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diff --git a/Engineering_Physics_Vijaya/chapter7_2.ipynb b/Engineering_Physics_Vijaya/chapter7_2.ipynb new file mode 100755 index 00000000..d4161b18 --- /dev/null +++ b/Engineering_Physics_Vijaya/chapter7_2.ipynb @@ -0,0 +1,1514 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b26f0e8151a54ecdc596868a34547e181ac6dce2c5aea4a02c15b80e1401fd4f" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Semiconductors" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.1, Page number 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "T1=300; #temp in K\n", + "T2=310; #temp in K\n", + "ni1=2.5*10**19; #per cubic metre\n", + "EgeV1=0.72; #value of Eg in eV\n", + "EgeV2=1.12; #value of Eg in eV\n", + "\n", + "#Calculation\n", + "Eg1=EgeV1*1.6*10**-19; #Eg in J\n", + "Eg2=EgeV2*1.6*10**-19; #Eg in J\n", + "KB=1.38*10**-23; #boltzmann constant in J/k\n", + "#density of electron hole pair is ni = A*(T**(3/2))*exp(-Eg/(2*KB*T))\n", + "#let (T**(3/2))*exp(-Eg/(2*KB*T)) be X\n", + "X1=(T1**(3/2))*math.exp(-Eg1/(2*KB*T1));\n", + "X2=(T2**(3/2))*math.exp(-Eg2/(2*KB*T2));\n", + "#therefore ni1=A*X1 and ni2=A*X2. dividing ni2/ni1 we get X2/X1\n", + "ni2=ni1*(X2/X1);\n", + "\n", + "#Result\n", + "print(\"the number of electron hole pairs per cubic metre is\",ni2);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the number of electron hole pairs per cubic metre is', 2.3207901206362184e+16)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.2, Page number 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "RH=3.66*10**-4; #hall coefficient in m^3/coulomb\n", + "sigma=112; #conductivity in ohm-1 m-1\n", + "e=1.6*10**-19;\n", + "\n", + "#Calculation\n", + "ne=1/(RH*e);\n", + "#sigma = e*ne*(mew_e+mew_h)\n", + "#assuming mew_h = 0\n", + "mew_e=sigma/(e*ne);\n", + "\n", + "#Result\n", + "print(\"the charge carrier density per m^3 is\",ne);\n", + "print(\"electron mobility in m^2/Vs is\",mew_e);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the charge carrier density per m^3 is', 1.7076502732240434e+22)\n", + "('electron mobility in m^2/Vs is', 0.040992)\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.3, Page number 252" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "ni=1.5*10**16; #intrinsic concentration per m^3\n", + "e=1.6*10**-19;\n", + "mew_e=0.13; #mobility of electrons in m^2/Vs\n", + "mew_h=0.05; #mobility of holes in m^2/Vs\n", + "ND=5*10**20; #conductivity in atoms/m^3\n", + "\n", + "#Calculation\n", + "sigma1=ni*e*(mew_e+mew_h);\n", + "nd=(ni**2)/ND;\n", + "sigma2=ND*e*mew_e;\n", + "NA=5*10**20;\n", + "na=(ni**2)/NA;\n", + "sigma3=NA*e*mew_h;\n", + "sigma1=math.ceil(sigma1*10**7)/10**7; #rounding off to 7 decimals\n", + "sigma2=math.ceil(sigma2*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"intrinsic conductivity of Si in ohm-1 m-1 is\",sigma1);\n", + "print(\"conductivity of Si during donor impurity in ohm-1 m-1 is\",sigma2);\n", + "print(\"conductivity of Si during acceptor impurity in ohm-1 m-1 is\",round(sigma3));" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('intrinsic conductivity of Si in ohm-1 m-1 is', 0.000432)\n", + "('conductivity of Si during donor impurity in ohm-1 m-1 is', 10.41)\n", + "('conductivity of Si during acceptor impurity in ohm-1 m-1 is', 4.0)\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.4, Page number 253" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "sigma1=2; #conductivity in