{ "metadata": { "name": "", "signature": "sha256:b86f6f4d444d5177f7a40efe10b2b4ac505571f2f5cf98eeaa6619afa2ee7d22" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 9: Semiconductors" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.1, Page number 9.11" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ni = 2.37*10**19 #intrinsic carrier density(m^-3)\n", "ue = 0.38 #electron mobility(m^2/V-s)\n", "uh = 0.18 #hole mobility(m^2/V-s)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "\n", "#Calculations\n", "sigma_i = ni*e*(ue+uh) #(1/ohm-m)\n", "p = 1/sigma_i\n", "\n", "#Result\n", "print \"Resistivity =\",round(p,3),\"m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistivity = 0.471 m\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.2, Page number 9.12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#Variable declaration\n", "Eg = 1.12 #bandgap(eV)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "T = 300 #Temperature(K)\n", "mh = 0.28 #Effective Mass of the hole(kg)\n", "me = 0.12 #Effective Mass of the hole(kg)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "\n", "#Calculation\n", "Ef = (Eg/2)+3/4*k*T*(math.log(mh/me))/e\n", "\n", "#Result \n", "print \"The position of the Fermi level is at\",round(Ef,2),\"from the top of valence band\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The position of the Fermi level is at 0.56 from the top of valence band\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.3, Page number 9.12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import pi, exp\n", "\n", "#Variable declaration\n", "m = 9.109*10**-31 #mass of an electron(kg)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "T = 300 #Temperature(K)\n", "h = 6.626*10**-34 #Planck's constant\n", "Eg = 0.7 #bandgap(eV)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "\n", "#Calculation\n", "C = (((2*pi*m*k)/h**2)**(3./2.)) \n", "T1 = T**(3./2.)\n", "E = exp((-Eg*e)/(2*k*T))\n", "ni = 2*C*T1*E\n", "\n", "#Result\n", "print \"Concentration of intrinsic charge carriers =\",round((ni/1E+18),2),\"*10**18/m^3\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Concentration of intrinsic charge carriers = 33.48 *10**18/m^3\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.4, Page number " ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ni = 2.4*10**19 #intrinsic carrier density(m^-3)\n", "ue = 0.39 #electron mobility(m^2/V-s)\n", "uh = 0.19 #hole mobility(m^2/V-s)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "\n", "#Calculations\n", "sigma_i = ni*e*(ue+uh) #(1/ohm-m)\n", "p = 1/sigma_i\n", "\n", "#Result\n", "print \"Resistivity =\",round(p,3),\"m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistivity = 0.449 m\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.5, Page number 9.13" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ni = 2.5*10**19 #intrinsic carrier density(m^-3)\n", "ue = 0.39 #electron mobility(m^2/V-s)\n", "uh = 0.19 #hole mobility(m^2/V-s)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "l = 1*10**-2 #length of rod(m)\n", "A = 10**-3*10**-3 #area(m^2)\n", "\n", "#Calculations\n", "sigma = ni*e*(ue+uh) #(1/ohm-m)\n", "R = 1/(sigma*A)\n", "\n", "#Result\n", "print \"Resistivity =\",round(R,3),\"Ohms\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resistivity = 431034.483 Ohms\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.6, Page number 9.14" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import pi, exp\n", "\n", "#Variable declaration\n", "ue = 0.48 #electron mobility(m^2/V-s)\n", "uh = 0.013 #hole mobility(m^2/V-s)\n", "Eg = 1.1 #bandgap(eV)\n", "T = 300 #assumption - Temperature(K)\n", "h = 6.626*10**-34 #Planck's constant\n", "e = 1.6*10**-19 #charge on electron(C)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "m = 9.1*10**-31 #mass of an electron(kg)\n", "\n", "#Calculation\n", "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", "ni = C*T**(3./2.)*exp((-Eg*e)/(2*k*T))\n", "sigma_i = ni*e*(ue+uh)\n", "\n", "#Result\n", "print \"Conductivity=\",round((sigma_i/1E-3),3),\"*10^-3/ohm-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Conductivity= 1.159 *10^-3/ohm-m\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.7, Page number 9.15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import pi, exp\n", "\n", "#Variable declaration\n", "ue = 0.4 #electron mobility(m^2/V-s)\n", "uh = 0.2 #hole mobility(m^2/V-s)\n", "Eg = 0.7 #bandgap(eV)\n", "T = 300 #assumption - Temperature(K)\n", "h = 6.626*10**-34 #Planck's constant\n", "e = 1.6*10**-19 #charge on electron(C)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "m = 9.1*10**-31 #mass of an electron(kg)\n", "\n", "#Calculation\n", "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", "ni = C*T**(3./2.)