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{
"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": {}
}
]
}
|