ohm-1 m-1\n", + "EgeV=0.72; #band gap in eV\n", + "KB=1.38*10**-23; #boltzmann constant\n", + "T1=20; #temp in C\n", + "T2=40; #temp in C\n", + "\n", + "#Calculation\n", + "Eg=EgeV*1.6*10**-19; #in J\n", + "T1=T1+273; #temp in K\n", + "T2=T2+273; #temp in K\n", + "#sigma2/sigma1 = exp((-Eg/(2*KB))*((1/T2)-(1/T1)))\n", + "#by taking log on both sides we get 2.303*log10(sigma2/sigma1) = (Eg/(2*KB))*((1/T1)-(1/T2))\n", + "#let (Eg/(2*KB))*((1/T1)-(1/T2)) be X\n", + "X=(Eg/(2*KB))*((1/T1)-(1/T2));\n", + "#let log10(sigma2/sigma1) be Y\n", + "Y=X/2.303;\n", + "#log10(sigma2/sigma1) = log10(sigma2)-log10(sigma1)\n", + "#let log10(sigma2) be A\n", + "A=Y+math.log10(sigma1);\n", + "sigma2=10**A;\n", + "sigma2=math.ceil(sigma2*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"the conductivity in mho m-1 is\",sigma2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the conductivity in mho m-1 is', 4.97)\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.5, Page number 253" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "mew_n=1300*10**-4; #in m^2/Vs\n", + "mew_p=500*10**-4; #in m^2/Vs\n", + "sigma=3*10**4; #conductivity in ohm-1 m-1\n", + "e=1.6*10**-19;\n", + "\n", + "#Calculation\n", + "N=sigma/(e*mew_n);\n", + "ni=1.5*10**16; #per m^3\n", + "p=(ni**2)/N;\n", + "P=sigma/(e*mew_p);\n", + "n=(ni**2)/P;\n", + "N=math.ceil(N*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"concentration of electrons in n-type per cubic metre are\",N);\n", + "print(\"concentration of holes in n-type per cubic metre are\",round(p));\n", + "print(\"concentration of electrons in p-type per cubic metre are\",round(n));\n", + "print(\"concentration of holes in p-type per cubic metre are\",P);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('concentration of electrons in n-type per cubic metre are', 1.4423076923076921e+24)\n", + "('concentration of holes in n-type per cubic metre are', 156000000.0)\n", + "('concentration of electrons in p-type per cubic metre are', 60000000.0)\n", + "('concentration of holes in p-type per cubic metre are', 3.7499999999999995e+24)\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.6, Page number 254" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "ni=2.37*10**19; #intrinsic carrier density per m^3\n", + "mew_e=0.38; #in m**2/Vs\n", + "mew_n=0.18; #in m**2/Vs\n", + "\n", + "#Calculation\n", + "e=1.6*10**-19;\n", + "sigmai=ni*e*(mew_e+mew_n);\n", + "rho=1/sigmai;\n", + "rho=math.ceil(rho*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"resistivity in ohm m is\",rho);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('resistivity in ohm m is', 0.471)\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.7, Page number 254" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "Eg=1.12; #band gap in eV\n", + "K=1.38*10**-23;\n", + "T=300; #temp in K\n", + "\n", + "#Calculation\n", + "#EF = (Eg/2)+(3*K*T/4)*log(mh/me)\n", + "#given me=0.12m0 and mh=0.28m0. therefore mh/me = 0.28/0.12 \n", + "#let mh/me be X. therefore X=0.28/0.12 \n", + "X=0.28/0.12;\n", + "EF=(Eg/2)+((3*K*T/4)*math.log(X));\n", + "\n", + "#Result\n", + "print(\"the position of fermi level in eV is\",EF);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the position of fermi level in eV is', 0.56)\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.8, Page number 254" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "KB=1.38*10**-23;\n", + "T=300; #temp in