{ "metadata": { "name": "", "signature": "sha256:87ec2de187104d95ee2f6c0506d06458448c9c71e8a53382b631624a9ef50d23" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter1:ELECTRONS IN SOLIDS" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.1:pg-06" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "A1=27#initializing value of atomic mass of alluminium\n", "AV = 6.023*10**23 #initializing value of avagadro number\n", "N = 13 #initializing value of number of electrons of alluminium per atom\n", "P1 = 2.7 #initializing value of density of alluminium\n", "E1=AV*(N*P1/A1)\n", "print\"Electrons density of alluminium,n(Al)= \",\"{:.2e}\".format(E1),\" cm**-3\"\n", "A2=12 #initializing value of atomic mass of carbon\n", "N1 = 6 #initializing value of number of electrons of carbon per atom\n", "P2 = 3.515 #initializing value of density of carbon\n", "E2=AV*(N1*P2/A2)\n", "print\"Electrons density of carbon,n(C)= \",\"{:.3e}\".format(E2),\" cm**-3\"\n", "A3=28 #initializing value of atomic mass of silicon\n", "N2 = 14 #initializing value of number of electrons of silicon per atom\n", "P3 = 2.33 #gcm**-3, initializing value of density of silicon\n", "E3=AV*(N2*P3/A3)\n", "print\"Electrons density of silicon,n(Si)=\",\"{:.2e}\".format(E3),\" cm**-3\"\n", "#using Drudes approach\n", "print\"using Drudes approach\"\n", "Zc1=3 ##initializing value of valence electron of alluminium atom\n", "E4=AV*(Zc1*P1/A1)\n", "print\"Electrons density of alluminium,n(Al)=\",\"{:.1e}\".format(E4),\" cm**-3\"\n", "Zc2=4 #initializing value of valence electron of carbon atom\n", "E5=AV*(Zc2*P2/A2)\n", "print\"Electrons density of carbon,n(C)=\",\"{:.2e}\".format(E5),\" cm**-3\"\n", "Zc3=4 #initializing value of valence electron of silicon atom\n", "E6=AV*(Zc3*P3/A3)\n", "print\"Electrons density of silicon,n(Si)=\",\"{:.1e}\".format(E6),\" cm**-3\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Electrons density of alluminium,n(Al)= 7.83e+23 cm**-3\n", "Electrons density of carbon,n(C)= 1.059e+24 cm**-3\n", "Electrons density of silicon,n(Si)= 7.02e+23 cm**-3\n", "using Drudes approach\n", "Electrons density of alluminium,n(Al)= 1.8e+23 cm**-3\n", "Electrons density of carbon,n(C)= 7.06e+23 cm**-3\n", "Electrons density of silicon,n(Si)= 2.0e+23 cm**-3\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.2:pg-13" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# silicon has diomond structure which is made up of FCC lattice \n", "N=4.0 #initializing value of number of points per cube of volume\n", "print\"N=4\"\n", "A = 5.43*10**-8 #\"cm**-1\" #initializing value of lattice constant of silicon\n", "D = 2.0 #initializing value of number of silicon atoms per lattice point\n", "E1 = N*D/A**3\n", "print\"number density of silicon,N(Si)= \",\"{:.3e}\".format(E1),\" atomscm**-3\"\n", "#for gallium in GaAs there is 1 Ga atom and 1 As atom as per lattice point , it also has fcc structure\n", "A1 = 5.65*10**-8 #initializing value of lattice constant of gallium\n", "D1 = 1.0 #initializing value of number of gallium atoms per lattice point\n", "E2 = N*D1/A1**3\n", "print\"number density of gallium atoms,N(Ga)=\"\"{:.2e}\".format(E2),\" atomscm**-3\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "N=4\n", "number density of silicon,N(Si)= 4.997e+22 atomscm**-3\n", "number density of gallium atoms,N(Ga)=2.22e+22 atomscm**-3\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.3:pg-14" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# silicon has diomond structure which is made up of FCC lattice \n", "\n", "N=4.0 #initializing value of number of points per cube of volume\n", "A = 5.43*10**-8 #\"cm**-3\" #initializing value of lattice constant of silicon\n", "D = 