{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 3 , Semiconductor Physics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.1 , Page Number 54"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Velocity of electron at fermi level is 859007.52 m/s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"m = 9.107 * 10**-31 #Mass of electron (in kilogram)\n",
"E = 2.1 #Energy associated (in electon-volt)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"\n",
"#Calculation\n",
"\n",
"E = E * e #Energy associated (in Joules)\n",
"v = (2 * E / m)**0.5 #Velocity of electron (in meter per second)\n",
"\n",
"#Result\n",
"\n",
"print \"Velocity of electron at fermi level is \",round(v,2),\" m/s.\"\n",
"\n",
"#Slight variation due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.2 , Page Number 63 "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Drift velocity is 0.0003 m/s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"J = 2.4 * 10**6 #Current Density (in Ampere per meter-square) \n",
"n = 5.0 * 10**28 #Electron density \n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"\n",
"#Calculation\n",
"\n",
"v = J / (e * n) #Drift velocity (in meter per second) \n",
"\n",
"#Result\n",
"\n",
"print \"Drift velocity is \",v,\" m/s.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.3 , Page Number 64"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Magnitude of current is 0.24 A.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"n = 10**24 #Electron density \n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"v = 1.5 * 10**-2 #Drift velocity (in meter per second)\n",
"A = 1.0 * 10**-4 #Area of cross-section (in meter-square)\n",
"\n",
"#Calculation\n",
"\n",
"I = e * n * v * A #Current (in Ampere) \n",
"\n",
"#Result\n",
"\n",
"print \"Magnitude of current is \",I,\" A.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.4 , Page Number 64"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Concentration of electrons is 4.44600943977e+16 /cm**3.\n",
"Concentration of holes is 14057550000.0 \\cm**3.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"p = 0.039 #Resistivity of doped material (in ohm-centimeter)\n",
"e = 1.602 * 10**-19 #Charge on electron (in Coulomb)\n",
"ue = 3600.0 #Carrier mobility (in centimeter-square per volt-second)\n",
"ni = 2.5 * 10**13 #Intrinsic concentration (in per cubic-centimeter)\n",
"\n",
"#Calculation\n",
"\n",
"\n",
"sign = 1/p #Conductivity (in per ohm-centimeter)\n",
"ND = sign /(e * ue) #Concentration of donor atoms (in per cubic-centimeter)\n",
"n = ND #Concentration of electron (per cubic-centimeter)\n",
"p = ni**2 / n #Concentration of hole (per cubic-centimeter)\n",
"\n",
"#Result\n",
"\n",
"print \"Concentration of electrons is \",n,\" /cm**3.\\nConcentration of holes is \",p,\" \\cm**3.\"\n",
"\n",
"#Slight variation due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.5 , Page Number 64 "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Resulting donor concentration is 50000000000000000 /cm**3.\n",
"Resulting mobile electron concentration is 50000000000000000 /cm**3.\n",
"Resulting hole concentration is 4205.0 /cm**3.\n",
"Conductivity of doped silicon sample is 10.413 (ohm-cm)**-1.\n",
"Resistivity is 0.096033803899 ohm-cm and Resistance is 1920.67607798 ohm.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"N = 5.0 * 10**22 #Number of silicon atoms (per cubic-centimeter)\n",
"N1 = 10**-6 #Donor impurity \n",
"ni = 1.45 * 10**10 #Intrinsic concentration (in per cubic-centimeter) \n",
"l = 0.5 #Length (in centimeter)\n",
"A = (50.0 * 10**-4)**2 #Area of cross-section (in centimeter-square)\n",
"ue = 1300.0 #Mobility of electron (in ) \n",
"\n",