K\n", + "h=6.626*10**-34;\n", + "m0=9.11*10**-31;\n", + "mh=m0;\n", + "me=m0;\n", + "EgeV=0.7; #energy gap in eV\n", + "\n", + "#Calculation\n", + "Eg=EgeV*1.6*10**-19; #in J\n", + "A=((2*math.pi*KB/(h**2))**(3/2))*(me*mh)**(3/4);\n", + "B=T**(3/2);\n", + "C=math.exp(-Eg/(2*KB*T));\n", + "ni=2*A*B*C;\n", + "\n", + "#Result\n", + "print(\"concentration of intrinsic charge carriers per cubic metre is\",ni);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('concentration of intrinsic charge carriers per cubic metre is', 3.3481803992458756e+19)\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.9, Page number 255" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "ni=2.4*10**19;\n", + "mew_e=0.39;\n", + "mew_h=0.19;\n", + "e=1.6*10**-19;\n", + "\n", + "#Result\n", + "sigmai=ni*e*(mew_e+mew_h);\n", + "rhoi=1/sigmai;\n", + "rhoi=math.ceil(rhoi*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"resistivity in ohm m is\",rhoi);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('resistivity in ohm m is', 0.45)\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.10, Page number 255" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "l=1; #length in cm\n", + "l=l*10**-2; #length in m\n", + "e=1.6*10**-19;\n", + "w=1; #width in mm\n", + "t=1; #thickness in mm\n", + "\n", + "#Calculation\n", + "w=w*10**-3; #width in m\n", + "t=t*10**-3; #thickness in m\n", + "A=w*t;\n", + "ni=2.5*10**19;\n", + "mew_e=0.39;\n", + "mew_p=0.19;\n", + "sigma=ni*e*(mew_p+mew_e);\n", + "R=l/(sigma*A);\n", + "\n", + "#Result\n", + "print(\"resistance of intrinsic Ge rod in ohm is\",R);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('resistance of intrinsic Ge rod in ohm is', 4310.3448275862065)\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.11, Page number 255" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "Eg=1.1; #energy gap in eV\n", + "m=9.109*10**-31;\n", + "k=1.38*10**-23;\n", + "T=300;\n", + "e=1.6*10**-19;\n", + "h=6.626*10**-34;\n", + "mew_e=0.48; #electron mobility\n", + "mew_h=0.013; #hole mobility\n", + "\n", + "#Calculation\n", + "C=2*(2*math.pi*m*k/(h**2))**(3/2);\n", + "X=2*k*T/e;\n", + "Y=-Eg/X;\n", + "A=math.exp(Y);\n", + "ni=C*(T**(3/2))*A;\n", + "sigma=ni*e*(mew_e+mew_h);\n", + "sigma=math.ceil(sigma*10**6)/10**6 #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"conductivity in ohm-1 m-1 is\",sigma);\n", + "\n", + "# answer given in the book is wrong, Page number 255" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('conductivity in ohm-1 m-1 is', 0.001162)\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.12, Page number 256" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "m=9.109*10**-31;\n", + "k=1.38*10**-23;\n", + "T=300;\n", + "e=1.6*10**-19;\n", + "h=6.626*10**-34;\n", + "Eg=0.7;\n", + "mew_e=0.4; #electron mobility\n", + "mew_h=0.2; #hole mobility\n", + "\n", + "#Calculation\n", + "C=2*(2*math.pi*m*k/((h**2)))**(3/2);\n", + "X=2*k*T/e;\n", + "ni=C*(T**(3/2))*math.exp(-Eg/X);\n", + "sigma=ni*e*(mew_e+mew_h);\n", + "sigma=math.ceil(sigma*10**3)/10**3 #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"conductivity in ohm-1 m-1\",sigma);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('conductivity in ohm-1 m-1', 3.214)\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.13, Page number 256" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "k=8.616*10**-5;\n", + "T1=20; #temp in C\n", + "T1=T1+273; #temp in K\n", + "T2=32; #temp in C\n", + "rho2=4.5; #resistivity in ohm m\n", + "rho1=2; #resistivity