n*e); #electron mobility(m**2/Vs)\n",
+ "\n",
+ "#Result\n",
+ "print \"concentration of electrons is\",round(n/10**29,1),\"*10**29 per m**3\"\n",
+ "print \"electron mobility is\",round(mew_e,3),\"m**2/Vs\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "concentration of electrons is 2.0 *10**29 per m**3\n",
+ "electron mobility is 0.035 m**2/Vs\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 18.12, Page number 33"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "i=50; #current(A)\n",
+ "B=1.5; #magnetic field(T)\n",
+ "n=8.4*10**28; #concentration of electrons(per m**3)\n",
+ "t=0.5; #thickness(cm)\n",
+ "w=2; #width of slab(cm)\n",
+ "e=1.6*10**-19; #charge of electron(c)\n",
+ "\n",
+ "#Calculation\n",
+ "w=w*10**-2; #width of slab(m)\n",
+ "VH=B*i/(n*e*w); #hall voltage(V)\n",
+ "\n",
+ "#Result\n",
+ "print \"hall voltage is\",round(VH*10**7,2),\"*10**-7 V\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "hall voltage is 2.79 *10**-7 V\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |