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diff --git a/Engineering_Physics_by_A._Marikani/Chapter_9.ipynb b/Engineering_Physics_by_A._Marikani/Chapter_9.ipynb new file mode 100755 index 00000000..bcdb04e8 --- /dev/null +++ b/Engineering_Physics_by_A._Marikani/Chapter_9.ipynb @@ -0,0 +1,593 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:0873412d6a4e98969b64a50f25d022cd9e4d104c8635e0bc9bd27817ed58d4b4" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Semiconducting materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.1, Page number 266" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#Variable declaration\n", + "mew_e=0.36; #mobility of electrons in m^2/Vs\n", + "mew_h=0.14; #mobility of holes in m^2/Vs\n", + "sigma=2.2; #conductivity in ohm-1 m-1\n", + "T=300; #temperature in K\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "ni=sigma/(e*(mew_e+mew_h)); #carrier concentration per m^3\n", + "\n", + "#Result\n", + "print(\"carrier concentration of an intrinsic semiconductor per m^3 is\",ni);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('carrier concentration of an intrinsic semiconductor per m^3 is', 2.75e+19)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.2, Page number 266" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "import numpy as np\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "T1=20; #temperature in C\n", + "T2=100; #temperature in C\n", + "sigma_i20=250; #conductivity in ohm-1 m-1\n", + "sigma_i100=1100; #conductivity in ohm-1 m-1\n", + "k=1.38*10**-23;\n", + "\n", + "#Calculation\n", + "T1K=T1+273; #temperature in K\n", + "T2K=T2+273; #temperature in K\n", + "T_1K=T1K**(-1);\n", + "T_2K=T2K**(-1);\n", + "T_1=T_2K-T_1K;\n", + "T_2=T2K/T1K;\n", + "Tk=T_1**(-1);\n", + "T_k=(T_2)**(3/2);\n", + "#intrinsic carrier concentration at T1K is ni20 = 2*((2*math.pi*k*m*293)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-Eg/(2*k*293))\n", + "#intrinsic carrier concentration at T2K is ni100 = 2*((2*math.pi*k*m*373)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-Eg/(2*k*373))\n", + "#dividing ni20/ni100 = (293/373)**(3/2)*(math.exp(-Eg/(2*k*293))/math.exp(-Eg/(2*k*373)))\n", + "#ni20/ni100 = (293/373)**(3/2)*math.exp((-Eg/(2*k))((1/293)-(1/373)))\n", + "#sigma_i20/sigma_i100 = (ni20*e*(mew_e+mew_h))/(ni100*e*(mew_e+mew_h)) = ni20/ni100\n", + "#therefore sigma_i20/sigma_i100 = ni20/ni100 = (293/373)**(3/2)*math.exp((-Eg/(2*k))((1/293)-(1/373)))\n", + "#math.exp((-Eg/(2*k))*((1/293)-(1/373))) = (sigma_i20/sigma_i100)*(373/293)**(3/2)\n", + "#by taking log on both sides we get (-Eg/(2*k))*((1/293)-(1/373)) = np.log((sigma_i20/sigma_i100)*(373/293)**(3/2))\n", + "#Eg=2*k*(((1/373)-(1/293))**(-1))*np.log((sigma_i20/sigma_i100)*(373/293)**(3/2))\n", + "Eg=2*k*Tk*np.log((sigma_i20/sigma_i100)*T_k); #band gap in J\n", + "EgeV=Eg*6.241*10**18; #converting J to eV\n", + "EgeV=math.ceil(EgeV*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"band gap of the semiconductor in J is\",Eg);\n", + "print(\"band gap of the semiconductor in eV is\",EgeV);\n", + "\n", + "#answer for band gap in eV given in the book is wrong in the 4th decimal point" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('band gap of the semiconductor in J is', 4.2210259829756855e-20)\n", + "('band gap of the semiconductor in eV is', 0.2635)\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.3, Page number 267" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#Variable declaration\n", + "I=10**-2; #current in Ampere\n", + "l=100; #length in mm\n", + "d=1; #thickness in mm\n", + "w=10; #breadth in mm\n", + "B=0.5; #magnetic field in Wb/m^2\n", + "RH=3.66*10**-4; #hall coefficient in m^3/C\n", + "\n", + "#Calculation\n", + "w=w*10**-3; #width in m\n", + "VH=(B*I*RH)/w; #hall voltage\n", + "VH=VH*10**4;\n", + "\n", + "#Result\n", + "print(\"Hall voltage in V is\",VH,\"*10**-4\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('Hall voltage in V is', 1.83, '*10**-4')\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.4, Page number 268" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "sigma=300; #conductivity in S/cm\n", + "T=300; #temperature in K\n", + "ni=1.5*10**10 #carrier concentration per cm^3\n", + "mew_e=1300; #mobility of electrons in cm^2/Vs\n", + "mew_h=500; #mobility of holes in cm^2/Vs\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "sigma=sigma*10**2; #sigma in S/m\n", + "mew_e=mew_e*10**-4; #mobility of electrons in m^2/Vs\n", + "ND=sigma/(e*mew_e); #concentration of electron per m^3\n", + "ni=ni*10**6; #carrier concentration per m^3\n", + "p=ni**2/ND; #hole concentration per m^3\n", + "p=p/10**8;\n", + "p=math.ceil(p*10**3)/10**3; #rounding off to 3 decimals\n", + "mew_h=mew_h*10**-4; #mobility of holes in m^2/Vs\n", + "NA=sigma/(e*mew_h); #concentration of hole per m^3\n", + "n=ni**2/NA; #electron concentration per m^3\n", + "n=n/10**7;\n", + "\n", + "#Result\n", + "print(\"concentration of electron for N-type semiconductor per m^3\",ND);\n", + "print(\"hole concentration per m^3\",p,\"*10**8\");\n", + "print(\"concentration of hole for P-type semiconductor per m^3\",NA);\n", + "print(\"electron concentration per m^3\",int(n),\"*10**7\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('concentration of electron for N-type semiconductor per m^3', 1.4423076923076921e+24)\n", + "('hole concentration per m^3', 1.561, '*10**8')\n", + "('concentration of hole for P-type semiconductor per m^3', 3.7499999999999995e+24)\n", + "('electron concentration per m^3', 6, '*10**7')\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.5, Page number 269" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "RH=-3.68*10**-5; #hall coefficient in m^3/C\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "#hall coefficient is negative implies charge carriers are electrons\n", + "n=(3*math.pi)/(8*(-RH)*e); #carrier concentration\n", + "\n", + "#Result\n", + "print(\"charge carriers are electrons\");\n", + "print(\"carrier concentration per m^3 is\",n);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "charge carriers are electrons\n", + "('carrier concentration per m^3 is', 2.000844505937792e+23)\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.6, Page number 269" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Eg1=0.36; #energy gap of 1st material in eV\n", + "Eg2=0.72; #energy gap of 2nd material in eV\n", + "T=300; #temperature in K\n", + "mh=9*10**-31;\n", + "me=9*10**-31; \n", + "#given that 2*k*T=0.052; \n", + "#consider X=2*k*T\n", + "X=0.052;\n", + "\n", + "#Calculation\n", + "#intrinsic carrier concentration for A niA = 2*((2*math.pi*k*T*m)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-0.36/(2*k*T))\n", + "#intrinsic carrier concentration for B niB = 2*((2*math.pi*k*T*m)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-0.72/(2*k*T))\n", + "#dividing niA/niB = math.exp(-0.36/(2*k*T))*math.exp(0.72/(2*k*T))\n", + "#let niA/niB be A\n", + "A = math.exp(-0.36/X)*math.exp(0.72/X);\n", + "A=A/10**3;\n", + "A=math.ceil(A*10**5)/10**5; #rounding off to 5 decimals\n", + "\n", + "#Result\n", + "print(\"ratio of intrinsic carrier densities of A and B is\",A,\"*10**3\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('ratio of intrinsic carrier densities of A and B is', 1.01544, '*10**3')\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.7, Page number 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "ND=2*10**22; #concentration of electron per m^3\n", + "sigma=112; #conductivity in ohm-1 m-1\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "mew=sigma/(ND*e); #mobility of electrons \n", + "mew=math.ceil(mew*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"mobility of electrons in m^2/Vs is\",mew);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('mobility of electrons in m^2/Vs is', 0.035)\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.8, Page number 270" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "w=500; #thickness in micrometre\n", + "A=2.5*10**-3; #area of cross section in cm^-2\n", + "Ix=1; #current in ampere\n", + "Bz=10; #magnetic field in Wb/cm^2\n", + "n=10**16; #donor concentration in m^-3\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "Bz=Bz*10**-4; #magnetic field in Wb/m^2\n", + "w=w*10**-6; #thickness in m\n", + "RH=(3*math.pi)/(8*n*e); #hall coefficient\n", + "VH=(Bz*Ix*RH)/w; #hall voltage\n", + "VH=VH/10**3;\n", + "VH=math.ceil(VH*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"hall voltage in V is\",VH,\"*10**3\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('hall voltage in V is', 1.4727, '*10**3')\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.9, Page number 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "#Variable declaration\n", + "Eg=1.2; #energy gap in eV\n", + "T1=300; #temperature in K\n", + "T2=600; #temperature in K\n", + "k=1.38*10**-23;\n", + "\n", + "#Calculation\n", + "T_1=T1**(-1);\n", + "T_2=T2**(-1);\n", + "T=T_1-T_2;\n", + "Eg=Eg*1.602*10**-19; #Eg in J\n", + "#sigma_300=ni300*e*(mew_e+mew_h)\n", + "#sigma_600=ni600*e*(mew_e+mew_h)\n", + "#sigma_600/sigma_300 = ni600/ni300\n", + "#ni600/ni300 =((T2/T1)**(3/2))*math.exp(-Eg/(2*k*T2))*math.exp(Eg/(2*k*T1));\n", + "#ni600/ni300 =((T2/T1)**(3/2))*math.exp((Eg/(2*k))*T;\n", + "#let ni600/ni300 be X\n", + "X=((T2/T1)**(3/2))*math.exp((Eg/(2*k))*T);\n", + "\n", + "\n", + "#Result\n", + "print(\"ratio between the conductivity of material is\",int(X));\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('ratio between the conductivity of material is', 311270)\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.10, Page number 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "sigma=10**-6; #electrical conductivity in ohm-1 m-1\n", + "mew_e=0.85; #electron mobility in m^2/Vs\n", + "mew_h=0.04; #hole mobility in m^2/Vs\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "ni=sigma/(e*(mew_e+mew_h)); #intrinsic carrier concentration\n", + "ni=ni/10**12;\n", + "ni=math.ceil(ni*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"intrinsic carrier concentration per m^3 is\",ni,\"*10**12\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('intrinsic carrier concentration per m^3 is', 7.0225, '*10**12')\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.11, Page number 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "rho_p=10; #resistivity of p-type Si in ohm cm\n", + "rho_n=10; #resistivity of n-type Si in ohm cm\n", + "mew_e=1350; #electron mobility in cm^2/Vs\n", + "mew_h=480; #hole mobility in cm^2/Vs\n", + "ni=1.5*10**10; #carrier concentration in cm^-3\n", + "e=1.6*10**-19; #electron charge in C\n", + "\n", + "#Calculation\n", + "rho_p=rho_p*10**-2;#resistivity of p-type Si in ohm m\n", + "sigma_p=1/rho_p; #electrical conductivity\n", + "mew_h=mew_h*10**-3;\n", + "NA=sigma_p/(e*mew_h); #acceptor concentration\n", + "ni=ni*10**6; #carrier concentration in m^-3\n", + "n=ni**2/NA; #concentration of minority carriers in m^-3\n", + "n=n/10**12;\n", + "n=math.ceil(n*10**4)/10**4; #rounding off to 4 decimals\n", + "rho_n=rho_n*10**-2; #resistivity of n-type Si in ohm m\n", + "sigma_n=1/rho_n; #electrical conductivity\n", + "mew_e=mew_e*10**-3;\n", + "ND=sigma_n/(e*mew_e); #donor concentration\n", + "p=(ni**2)/ND; #concentration of minority carriers in m^-3\n", + "p=p/10**12;\n", + "p=math.ceil(p*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"donor concentration per m^3 is\",ND);\n", + "print(\"concentration of minority carriers per m^3\",p,\"*10**12\");\n", + "print(\"acceptor concentration per m^3 is\",NA);\n", + "print(\"concentration of minority carriers per m^3 is\",n,\"*10**12\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('donor concentration per m^3 is', 4.6296296296296284e+19)\n", + "('concentration of minority carriers per m^3', 4.861, '*10**12')\n", + "('acceptor concentration per m^3 is', 1.3020833333333331e+20)\n", + "('concentration of minority carriers per m^3 is', 1.7281, '*10**12')\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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