in ohm m\n", + "\n", + "#Calculation\n", + "T2=T2+273; #temp in K\n", + "dy=math.log10(rho2)-math.log10(rho1);\n", + "dx=(1/T1)-(1/T2);\n", + "Eg=2*k*dy/dx;\n", + "Eg=math.ceil(Eg*10**3)/10**3 #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"energy band gap in eV is\",Eg);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('energy band gap in eV is', 0.452)\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.13, Page number 256" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "k=8.616*10**-5;\n", + "T1=20; #temp in C\n", + "T2=32; ##temp in C\n", + "rho2=4.5; #resistivity in ohm m\n", + "rho1=2; #resistivity in ohm m\n", + "\n", + "#Calculation\n", + "T1=T1+273; #temp in K\n", + "T2=T2+273; #temp in K\n", + "dy=math.log10(rho2)-math.log10(rho1);\n", + "dx=(1/T1)-(1/T2);\n", + "Eg=2*k*dy/dx;\n", + "Eg=math.ceil(Eg*10**3)/10**3 #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"energy band gap in eV is\",Eg);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('energy band gap in eV is', 0.452)\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.14, Page number 257" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "EgeV=1; #energy in eV\n", + "k=1.38*10**-23;\n", + "Eg=EgeV*1.602*10**-19; #in J\n", + "#EF can be taken as (Ev+0.5)eV\n", + "#therefore (Ev+0.5)eV = (Ec+Ev)/2--------(1)\n", + "#let fermi level shift by 10% then (Ev+0.6)eV = ((Ec+Ev)/2)+((3*k*T/4)*log(4))-----(2)\n", + "#subtracting (1) from (2)\n", + "#0.1 eV = (3*k*T/4)*math.log(4)\n", + "E=0.1; #energy in eV\n", + "E=E*1.602*10**-19; #energy in J\n", + "T=(4*E)/(3*k*math.log(4));\n", + "\n", + "#Result\n", + "print(\"temperature in K is\",T);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('temperature in K is', 1116.520509905372)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.15, Page number 257" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "ni=1.5*10**16;\n", + "e=1.6*10**-19;\n", + "mew_e=0.13;\n", + "mew_h=0.05;\n", + "\n", + "#Calculation\n", + "sigma=ni*e*(mew_e+mew_h);\n", + "M=28.1; #atomic weight of Si\n", + "d=2.33*10**3; #density in kg/m^3\n", + "v=M/d;\n", + "N=6.02*10**26;\n", + "N1=N/v;\n", + "#1 donor type impurity is added to 1 impurity atom\n", + "ND=N1/(10**8);\n", + "p=(ni**2)/ND;\n", + "sigma_exd=ND*e*mew_e;\n", + "#1 acceptor type impurity is added to 1 impurity atom\n", + "Na=N1/(10**8);\n", + "n=(ni**2)/Na;\n", + "sigma_exa=Na*e*mew_h;\n", + "sigma=math.ceil(sigma*10**7)/10**7 #rounding off to 7 decimals\n", + "sigma_exd=math.ceil(sigma_exd*10**3)/10**3 #rounding off to 3 decimals\n", + "sigma_exa=math.ceil(sigma_exa*10**3)/10**3 #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"conductivity in ohm-1 m-1 is\",sigma);\n", + "print(\"number of Si atoms per m^3 is\",N1);\n", + "print(\"conductivity for donor type impurity in ohm-1 m-1 is\",sigma_exd);\n", + "print(\"conductivity for acceptor type impurity in ohm-1 m-1 is\",sigma_exa);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('conductivity in ohm-1 m-1 is', 0.000432)\n", + "('number of Si atoms per m^3 is', 4.991672597864769e+28)\n", + "('conductivity for donor type impurity in ohm-1 m-1 is', 10.383)\n", + "('conductivity for acceptor type impurity in ohm-1 m-1 is', 3.994)\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.16, Page number 258" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "T=300; #temperature in K\n", + "KB=1.38*10**-23;\n", + "e=1.6*10**-19;\n", + "mew_e=0.19; #mobility of electrons