"#Calculation\n",
"\n",
"ND = 5 * 10**16 #Donor concentration (in per cubic-centimeter)\n",
"n = ND #Mobile electron concentration (in per cubic-centimeter)\n",
"p = ni**2 / ND #Hole concentration (in centimeter-square per volt-second)\n",
"sig = n * e * ue #Conductivity of doped silicon sample (in per ohm-cetimeter)\n",
"p1 = 1/sig #Resistivity (in ohm-centimeter)\n",
"R = p1 * l / A #Resistance (in ohm)\n",
"\n",
"#Result\n",
"\n",
"print \"Resulting donor concentration is \",ND,\" /cm**3.\\nResulting mobile electron concentration is \",n,\" /cm**3.\\nResulting hole concentration is \",p,\" /cm**3.\"\n",
"print \"Conductivity of doped silicon sample is \",sig,\" (ohm-cm)**-1.\\nResistivity is \",p1,\" ohm-cm and Resistance is \",R,\" ohm.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.6 , Page Number 65 "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ratio of electron to hole concentration is 1e+12 .\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ni = 1.4 * 10**18 #intrinsic concentration (in per cubic-centimeter)\n",
"ND = 1.4 * 10**24 #Donor concentration (in per cubic-centimeter)\n",
"n = ND #Concentration of electrons (in per cubic-centimeter)\n",
"\n",
"#Calculation\n",
"\n",
"p = ni**2 / ND #Concentration of holes (in per cubic-centime) \n",
"ratio = n / p #Ratio of electron to hole concentration \n",
"\n",
"#Result\n",
"\n",
"print \"Ratio of electron to hole concentration is \",ratio,\".\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.7 , Page Number 65"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relaxation time is 4.004e-14 s.\n",
"Resistivity of conductor is 1.53066222571e-08 ohm-meter.\n",
"Velocity of electrons with fermi energy is 1390706.99073 m/s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"Ef = 5.5 #Fermi energy (in electron-volt)\n",
"ue = 7.04 * 10**-3 #Mobility of electrons (in meter-square per volt-second)\n",
"n = 5.8 * 10**28 #Concentration of electrons (in per cubic-centimeter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"m = 9.1 * 10**-31 #Mass of electron (in kilogram) \n",
"\n",
"#Calculation\n",
"\n",
"tau = ue * m / e #Relaxation time (in seconds)\n",
"p = 1 / (n * e * ue) #Resistivity (in ohm-meter) \n",
"vf = (2 * Ef * e / m)**0.5 #Velocity of electron with fermi energy (in meter per second)\n",
"\n",
"#Result\n",
"\n",
"print \"Relaxation time is \",tau,\" s.\\nResistivity of conductor is \",p,\"ohm-meter.\\nVelocity of electrons with fermi energy is \",vf,\" m/s.\"\n",
"\n",
"#Slight variation due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.8 , Page Number 68"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Conductivity is 0.0224 (ohm-cm)**-1.\n",
"Resistivity is 44.64 ohm-cm.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ni = 2.5 * 10**13 #Intrinsic concentration (in per cubic-centimeter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"uh = 1800.0 #Mobility of holes (in per cubic-centimeter)\n",
"ue = 3800.0 #Mobility of electrons (in per cubic-centimeter)\n",
"\n",
"#Calculation\n",
"\n",
"sigi = ni * e * (ue + uh) #Conductivity (in per ohm-centimeter)\n",
"pi = 1/sigi #Resistivity (in ohm-centimeter)\n",
"\n",
"#Result\n",
"\n",
"print \"Conductivity is \",sigi,\" (ohm-cm)**-1.\\nResistivity is \",round(pi,2),\" ohm-cm.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.9 , Page Number 68 "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Density of electrons is 2.29273661042e+19 /m**3.\n",
"Drift velocity of electrons is 3900.0 m/s.\n",
"Drift velocity of holes is 1900.0 m/s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"pi = 0.47 #intrinsic resistivity (in ohm-meter)\n",
"ue = 0.39 #Electron mobility (in meter-square per volt-second)\n",
