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1 files changed, 333 insertions, 154 deletions
diff --git a/Engineering_Physics/Chapter7_1.ipynb b/Engineering_Physics/Chapter7_1.ipynb index cd558c19..d6a7ab3d 100755 --- a/Engineering_Physics/Chapter7_1.ipynb +++ b/Engineering_Physics/Chapter7_1.ipynb @@ -1,7 +1,7 @@ { "metadata": { - "name": "", - "signature": "sha256:7187247d22d4e816cffb8e16cb739591c46b8ff453a1af7a76514de7cc4fae35" + "name": "Chapter7", + "signature": "sha256:043709ddd748250fcd3232cc251c6d71d665f281189e172a4c8d9b59233bdcee" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,48 +12,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "7: Superconductivity" - ] + "source": "7: Semiconducting Materials" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.1, Page number 152" - ] + "source": "Example number 7.1, Page number 208" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "Tc=3.722; #critical temperature(K)\n", - "T=2; #temperature(K)\n", - "Bc_0=0.0305; #critical field(T)\n", - "\n", - "#Calculation\n", - "Bc_T=Bc_0*(1-(T/Tc)**2); #critical field at 2K(T)\n", - "Bc_T = math.ceil(Bc_T*10**4)/10**4; #rounding off the value of Bc_T to 4 decimals\n", - "\n", - "#Result\n", - "print \"The critical field at 2K is\",Bc_T, \"T\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nme = 9.11*10**-31; #mass of electron(kg)\nepsilon_r = 13.2; \nepsilon0 = 8.85*10**-12;\nh = 6.63*10**-34;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nm_nc = 0.067*me;\nE = m_nc*e**4/(8*(epsilon0*epsilon_r*h)**2); #energy(J)\nE = E/e; #energy(eV)\nE = math.ceil(E*10**5)/10**5; #rounding off to 5 decimals\nE_meV = E*10**3; #energy(meV)\n\n#Result\nprint \"donor binding energy is\",E,\"eV or\",E_meV,\"meV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The critical field at 2K is 0.0217 T\n" - ] + "text": "donor binding energy is 0.00521 eV or 5.21 meV\n" } ], "prompt_number": 1 @@ -62,42 +39,19 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.2, Page number 152" - ] + "source": "Example number 7.2, Page number 208" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "V = 1; #DC voltage applied across the Josephson junction(micro-volt)\n", - "e = 1.6*10**-19; #Charge on an electron(C)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "\n", - "#Calculation\n", - "V = V*10**-6; #DC voltage applied across the Josephson junction(V)\n", - "f = 2*e*V/h; #Frequency of Josephson current(Hz)\n", - "f = f*10**-6; #Frequency of Josephson current(MHz)\n", - "f = math.ceil(f*10**2)/10**2; #rounding off the value of f to 2 decimals\n", - "\n", - "#Result\n", - "print \"The frequency of Josephson current is\",f, \"MHz\"" - ], + "input": "#importing modules\nimport math\nimport numpy as np\n\n#Variable declaration\nNd = 10**16; #donor concentration(atoms/cm**3)\nni = 1.5*10**10; #concentration(per cm**3)\nT = 300; #temperature(K)\nkT = 0.0259;\n\n#Calculation\nn0 = Nd; #for Nd>>ni, assume n0=Nd\np0 = ni**2/n0; #equilibrium hole concentration(per cm**3)\np0 = p0*10**-4;\nEF_Ei = kT*np.log(n0/ni);\nEF_Ei = math.ceil(EF_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n\n#Result\nprint \"equilibrium hole concentration is\",p0,\"*10**4 per cm**3\"\nprint \"value of EF-Ei is\",EF_Ei,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The frequency of Josephson current is 482.95 MHz\n" - ] + "text": "equilibrium hole concentration is 2.25 *10**4 per cm**3\nvalue of EF-Ei is 0.3474 eV\n" } ], "prompt_number": 2 @@ -106,41 +60,109 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.3, Page number 152" - ] + "source": "Example number 7.3, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nNd = 10**14; #donor density(atoms/cm**3)\nmew_n = 3900;\n\n#Calculation\nn = Nd;\nsigma = n*e*mew_n; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*100)/100; #rounding off to 2 decimals\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 16.03 ohm