2.0 #initializing value of number of silicon atoms per lattice point\n", "E1 = N*D/A**3\n", "print\"number density of silicon,Nsi = \"\"{:.2e}\".format(E1),\" atomscm**-3\"\n", "\n", "#for gallium in GaAs there is 1 Ga atom and 1 As atom as per lattice point , it also has fcc structure\n", "\n", "A1 = 5.65*10**-8 #initializing value of lattice constant of gallium\n", "D1 = 1.0 #initializing value of number of gallium atoms per lattice point\n", "E2 = N*D1/A1**3\n", "print\"number density of gallium atoms,NGa= \"\"{:.2e}\".format(E2),\" atomscm**-3\"\n", "\n", "# using above answer in following part\n", "S1=10*10**-12 #initializing value of dimensions of silicon transistor\n", "N1 = (E1*S1)\n", "print\"number Si atom in silicon transistor,N(Si)= \",\"{:.2e}\".format(N1),\" atoms\"\n", "S2 = 200*10*5*10**(-12) #\" cm**3\", #initializing value of dimensions of GaAs semiconductor laser\n", "N2 = (E2*S2)\n", "print\"number of Ga atom in GaAs semiconductor,N(Ga)= \",\"{:.2e}\".format(N2),\" atoms\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number density of silicon,Nsi = 5.00e+22 atomscm**-3\n", "number density of gallium atoms,NGa= 2.22e+22 atomscm**-3\n", "number Si atom in silicon transistor,N(Si)= 5.00e+11 atoms\n", "number of Ga atom in GaAs semiconductor,N(Ga)= 2.22e+14 atoms\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.4:pg-15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# In the (001) surface the top atoms are either Ga or As\n", "#A square of area a**2 has 4 atoms on the edges of square shared by 4 other square and 1 atom in centre\n", "\n", "N=2.0 #initializing value of total number of atoms per square\n", "a = 5.65*10**-8 #\"cm**-1\", #initializing value of lattice constant of gallium\n", "SD = N/(a**2)\n", "print\"surface density of Ga,N(Ga)= \",\"{:.3e}\".format(SD),\"cm**-2\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "surface density of Ga,N(Ga)= 6.265e+14 cm**-2\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.5:pg-15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "a = 5.65*10**-8 #initializing value of lattice constant of gallium\n", "A = a/2\n", "print\"monolayer distance in the (001) direction,(A(ml)=\",\"{:.3e}\".format(A),\" cm**-1\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "monolayer distance in the (001) direction,(A(ml)= 2.825e-08 cm**-1\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "\n", "Ex1.6:pg-22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "h=6.6*10**-34 #\"Js\", # plancks constant\n", "c = 3*10**8 #\"m/s\", # velocity of light\n", "E1 = 1.6*10**-19 #\"J\", #initializing value of energy of photon\n", "L1 = h*c/E1\n", "print\"wavelengh of photon,L(ph)= \"\"{:.2e}\".format(L1),\" m\"\n", "E2 = 1.6*10**-19 #\"J\", #initializing value of energy of electron\n", "mo = 9.1*10**-31 #\"kg\", #initializing value of mass of electron\n", "L2 = h/sqrt(2*mo*E2)\n", "print\"wavelengh of electron,L(e)= \"\"{:.2e}\".format(L2),\" m\"\n", "m=1.0/1824 #initializing value of ratio of mass of electron to mass of neutron\n", "L3 = L2*sqrt(m)\n", "print\"wavelengh of neutron,L(n)=\"\"{:.2e}\".format(L3),\" m\"\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "wavelengh of photon,L(ph)= 1.24e-06 m\n", "wavelengh of electron,L(e)= 1.22e-09 m\n", "wavelengh of neutron,L(n)=2.86e-11 m\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "\n", "Ex1.7:pg-25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "h=1.05*10**-34 #initializing value of reduced plancks constant or dirac constant or h-bar\n", "m = 9.1*10**-31 #initializing value of mass of electron\n", "E = 0.1 #initializing value of energy of electron\n", "N = (sqrt(2)*(m)**(3.0/2))/((math.pi)**2*(h)**3)\n", "print\"density