"uh = 0.19 #Hole mobility (in meter-square per volt-second)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"E = 10**4 #Electric field (in volt per meter)\n",
"\n",
"#Calculation\n",
"\n",
"sigi = 1 / pi #Conductivity (in per ohm-meter)\n",
"ni = sigi/(e * (ue + uh)) #Intrinsic concentration (in per cubic-meter)\n",
"vn = ue * E #Drift velocity of electrons (in meter per second)\n",
"vh = uh * E #Drift velocity of holes (in meter per second) \n",
"\n",
"#Result\n",
"\n",
"print \"Density of electrons is \",ni,\" /m**3.\\nDrift velocity of electrons is \",vn,\" m/s.\\nDrift velocity of holes is \",vh,\" m/s.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.10 , Page Number 69 "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Conductivity of intrinsic silicon is 4.2e-06 /ohm-cm.\n",
"Conductivity of P type silicon is 72.0 ohm-cm.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ni = 1.5 * 10**10 #Intrinsic concentration (in per cubic-centimeter)\n",
"uh = 450.0 #mobility of holes (in centimeter-square per volt-second)\n",
"ue = 1300.0 #mobility of electrons (in centimeter-square per volt-second)\n",
"NA = 10**18 #Doping level (in per cubic-centimeter)\n",
"\n",
"#Calculation\n",
"\n",
"sigi = ni * e * (ue + uh) #Conductivity of silicon (in per ohm-centimeter)\n",
"sigp = e * NA * uh #COnductivity of P-type silicon (in per ohm-centimeter)\n",
"\n",
"#Result\n",
"\n",
"print \"Conductivity of intrinsic silicon is \",sigi,\" /ohm-cm.\\nConductivity of P type silicon is \",sigp,\" ohm-cm.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.11 , Page Number 69 "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Conductivity of intrinsic semiconductor is 0.0224 /ohm-cm.\n",
"Conductivity of N-type semiconductor is 2.68 /ohm-cm.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ni = 2.5 * 10**13 #Intrinsic concentration (in per cubic-centimeter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"uh = 1800.0 #mobility of holes (in centimeter-square per volt-second)\n",
"ue = 3800.0 #mobility of electrons (in centimeter-square per volt-second)\n",
"ND = 4.41 * 10**22 * 10**-7 #Number of Germanium atoms (in per cubic-centimeter)\n",
"\n",
"#Calculation\n",
"\n",
"sigi = ni * e * (uh + ue) #Intrinsic concentration (in per ohm-centimeter)\n",
"n = ND #Concentration of electrons (in per cubic-centimeter)\n",
"p = ni**2 / ND #Concentration of holes (in per cubic-centimeter)\n",
"sign = e * ND * ue #Conductivity of N-type germanium semiconductor (in per ohm-meter)\n",
"\n",
"#Result\n",
"\n",
"print \"Conductivity of intrinsic semiconductor is \",sigi,\" /ohm-cm.\\nConductivity of N-type semiconductor is \",round(sign,2),\" /ohm-cm.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.12 , Page Number 69"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Electron drift velocity is 152.0 m/s.\n",
"Holes drift velocity is 72.0 m/s.\n",
"Intrinsic conductivity of Ge is 2.24 /ohm-m.\n",
"Total current is 5.376 mA.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"V = 10.0 #Voltage (in volts)\n",
"l = 0.025 #Length (in meter)\n",
"uh = 0.18 #mobility of holes (in meter-square per volt-second)\n",
"ue = 0.38 #mobility of electrons (in meter-square per volt-second)\n",
"ni = 2.5 * 10**19 #Intrinsic concentration (in per cubic-imeter)\n",
"a = 4.0 * 1.5 *10**-6 #Area of cross-section (in meter-square)\n",
"\n",
"#Calculation\n",
"\n",
"E = V / l #Electric field (in volt per meter)\n",
"ve = ue * E #Drift velocity of electrons (in meter per second)\n",
"vh = uh * E #Drift velocity of holes (in meter per second)\n",
"sigi = ni * e * (ue + uh) #Conductivity of intrinsic semiconductor (in per ohm-meter)\n",