in m^2/Vs\n", + "\n", + "#Calculation\n", + "Dn=mew_e*KB*T/e;\n", + "Dn=math.ceil(Dn*10**6)/10**6 #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"diffusion coefficient of electrons in m^2/s is\",Dn);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('diffusion coefficient of electrons in m^2/s is', 0.004917)\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.17, Page number 259" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "\n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "RH=3.66*10**-4; #hall coefficient in m^3/coulomb\n", + "I=10**-2; #current in amp\n", + "B=0.5; #magnetic field in wb/m^2\n", + "t=1; #thickness in mm\n", + "\n", + "#Calculation\n", + "t=t*10**-3; #thickness in m\n", + "VH=(RH*I*B)/t;\n", + "VH=VH*10**3; #converting from Volts to mV\n", + "\n", + "#Result\n", + "print(\"Hall voltage in mV is\",VH);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('Hall voltage in mV is', 1.83)\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.18, Page number 259" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "RH=-7.35*10**-5; #hall coefficient\n", + "e=1.6*10**-19;\n", + "sigma=200;\n", + "\n", + "#Calculation\n", + "n=(-1/(RH*e));\n", + "mew=sigma/(n*e);\n", + "\n", + "#Result\n", + "print(\"density of charge carriers in m^3 is\",n);\n", + "print(\"mobility of charge carriers in m^2/Vs is\",mew);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('density of charge carriers in m^3 is', 8.503401360544217e+22)\n", + "('mobility of charge carriers in m^2/Vs is', 0.0147)\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.19, Page number 259" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "I=50; #current in amp\n", + "B=1.5; #magnetic field in T\n", + "n=8.4*10**28; #free electron concentration in electron/m^3\n", + "t=0.5; #thickness in cm\n", + "e=1.6*10**-19;\n", + "\n", + "#Calculation\n", + "t=t*10**-2; #thickness in m\n", + "VH=(I*B)/(n*e*t);\n", + "VH=VH*10**6; #converting VH from V to micro V\n", + "VH=math.ceil(VH*10**4)/10**4 #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"magnitude of Hall voltage in microVolt is\",VH);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('magnitude of Hall voltage in microVolt is', 1.1161)\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.20, Page number 260" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "\n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "RH=3.66*10**-4;\n", + "e=1.6*10**-19;\n", + "rho_n=8.93*10**-3;\n", + "\n", + "#Calculation\n", + "n=1/(RH*e);\n", + "mew_e=RH/rho_n;\n", + "mew_e=math.ceil(mew_e*10**5)/10**5 #rounding off to 5 decimals\n", + "\n", + "#Result\n", + "print(\"n per m^3 is\",n);\n", + "print(\"mew_e in m^2/V is\",mew_e);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('n per m^3 is', 1.7076502732240434e+22)\n", + "('mew_e in m^2/V is', 0.04099)\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.21, Page number 260" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "mew_e=0.13; #electron mobility in m^2/Vs\n", + "mew_h=0.048; #hole mobility in m^2/Vs\n", + "ni=1.5*10**16;\n", + "e=1.6*10**-19;\n", + "T=300; #temp in K\n", + "ND=10**23; #density per m^3\n", + "\n", + "#Calculation\n", + "sigmai=ni*e*(mew_e+mew_h);\n", + "sigma=ND*mew_e*e;\n", + "p=(ni**2)/ND;\n", + "sigmai=math.ceil(sigmai*10**5)/10**5 #rounding off to 5 decimals\n", + "\n", + "#Result\n", + "print(\"conductivity of intrinsic Si in s is\",sigmai);\n", + "print(\"conductivity in s