{
"metadata": {
"name": "",
"signature": "sha256:b86f6f4d444d5177f7a40efe10b2b4ac505571f2f5cf98eeaa6619afa2ee7d22"
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"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": {}
}
]
}