cm\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.4, Page number 209" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #charge of electron(C)\nn0 = 5*10**16; #donor density(atoms/cm**3)\nmew_0 = 800;\nIx = 2; #current(mA)\nBz = 5*10**-5;\nd = 200; #thickness(micrometre)\n\n#Calculation\nIx = Ix*10**-3; #current(A)\nd = d*10**-4; #thickness(m)\nsigma = e*n0*mew_0; #conductivity(ohm-1 cm-1)\nrho = 1/sigma; #resistivity(ohm cm)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\nRH = -1/(e*n0); #Hall coefficient(cm**3/C)\nVH = Ix*Bz*RH/d; #Hall voltage(V)\nVH = VH*10**5;\n\n\n#Result\nprint \"resistivity of sample is\",rho,\"ohm cm\"\nprint \"Hall coefficient is\",RH,\"cm**3/C\"\nprint \"Hall voltage is\",VH,\"*10**-5 V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "resistivity of sample is 0.1563 ohm cm\nHall coefficient is -125.0 cm**3/C\nHall voltage is -62.5 *10**-5 V\n" + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.5, Page number 210" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "T_c = 0.517; #Critical temperature for cadmium(K)\n", - "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "\n", - "#Calculation\n", - "E_g = 3.5*k*T_c/e; #Superconducting energy gap at absolute zero(eV)\n", - "E_g = E_g*10**4;\n", - "E_g = math.ceil(E_g*10**3)/10**3; #rounding off the value of E_g to 3 decimals\n", - "\n", - "#Result\n", - "print \"The superconducting energy gap for Cd at absolute zero is\",E_g,\"*10**-4 eV\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\nEg = 0.7; #band gap(eV)\nme = 9.11*10**-31; #mass of electron(kg)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nh = 6.625*10**-34;\nkT = 0.0259;\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\na = (2*math.pi*k*T/(h**2))**(3/2);\nb = (mn_star*mp_star)**(3/4);\nc = math.exp(-Eg/(2*kT));\nni = 2*a*b*c; #intrinsic concentration(per m**3)\nsigma = ni*e*(mew_n+mew_p); #intrinsic conductivity(per ohm m)\nsigma = math.ceil(sigma*10**4)/10**4; #rounding off to 4 decimals\nrho = 1/sigma; #intrinsic resistivity(ohm m)\nrho = math.ceil(rho*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"intrinsic concentration is\",ni,\"per m**3\"\nprint \"intrinsic conductivity is\",sigma,\"per ohm m\"\nprint \"intrinsic resistivity is\",rho,\"ohm m\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic concentration is 1.02825111151e+19 per m**3\nintrinsic conductivity is 0.9872 per ohm m\nintrinsic resistivity is 1.013 ohm m\nanswers given in the book are wrong\n" + } ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.6, Page number 211" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nNd = 10**16; #donor concentration(per cm**3)\nni = 1.45*10**10; #concentration(per cm**3)\nkT = 0.0259;\n\n#Calculation\n#ni = Nc*math.exp(-(Ec-Ei)/kT)\n#Nd = Nc*(math.exp(-(Ec-Efd)/kT)\n#dividing Nd/ni we get \nEFd_Ei = kT*np.log(Nd/ni);\nEFd_Ei = math.ceil(EFd_Ei*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"Fermi energy is\",EFd_Ei,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The superconducting energy gap for Cd at absolute zero is 1.561 *10**-4 eV\n" - ] + "text": "Fermi energy is 0.3482 eV\n" + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.7, Page number 211, theoretical" + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.8, Page number 212" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nT = 300; #temperature(K)\nmew_n = 0.36; #electron mobility(m**2/Vs)\nmew_p = 0.17; #hole mobility(m**2/Vs)\nrho = 2.12; #resistivity(ohm m)\nme = 9.11*10**-31; #mass of electron(kg)\nkT = 0.0259;\nh = 6.625*10**-34;\nk = 1.38*10**-23; #boltzmann constant\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nmn_star = 0.55*me; #electron effective mass(kg)\nmp_star = 0.37*me; #hole effective mass(kg)\nsigma = 1/rho; #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\nni = sigma/(e*(mew_n+mew_p)); #concentration of electrons(per m**3)\na = (2*math.pi*kT/(h**2))**(3/2);\nNc = 