is\",sigma);\n", + "print(\"equilibrium hole concentration per m^3 is\",round(p));\n", + "\n", + "#answers for sigmai and sigma given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('conductivity of intrinsic Si in s is', 0.00043)\n", + "('conductivity in s is', 2080.0)\n", + "('equilibrium hole concentration per m^3 is', 2250000000.0)\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.22, Page number 261" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "T=300; #temp in K\n", + "kB=1.38*10**-23;\n", + "mew_e=0.36; #mobility of electrons in m^2/Vs\n", + "e=1.6*10**-19;\n", + "mew_h=0.7; #mobility of electrons in m^2/Vs\n", + "sigma=2.12; #conductivity in ohm-1 m-1\n", + "C=4.83*10**21; #proportional constant\n", + "\n", + "#Calculation\n", + "ni=sigma/(e*(mew_e+mew_h));\n", + "#exp(-Eg/(2*kB*T)) = (C*(T^(3/2)))/ni\n", + "#let X be (C*(T^(3/2)))/ni\n", + "X=(C*(T**(3/2)))/ni;\n", + "#exp(-Eg/(2*kB*T)) = X \n", + "#applyinf log on both sides\n", + "#Eg/(2*kB*T) = log(X)\n", + "Eg=2*kB*T*math.log(X);\n", + "\n", + "#Result\n", + "print(\"forbidden energy gap in eV is\",Eg);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('forbidden energy gap in eV is', 1.2016388762259164e-19)\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.23, Page number 261" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "Eg=0.4; #energy gap in eV\n", + "Eg=Eg*1.6*10**-19; #Eg in J\n", + "KB=1.38*10**-23;\n", + "T1=0; #temp 1 in C\n", + "T2=50; #temp 2 in C\n", + "T3=100; #temp 3 in C\n", + "\n", + "#Calculation\n", + "T1k=T1+273; #temp 1 in K\n", + "T2k=T2+273; #temp 2 in K\n", + "T3k=T3+273; #temp 3 in K\n", + "#F(E) = 1/(1+(exp((E-Ep)/(KB*T))))\n", + "#but E-Ep = (1/2)*Eg\n", + "#therefore F(E) = 1/(1+(exp(Eg/(2*KB*T))))\n", + "FE1=1/(1+(math.exp(Eg/(2*KB*T1k))));\n", + "FE2=1/(1+(math.exp(Eg/(2*KB*T2k))));\n", + "FE3=1/(1+(math.exp(Eg/(2*KB*T3k))));\n", + "FE1=math.ceil(FE1*10**6)/10**6 #rounding off to 6 decimals\n", + "FE2=math.ceil(FE2*10**6)/10**6 #rounding off to 6 decimals\n", + "FE3=math.ceil(FE3*10**6)/10**6 #rounding off to 6 decimals\n", + "\n", + "#Result\n", + "print(\"probability of occupation at 0 C in eV is\",FE1);\n", + "print(\"probability of occupation at 50 C in eV is\",FE2);\n", + "print(\"probability of occupation at 100 C in eV is\",FE3);\n", + "\n", + "#answers given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('probability of occupation at 0 C in eV is', 0.000205)\n", + "('probability of occupation at 50 C in eV is', 0.000762)\n", + "('probability of occupation at 100 C in eV is', 0.001992)\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.24, Page number 262" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "Eg=1.2; #energy in eV\n", + "Eg=Eg*1.6*10**-19; #in J\n", + "KB=1.38*10**-23;\n", + "T1=600; #temp in K\n", + "T2=300; #temp in K\n", + "\n", + "#Calculation\n", + "#sigma is proportional to exp(-Eg/(2*KB*T))\n", + "#let sigma1/sigma2 be R\n", + "R=math.exp((Eg/(2*KB))*((1/T2)-(1/T1)));\n", + "\n", + "#Result\n", + "print(\"the ratio between conductivity is\",round(R));\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the ratio between conductivity is', 108467.0)\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.25, Page number 263" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "ni=2.5*10**19; #density of charge carriers in m^3\n", + "r=1/(10**6); #ratio\n", + "e=1.6*10**-19;\n", + "mew_e=0.36; #mobility of electrons in m^2/Vs\n", + "mew_h=0.18; #mobility