*exp((-Eg*e)/(2*k*T))\n", "sigma_i = ni*e*(ue+uh)\n", "\n", "#Result\n", "print \"Intrinsic carrier density =\",round((ni/1E+19),2),\"*10^19 per m^3\"\n", "print \"Conductivity=\",round(sigma_i,2),\"/ohm-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Intrinsic carrier density = 3.34 *10^19 per m^3\n", "Conductivity= 3.21 /ohm-m\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.8, Page number 9.15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ue = 0.36 #electron mobility(m^2/V-s)\n", "uh = 0.17 #hole mobility(m^2/V-s)\n", "P = 2.12 #resistivity(ohm-m)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "m = 9.1*10**-31 #mass of an electron(kg)\n", "h = 6.626*10**-34 #Planck's constant\n", "T = 300 #assumption - Temperature(K)\n", "\n", "#Calculations\n", "sigma = 1/P\n", "ni = sigma/(e*(ue+uh))\n", "C = 2*(((2*pi*m*k)/h**2))**(3./2.)\n", "Eg = ((2*k*T)/e)*math.log(C*(T**(3./2.))/ni)\n", "\n", "#Result\n", "print \"Forbidden energy gap =\",round(Eg,3),\"eV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Forbidden energy gap = 0.793 eV\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.9, Page number 9.16" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import log10\n", "\n", "#Variable declaration\n", "p1 = 2 #resistivity(ohm-m)\n", "p2 = 4.5 #resistivity(ohm-m)\n", "T1 = 20.+273 #Temperature(K)\n", "T2 = 32.+273 #temperature(K)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "\n", "#Calculations\n", "dy = log10(p2)-log10(p1)\n", "dx = (1/T1)-(1/T2)\n", "dy_by_dx = dy/dx\n", "Eg = (2*k*dy_by_dx)/e\n", "\n", "#Result\n", "print \"Energy band gap =\",round(Eg,3),\"eV\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Energy band gap = 0.452 eV\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.10, Page number 9.16" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import log\n", "\n", "#Variable declaration\n", "e = 1.602*10**-19 #charge on electron(C)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "Eg = 1*e #bandgap(J)\n", "\n", "#Calculations\n", "'''At T = 0K\n", "(Ev+0.5)=(Ec+Ev)/2 -----(1)\n", "\n", "Let at temperature T, fermi level be shited by 10%\n", "(Ev+06) = (Ec+Ev)/2 +(3kT*ln(4))/4 ----(2)\n", "\n", "Subtracting (1) from (2), we get the following expression'''\n", "\n", "T = (4*e/10)/(3*k*log(4))\n", "\n", "#Result\n", "print \"Temperature =\",round(T,2),\"K\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature = 1116.52 K\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.11, Page number 9.17" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "Na = 5*10**23 #no. of atoms of boron\n", "Nd = 3*10**23 #no. of atoms of arsenic\n", "ni = 2*10**16 #intrinsic charge carriers(/m^3)\n", "\n", "#Calculations\n", "p = (2*(Na-Nd))/2 #hole concentration(/m^3)\n", "n = ni**2/p #electron concentration(/m^3)\n", "\n", "#Result\n", "print \"Hole concentration =\",round((p/1E+23),2),\"*10^23 per m^3\"\n", "print \"Electron concentration =\",round((n/1E+9),2),\"*10^9 per m^3\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Hole concentration = 2.0 *10^23 per m^3\n", "Electron concentration = 2.0 *10^9 per m^3\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.12, Page number 9.18" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ue = 0.13 #electron mobility(m^2/V-s)\n", "uh = 0.05 #hole mobility(m^2/V-s)\n", "e = 1.602*10**-19 #charge on electron(C)\n", "ni = 1.5*10**16 #intrinsic charge carriers(/m^3) \n", "\n", "\n", "#Calculations\n", "#Part a\n", "sigma = ni*e*(ue+uh) #conductivity(1/ohm-m)\n", "\n", "#Part b\n", "w = 28.1 #atomic weight of Si\n", "den = 2.33*10**3 #density of Si(kg/m^3)\n", "n = (den*6.02*10**26)/w #no. of atoms of silicon\n", "#Since one donor type impurity atom is added in 10^8 Si atoms, \n", "Nd = n/10**8\n", "p = ni**2/Nd\n", "sigma_ex = Nd*e*ue #(per ohm-m)\n", "\n", "#Part c\n", "Na = Nd #Since one acceptor type impurity atom is added in 10^8 Si atoms\n", "n2 = ni**2/Na\n", "sigma_ax = Na*e*uh #(per ohm-m)\n", "\n", "#Results\n", "print \"a)Conductivity =\",round((sigma/1E-3),3),\"*10^-3 per ohm-m\"\n", "print \"b)Conductivity if donor type impurity is added =\",round(sigma_ex,2),\"per ohm-m\"\n", "print \"c)Conductivity if acceptor type impurity is added =\",round(sigma_ax,2),\"per ohm-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "a)Conductivity = 0.433 *10^-3 per ohm-m\n", "b)Conductivity if donor type impurity is added = 10.4 per ohm-m\n", "c)Conductivity if acceptor type impurity is added = 4.0 