"I = sigi * E * a #Total current (in Ampere) \n",
"\n",
"#Result\n",
"\n",
"print \"Electron drift velocity is \",ve,\" m/s.\\nHoles drift velocity is \",vh,\" m/s.\\nIntrinsic conductivity of Ge is \",sigi,\" /ohm-m.\\nTotal current is \",I * 10**3,\" mA.\" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.13 , Page Number 70 "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Diffusion constant of electron is 93.0 cm**2/s.\n",
"Diffusion constant of holes is 43.9875 cm**2/s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ni = 2.5 * 10**13 #Intrinsic concentration (in per cubic-centimeter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"uh = 1700.0 #mobility of holes (in centimeter-square per volt-second)\n",
"ue = 3600.0 #mobility of electrons (in centimeter-square per volt-second)\n",
"k = 1.38 * 10**-23 #Boltzmann constant (in Joule per kelvin)\n",
"T = 300.0 #Temperature (in kelvin)\n",
"\n",
"#Calculation\n",
"\n",
"De = ue * k * T / e #Diffusion constant of electrons (in centimeter-square per second)\n",
"Dh = uh * k * T / e #Diffusion constant of holes (in centimeter-square per second)\n",
"\n",
"#Result\n",
"\n",
"print \"Diffusion constant of electron is \",round(De),\" cm**2/s.\\nDiffusion constant of holes is \",Dh,\" cm**2/s.\"\n",
"\n",
"#Slight variation in Dh due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.14 , Page Number 72"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mobility of charge carriers is 4e-08 m**2/V-s.\n",
"Density of charge carriers is 1.73611111111e+22 /m**3.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"p = 9.0 * 10**3 #Resistivity (in ohm-meter)\n",
"RH = 3.6 * 10**-4 #Hall coefficient (in cubic-meter per Coulomb) \n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"\n",
"#Calculation\n",
"\n",
"sig = 1/p #Conductivity (in per ohm-meter)\n",
"P = 1/ RH #Charge density (in Coulomb per cubic meter)\n",
"n = P / e #Density of charge carriers (in per cubic-meter)\n",
"u = sig * RH #Mobility (in meter-square per volt-second)\n",
"\n",
"#Result\n",
"\n",
"print \"Mobility of charge carriers is \",u,\" m**2/V-s.\\nDensity of charge carriers is \",n,\" /m**3.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.15 , Page Number 73"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The current density in the specimen is 2482.76 A/m**2\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"E = 100.0 #Electric field (in volt per meter)\n",
"RH = 0.0145 #Hall coefficient (in cubic-meter per Coulomb)\n",
"un = 0.36 #Mobility of electrons (in meter-square per volt-second)\n",
"\n",
"#Calculation\n",
"\n",
"n = 1/(e * RH) #Concentration (in per cubic-meter)\n",
"J = n * e * un * E #Current density (in Ampere per cubic-meter) \n",
"\n",
"#Result\n",
"\n",
"print \"The current density in the specimen is \",round(J,2),\" A/m**2\"\n",
"\n",
"#Slight variation due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.16 , Page Number 73"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hall coefficient is 0.00027 m**3/C.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"p = 9.0 * 10**-3 #Resistivity (in ohm-meter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"u = 0.03 #Mobility of carrier ion (in meter-square per volt-second)\n",
"\n",
"\n",
"#Calculation\n",
"\n",
"sig = 1/p #Conductivity (in per ohm-meter)\n",
"RH = u / sig #Hall coefficient (in cubic-meter per Coulomb) \n",
"\n",
"#Result\n",
"\n",
"print \"Hall coefficient is \",RH,\" m**3/C.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.17 , Page Number 73"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Hall coefficient is 0.0003049 m**3/C.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"p = 9.0 * 10**3 #Resistivity (in ohm-meter)\n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"n = 2.05 * 10**22 #Charge carrier density (in per cubic-meter) \n",