of holes in m^2/Vs\n", + "N=4.2*10**28; #number of Si atoms per m^3\n", + "\n", + "#Calculation\n", + "Ne=r*N;\n", + "Nh=(ni**2)/Ne;\n", + "sigma=(Ne*e*mew_e)+(Nh*e*mew_h);\n", + "rho=1/sigma;\n", + "rho=math.ceil(rho*10**8)/10**8 #rounding off to 8 decimals\n", + "\n", + "#Result\n", + "print(\"number of impurity atoms per m^3 is\",Ne);\n", + "print(\"the resistivity of doped Ge in ohm m is\",rho);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('number of impurity atoms per m^3 is', 4.2e+22)\n", + "('the resistivity of doped Ge in ohm m is', 0.00041336)\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.26, Page number 264" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "n=5*10**17; #concentration in m^3\n", + "vd=350; #drift velocity in m/s\n", + "E=1000; #electric field in V/m\n", + "e=1.6*10**-19;\n", + "\n", + "#Calculation\n", + "mew=vd/E;\n", + "sigma=n*e*mew;\n", + "sigma=math.ceil(sigma*10**4)/10**4 #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"the conductivity of material in ohm m is\",sigma);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('the conductivity of material in ohm m is', 0.028)\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.27, Page number 264" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "sigma_e=2.2*10**-4; #conductivity\n", + "mew_e=125*10**-3; #mobility of electrons in m^2/Vs\n", + "e=1.602*10**-19;\n", + "\n", + "#Calculation\n", + "ne=sigma_e/(e*mew_e);\n", + "\n", + "#Result\n", + "print(\"concentration in m^3 is\",ne);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('concentration in m^3 is', 1.0986267166042448e+16)\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.28, Page number 265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "RH=3.66*10**-4; #hall coefficient in m^3/c\n", + "rho_i=8.93*10**-3; #resistivity in ohm m\n", + "e=1.6*10**-19;\n", + "\n", + "#Calculation\n", + "nh=1/(RH*e);\n", + "mew_h=1/(rho_i*nh*e);\n", + "mew_h=math.ceil(mew_h*10**4)/10**4 #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"density of charge carriers in m^3 is\",nh);\n", + "print(\"mobility of charge carriers is %f m^2/Vs\",mew_h);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('density of charge carriers in m^3 is', 1.7076502732240434e+22)\n", + "('mobility of charge carriers is %f m^2/Vs', 0.041)\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.29, Page number 265" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "#import module\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable decleration\n", + "I=3; #current in mA\n", + "I=I*10**-3; #current in amp\n", + "e=1.6*10**-19;\n", + "RH=3.66*10**-4; #hall coefficient in m^3/C\n", + "B=1; #flux density in w/m^2\n", + "d=2; #dimension along Y in cm\n", + "z=1; #dimension along z in mm\n", + "\n", + "#Calculation\n", + "d=d*10**-2; #dimension along Y in m\n", + "z=z*10**-3; #dimension along z in m\n", + "A=d*z; #area in m^2\n", + "EH=RH*I*B/A;\n", + "VH=EH*d;\n", + "VH=VH*10**3; #converting from V to mV\n", + "n=1/(RH*e);\n", + "VH=math.ceil(VH*10**2)/10**2 #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"Hall voltage in mV is\",VH);\n", + "print(\"charge carrier concentration in m^3 is\",n);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('Hall voltage in mV is', 1.1)\n", + "('charge carrier concentration in m^3 is', 1.7076502732240434e+22)\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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