2*a*(mn_star**(3/2)); \nNv = 2*a*(mp_star**(3/2)); \nb = (Nc*Nv)**(1/2);\nEg = 2*kT*np.log(b/ni);\n\n#Result\nprint \"forbidden energy gap is\",Eg,\"eV\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "forbidden energy gap is 4.09465494989 eV\nanswer given in the book is wrong\n" } ], "prompt_number": 8 @@ -149,84 +171,103 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.4, Page number 152" - ] + "source": "Example number 7.9, Page number 213" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", - "c = 3*10**8; #Speed of light in free space(m/s)\n", - "h = 6.626*10**-34; #Planck's constant(Js)\n", - "E_g = 1.5*10**-4; #Superconducting energy gap for a material(eV)\n", - "\n", - "#Calculation\n", - "#As E_g = h*new = h*c/lamda, solving for lambda\n", - "lamda = h*c/(E_g*e); #Wavelength of photon to break up a Cooper-pair(m)\n", - "lamda = lamda*10**3;\n", - "lamda = math.ceil(lamda*10**3)/10**3; #rounding off the value of lamda to 3 decimals\n", - "\n", - "#Result\n", - "print \"The wavelength of photon to break up a Cooper-pair is\",lamda,\"*10**-3 m\"" + "input": "#importing modules\nimport math\n\n#Variable declaration\nni = 2.4*10**19; #concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #conductivity(per ohm m)\nsigma = math.ceil(sigma*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"conductivity of sample is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "conductivity of sample is 2.228 ohm-1 m-1\n" + } ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.10, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nEc = 0.3; #initial position(eV)\nT1 = 300; #initial temperature(K)\nT2 = 330; #increased temperature\n\n#Calculation\n#Ec/T1 = Ec_EF330/T2\nEc_EF330 = Ec*T2/T1; #new position of Fermi level(eV)\n\n#Result\nprint \"new position of Fermi level is\",Ec_EF330,\"eV\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The wavelength of photon to break up a Cooper-pair is 8.283 *10**-3 m\n" - ] + "text": "new position of Fermi level is 0.33 eV\n" } ], - "prompt_number": 12 + "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.5, Page number 153" - ] + "source": "Example number 7.11, Page number 214" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lambda_0 = 37; #Penetration depth of lead at 0 kelvin(nm)\n", - "T_c = 7.193; #Critical temperature of superconducting transition for lead(kelvin)\n", - "T = 5.2; #Temperature at which penetration depth for lead becomes lambda_T(kelvin) \n", - "\n", - "#Calculation\n", - "lambda_T = lambda_0*(1-(T/T_c)**4)**(-1/2); #Penetration depth of lead at 5.2 kelvin(nm)\n", - "lambda_T = math.ceil(lambda_T*10)/10; #rounding off the value of lamda_T to 1 decimal\n", - "\n", - "#Result\n", - "print \"The penetration depth of lead is\",lambda_T, \"nm\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature(K)\nme = 9.1*10**-31; #mass of electron(kg)\nh = 6.63*10**-34; #planck's constant\nEc_Ev = 1.1; #energy gap(eV)\ne = 1.6*10**-19; #charge of electron(C)\n\n#Calculation\nme_star = 0.31*me;\nA = (2*math.pi*k*T*me_star/(h**2))**(3/2);\nB = math.exp(-(Ec_Ev*e)/(2*k*T));\nni = A*B; #concentration in conduction band(per m**3)\n\n#Result\nprint \"intrinsic electron concentration is\",ni,\"per m**3\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic electron concentration is 1.26605935487e+15 per m**3\nanswer given in the book is wrong\n" + } ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.12, Page number 214" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\nRH = 0.55*10**-10; #Hall coefficient(m**3/As)\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nmew = RH*sigma; #drift mobility(m**2/Vs)\nmew = mew*10**3;\nmew = math.ceil(mew*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"drift mobility of electrons is\",mew,\"*10**-3 m**2/Vs\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The penetration depth of lead is 43.4 nm\n" - ] + "text": "drift mobility of electrons