of states in 3D is ,N(E)= \",\"{:.2e}\".format(N),\"E**1/2 J**-1m**-3\"\n", "\n", "#Expressing E in eV and the density of states in commonly used units of eV**-1cm**-3\n", "N1 = 6.8*10**21*sqrt(E)\n", "print\"density of states in 3D is ,N(E)= \"\"{:.2e}\".format(N1),\"eV**-1cm**-3\"\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "density of states in 3D is ,N(E)= 1.07e+56 E**1/2 J**-1m**-3\n", "density of states in 3D is ,N(E)= 2.15e+21 eV**-1cm**-3\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.8:pg-25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "h=1.05*10**-34 #initializing value of reduced plancks constant or dirac constant or h-bar\n", "m = 9.1*10**-31 #initializing value of mass of electron\n", "E = 2.0 #initializing value of energy of electron\n", "#N = (sqrt(2)*(m)**(3.0/2))/((math.pi)**2*(h)**3)\n", "#Expressing E in eV and the density of states in commonly used units of eV**-1cm**-3\n", "N1 = 6.8*10**21*sqrt(E-2.0)\n", "print\"density of states in 3D is ,N(E)= \",round(N1,2),\"eV**-1cm**-3\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "density of states in 3D is ,N(E)= 0.0 eV**-1cm**-3\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "\n", "Ex1.9:pg-38" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "h=1.05*10**-34 #initializing value of reduced plancks constant or dirac constant or h-bar\n", "m = 9.1*10**-31 #initializing value of mass of electron\n", "n = 10**28 #initializing value of mass of electron\n", "E = (3*(math.pi)**(2)*n)**(2/3)*(h**2/(2*m))\n", "print\"The fermi energy at 0K is ,E[F]= \",\"{:.2e}\".format(E),\"J\"\n", "Ef= E/(1.6*10**(-19))\n", "print\"The fermi energy at 0K in eV is ,E[F] = \",\"{:.2e}\".format(Ef),\"eV\"\n", "# Answer givenin the textbook is wrong" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The fermi energy at 0K is ,E[F]= 6.06e-39 J\n", "The fermi energy at 0K in eV is ,E[F] = 3.79e-20 eV\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex1.10:pg-39" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "print\"for temperature T1=77K\"\n", "kBT1=0.0067 #initializing value of multiplication of boltzmann constant and temperature T1\n", "n1 = 10**19 #initializing value of density of electron\n", "Nc1 = 3.34*10**18#initializing value of effective density of electron\n", "print\"Nc1 = 3.34*10**18 cm**-3\"\n", "Ef1= kBT1*((log(n1/Nc1)))\n", "print\"The fermi level at 77K (using boltzmann static) is ,Ef1(B)= \",\"{:.2e}\".format(Ef1),\"eV\"\n", "Ef2= kBT1*((log(n1/Nc1))+(1.0/sqrt(8))*(n1/Nc1))\n", "print\"The fermi level at 77K (using Joyce-Dixon static) is ,Ef1(J)= \",\"{:.2e}\".format(Ef2),\"eV\"\n", "print\"for temperature T2=300K\"\n", "kBT2=0.026 #initializing value of multiplication of boltzmann constant and temperature T2\n", "Nc2 = 2.56*10**19 #initializing value of effective density of electron\n", "print\"Nc2 = 2.56*10**19 cm**-3\"\n", "Ef3= kBT2*((log(n1/Nc2)))\n", "print\"The fermi level at 300K (using boltzmann static) is ,Ef2(B)= \",\"{:.2e}\".format(Ef3),\"eV\"\n", "Ef4= kBT2*((log(n1/Nc2))+(1.0/sqrt(8))*(n1/Nc2))\n", "print\"The fermi level at 300K (using Joyce-Dixon static) is ,Ef2(J)= \",\"{:.2e}\".format(Ef4),\"eV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "for temperature T1=77K\n", "Nc1 = 3.34*10**18 cm**-3\n", "The fermi level at 77K (using boltzmann static) is ,Ef1(B)= 7.35e-03 eV\n", "The fermi level at 77K (using Joyce-Dixon static) is ,Ef1(J)= 1.44e-02 eV\n", "for temperature T2=300K\n", "Nc2 = 2.56*10**19 cm**-3\n", "The fermi level at 300K (using boltzmann static) is ,Ef2(B)= -2.44e-02 eV\n", "The fermi level at 300K (using Joyce-Dixon static) is ,Ef2(J)= -2.08e-02 eV\n" ] } ], "prompt_number": 35 } ], "metadata": {} } ] }