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diff --git a/Solid_state_physics/Chapter_9_1.ipynb b/Solid_state_physics/Chapter_9_1.ipynb new file mode 100755 index 00000000..70a3843c --- /dev/null +++ b/Solid_state_physics/Chapter_9_1.ipynb @@ -0,0 +1,845 @@ +{ + "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": {} + } + ] +}
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