is 3.25 *10**-3 m**2/Vs\n" + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.13, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nA = 6.022*10**23; #avagadro constant\nd = 8.96*10**-9; #density(kg/m**3)\nn = 9.932*10**14; #no. of free electrons per atom\nsigma = 5.9*10**7; #conductivity(ohm-1 m-1)\ne = 1.6*10**-19; #electron charge(C)\nmew = 3.2*10**-3; #drift mobility(m**2/Vs)\nw = 63.5; #atomic weight of Cu(kg)\n\n#Calculation\nni = sigma/(mew*e); #conductivity(per m**3)\nN = A*d*n/w; #concentration of free electrons in pure Cu\nAN = ni/N; #average number of electrons contributed per Cu atom\n\n#Result\nprint \"concentration of free electrons in pure Cu is\",N,\"per m**3\"\nprint \"average number of electrons contributed per Cu atom is\",int(AN)", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "concentration of free electrons in pure Cu is 8.43940339906e+28 per m**3\naverage number of electrons contributed per Cu atom is 1\n" } ], "prompt_number": 13 @@ -235,52 +276,190 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 7.6, Page number 153" - ] + "source": "Example number 7.14, Page number 215" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nRH = 3.66*10**-11; #hall coefficient(m**3/As)\ne = 1.6*10**-19; #electron charge(C)\nsigma = 112*10**7; #conductivity(ohm-1 m-1)\n\n#Calculation\nn = 1/(e*RH); #charge carrier density(per m**3)\nmew_n = sigma/(n*e); #electron mobility(m**2/As)\nmew_n = math.ceil(mew_n*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"charge carrier density is\",n,\"per m**3\"\nprint \"electron mobility is\",mew_n,\"m**2/As\"\nprint \"answers given in the book are wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "charge carrier density is 1.70765027322e+29 per m**3\nelectron mobility is 0.041 m**2/As\nanswers given in the book are wrong\n" + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.15, Page number 216" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "M1 = 199; #Mass of an isotope of mercury(amu)\n", - "T_C1 = 4.185; #Transition temperature of the isoptope of Hg(K)\n", - "T_C2 = 4.153; #Transition temperature of another isoptope of Hg(K)\n", - "alpha = 0.5; #Isotope coefficient\n", - "\n", - "#Calculation\n", - "M2 = M1*(T_C1/T_C2)**(1/alpha); #Mass of another isotope of mercury(amu)\n", - "M2 = math.ceil(M2*100)/100; #rounding off the value of M2 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The mass of another isotope of mercury is\",M2, \"amu\"" + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nB = 1.5; #magnetic field(T)\nI = 50; #current(Amp)\nn = 8.4*10**28; #free electron concentration(per m**3)\nd = 0.2; #thickness of slab(cm)\n\n#Calculation\nd = d*10**-2; #thickness of slab(m)\nVH = B*I/(n*e*d); #hall voltage(V)\n\n#Result\nprint \"magnitude of Hall voltage is\",VH,\"V\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "magnitude of Hall voltage is 2.79017857143e-06 V\nanswer given in the book is wrong\n" + } ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.16, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nn = 2.5*10**19; #free electron concentration(per m**3)\nmew_n = 0.39; #electron mobility(m**2/Vs)\nmew_p = 0.19; #hole mobility(m**2/Vs)\nL = 1; #length(cm)\nw = 1; #width(mm)\nt = 1; #thickness(mm)\n\n#Calculation\nL = L*10**-2; #length(m)\nw = w*10**-3; #width(m)\nt = t*10**-3; #thickness(m)\nA = w*t; #area(m**2)\nsigma = n*e*(mew_n+mew_p); #conductivity(ohm-1 m-1)\nR = L/(sigma*A); #resistance(ohm)\n\n#Result\nprint \"resistance of intrinsic Ge rod is\",int(R),\"ohm\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The mass of another isotope of mercury is 202.08 amu\n" - ] + "text": "resistance of intrinsic Ge rod is 4310 ohm\n" } ], "prompt_number": 16 }, { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.17, Page number 216" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nEg = 1.12; #band gap(eV)\nme = 1;\nmn_star = 0.12*me; #electron