per ohm-m\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.13, Page number 9.20" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from math import log\n", "\n", "#Variable declaration\n", "ue = 0.135 #electron mobility(m^2/V-s)\n", "uh = 0.048 #hole mobility(m^2/V-s)\n", "e = 1.602*10**-19 #charge on electron(C)\n", "ni = 1.5*10**16 #intrinsic charge carriers(atoms/m^3)\n", "k = 1.38*10**-23 #Boltzman constant(J/K)\n", "T = 300 #assumption - Temperature(K)\n", "Nd = 10**23 #doping concentration(atoms/m^3)\n", "\n", "#Calculations\n", "sigma = ni*e*(ue+uh) #conductivity of intrinsic Si\n", "\n", "p = ni**2/Nd #hole concentration\n", "\n", "sigma_ex = Nd*e*ue #conductivity at equilibrium\n", "F = (3*k*T)/(4*e)*log(ue/uh) #position of Fermi level\n", "\n", "#Results\n", "print \"Conductivity of intrinsic Si is\",round((sigma/1E-3),4),\"*10^-3 per ohm-m\"\n", "print \"Hole concentration at equilibrium is\",round((Nd/1E+23)),\"*10^23 per m^3\"\n", "print \"Conductivity at equilibrium is\",round((sigma_ex/1E+3),2),\"*10^3 per m^3\"\n", "print \"Fermi level will be\",round(F,2),\"eV above intrinsic level\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Conductivity of intrinsic Si is 0.4397 *10^-3 per ohm-m\n", "Hole concentration at equilibrium is 1.0 *10^23 per m^3\n", "Conductivity at equilibrium is 2.16 *10^3 per m^3\n", "Fermi level will be 0.02 eV above intrinsic level\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.14, Page number 9.35" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "ue = 0.19 #electron mobility(m^2/V-s)\n", "e = 1.602*10**-19 #charge on electron(C)\n", "T = 300 #Temperature(K)\n", "\n", "#Calculation\n", "Dn = (ue*k*T)/e\n", "\n", "#Result\n", "print \"Diffusion co-efficient =\",round((Dn/1E-4),2),\"*10^-4 m^2/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Diffusion co-efficient = 49.1 *10^-4 m^2/s\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.15, Page number 9.45" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "Rh = 3.66*10**-4 #Hall coefficient\n", "I = 10**-2 #current(A)\n", "B = 0.5 #magnetic field intensity(wb/m^2)\n", "t = 1.*10**-3 #thickness of plate(m)\n", "\n", "#Calculations\n", "Vh = (Rh*I*B)/t\n", "\n", "#Result\n", "print \"Hall coefficient =\",(Vh/1E-3),\"mV\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Hall coefficient = 1.83 mV\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.16, Page number 9.46" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "Vy = 37*10**-6 #voltage(V)\n", "t = 10**-3 #thickness of crystal(m)\n", "Bz = 0.5 #magnetic field intensity(Wb/m^2)\n", "Ix = 20*10**-3 #current(A)\n", "\n", "#Calculations\n", "Vh = (Vy*t)/(Ix*Bz)\n", "\n", "#Result\n", "print \"Hall coefficient =\",(Vh/1E-6),\"*10^-6 m^3/C\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Hall coefficient = 3.7 *10^-6 m^3/C\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.17, Page number 9.46" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "Rh = 7.35*10**-5 #Hall coefficient(m^3/C)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "sigma = 200 #conductivity(/ohm-m)\n", "n = 8.023*10**22 #Avogadro's number\n", "\n", "#Calculations\n", "n = 1/(Rh*e)\n", "\n", "u = sigma/(n*e)\n", "\n", "#Results\n", "print \"Density =\",round((n/1E+22),3),\"*10^22 m^3\"\n", "print \"Conductivity =\",round((u/1E-3),2),\"*10^-3 m^2/V-s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Density = 8.503 *10^22 m^3\n", "Conductivity = 14.7 *10^-3 m^2/V-s\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.18, Page number 9.47" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "I = 50 #current(A)\n", "B = 1.5 #magnetic field intensity(T)\n", "n = 8.4*10**28 #free electron concentration in copper(electron/m^3)\n", "t = 0.5*10**-2 #thickness of slab(m)\n", "\n", "#Calculation\n", "Vh = (I*B)/(n*e*t)\n", "\n", "#Result\n", "print \"The magnitude of Hall voltage is\",round((Vh/1E-6),3),\"*10^-6 V\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The magnitude of Hall voltage is 1.116 *10^-6 V\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9.19, Page number 9.48" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "Rh = 3.66*10**-4 #Hall coefficient(m^3/C)\n", "e = 1.6*10**-19 #charge on electron(C)\n", "Pn = 8.93*10**-3 #resistivity(ohm-m)\n", "\n", "#Calculation\n", "n = 1/(Rh*e)\n", "\n", "ue = Rh/Pn\n", "\n", "#Result\n", "print \"n =\",round((n/1E+22),3),\"*10^22/m^3\"\n", "print \"u =\",round(ue,3),\"m^2/V-s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "n = 1.708 *10^22/m^3\n", "u = 0.041 m^2/V-s\n" ] } ], "prompt_number": 10 } ], "metadata": {} } ] }