mobility(m**2/Vs)\nmp_star = 0.28*me; #hole mobility(m**2/Vs)\nk = 1.38*10**-23; #boltzmann constant\nT = 300; #temperature\n\n#Calculation\na = mp_star/mn_star;\nEF = (Eg/2)+((3*k*T/(4*e))*np.log(a));\nEF = math.ceil(EF*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"position of Fermi level is\",EF,\"eV\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "position of Fermi level is 0.577 eV\n" + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.18, Page number 217" + }, + { "cell_type": "code", "collapsed": false, - "input": [], + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 1.5*10**16; #intrinsic carrier density(per m**3)\nmew_n = 0.13; #electron mobility(m**2/Vs)\nmew_p = 0.05; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\nsigma = sigma*10**4;\n\n#Result\nprint \"electrical conductivity is\",sigma,\"*10**-4 ohm-1 m-1\"", "language": "python", "metadata": {}, - "outputs": [] + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "electrical conductivity is 4.32 *10**-4 ohm-1 m-1\n" + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.19, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.15*10**-13; #intrinsic carrier density(per cm**3)\nmew_n = 3900; #electron mobility(cm**2/Vs)\nmew_p = 1900; #hole mobility(cm**2/Vs)\n\n#Calculation\nsigmai = ni*e*(mew_n+mew_p); #electrical conductivity(ohm-1 cm-1)\nrhoi = 1/sigmai; #intrinsic resistivity(ohm cm)\n\n#Result\nprint \"intrinsic resistivity is\",rhoi,\"ohm cm\"\nprint \"answer given in the book is wrong\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 5.01202886929e+27 ohm cm\nanswer given in the book is wrong\n" + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.20, Page number 217" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nni = 2.1*10**19; #intrinsic carrier density(per m**3)\nmew_n = 0.4; #electron mobility(m**2/Vs)\nmew_p = 0.2; #hole mobility(m**2/Vs)\n\n#Calculation\nsigma = ni*e*(mew_n+mew_p); #electrical conductivity\n\n#Result\nprint \"intrinsic resistivity is\",sigma,\"ohm-1 m-1\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "intrinsic resistivity is 2.016 ohm-1 m-1\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.21, Page number 218" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nV = 1.35; #voltage supply(V)\nI = 5; #current(mA)\nb = 5; #breadth(mm)\nd = 1; #thickness(mm)\nL = 1; #length(cm)\nH = 0.45; #magnetic field(Wb/m**2)\nVy =20; #Hall voltage(mV)\n\n#Calculation\nVy = Vy*10**-3; #Hall voltage(V)\nL = L*10**-2; #length(m)\nd = d*10**-3; #thickness(m)\nb = b*10**-3; #breadth(m)\nI = I*10**-3; #current(A)\nR = V/I; #resistance(ohm)\nA = b*d; #area(m**2)\nrho = R*A/L; #resistivity(ohm m)\nEy = Vy/d; #Hall field(V/m)\nJx = I/A; \na = Ey/(H*Jx); #current density(m**3/C).Here a is 1/ne \nRH = a; #Hall coefficient(m**3/C)\nRH = math.ceil(RH*10**4)/10**4; #rounding off to 4 decimals\nmew_n = RH/rho; #electron mobility(m**2/Vs)\nmew_n = math.ceil(mew_n*10**2)/10**2; #rounding off to 2 decimals\n\n#Result\nprint \"Hall coefficient is\",RH,\"m**3/C\"\nprint \"electron mobility is\",mew_n,\"m**2/Vs\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall coefficient is 0.0445 m**3/C\nelectron mobility is 0.33 m**2/Vs\n" + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": "Example number 7.22, Page number 219" + }, + { + "cell_type": "code", + "collapsed": false, + "input": "#importing modules\nimport math\n\n#Variable declaration\ne = 1.6*10**-19; #electron charge(C)\nIx = 200; #current(A)\nBz = 1.5; #magnetic field(Wb/m**2)\np = 8.4*10**28; #electron concentration(per m**3)\nd = 1; #thickness(mm)\n\n#Calculation\nd = d*10**-3; #thickness(m)\nVH = Ix*Bz/(e*p*d); #Hall potential(V)\nVH = VH*10**6; #Hall potential(micro V)\n\n#Result\nprint \"Hall potential is\",int(VH),\"micro V\"", + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": "Hall potential is 22 micro V\n" + } + ], + "prompt_number": 22 } ], "metadata": {} |