"\n",
"#Calculation\n",
"\n",
"RH = 1/(n * e) #Hall coefficient (in cubic-meter per Coulomb) \n",
"\n",
"#Result\n",
"\n",
"print \"Hall coefficient is \",round(RH,7),\" m**3/C.\"\n",
"\n",
"#Slight variation due to higher precision."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.18 , Page Number 73"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hall voltage is 76.0 mV.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"Ex = 5.0 * 10**2 #Applied Electric field (in volt per meter)\n",
"ue = 3800.0 * 10**-4 #Mobility of electron (in meter-square per volt-second) \n",
"Bz = 0.1 #Magnetic flux density (in Weber per meter-square) \n",
"d = 4.0 * 10**-3 #width (in meter) \n",
"\n",
"#Calculation\n",
"\n",
"v = ue * Ex #Drift velocity (in meter per second)\n",
"VH = Bz * v * d #Hall voltage (in volts) \n",
"\n",
"#Result\n",
"\n",
"print \"Hall voltage is \",VH * 10**3,\" mV.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.19 , Page Number 74"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mobility of holes is 0.075 m**2/V-s.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"p = 200.0 * 10 #Bar resistivity (in ohm-meter) \n",
"VH = 50.0 * 10**-3 #Hall voltage (in volts)\n",
"BZ = 0.1 #Magnetic flux density (in Weber per meter-square) \n",
"w = 3.0 * 10**-3 #width (in meter)\n",
"d = w #length (in meter)\n",
"I = 10.0 * 10**-6 #Current (in Ampere)\n",
"\n",
"#Calculation\n",
"\n",
"RH = VH * w / (BZ * I) #Hall coefficient (in cubic-meter per Coulomb)\n",
"uh = RH / p #Mobility of holes (in meter-square per volt-second) \n",
"\n",
"#Result\n",
"\n",
"print \"Mobility of holes is \",uh,\" m**2/V-s.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.20 , Page Number 74"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hall voltage is 3.0 mV.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ND = 1.0 * 10**21 #Concentration of donor atoms (in per cubic-meter)\n",
"BZ = 0.2 #Magnetic field density (in Tesla)\n",
"J = 600.0 #Current density (in Ampere per meter-square)\n",
"n = ND #Concentration of electrons (in per cubic-meter)\n",
"d = 4.0 * 10**-3 #Length (in meter) \n",
"e = 1.6 * 10**-19 #Charge on electron (in Coulomb)\n",
"\n",
"#Calculation\n",
"\n",
"VH = BZ * J * d / (n * e) #Hall voltage (in volts) \n",
"\n",
"#Result\n",
"\n",
"print \"Hall voltage is \",VH * 10**3,\" mV.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.21 , Page Number 82 "
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"New position of Fermi level is 0.328 eV\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"T = 300.0 #Temperature (in kelvin)\n",
"Ec_Ef = 0.3 #Energy level (in electron-volt) \n",
"T1 = 273 + 55 #New temperature (in kelvin)\n",
"\n",
"#Calculation\n",
"\n",
"logencbyND = Ec_Ef/T #Value of loge(nc / ND)\n",
"Ec_Ef1 = T1 * logencbyND #New position of Fermi level (in electron-volt) \n",
"\n",
"#Result\n",
"\n",
"print \"New position of Fermi level is \",Ec_Ef1,\" eV\"\n",
"\n",
"#Unit in the book should be eV instead of V."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.22 , Page Number 83"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Potential barrier is 0.19 eV.\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variables\n",
"\n",
"ND = NA = 8.0 * 10**14 #Concentration (in per cubic-meter)\n",
"ni = 2.0 * 10**13 #Intrinsic concentration (in per cubic-meter)\n",
"k = 8.61 * 10**-5 #Boltzmann constant (in electron-volt per kelvin)\n",
"T = 300.0 #Temperature (in kelvin)\n",
"\n",
"#Calculation\n",
"\n",
"Vo = k * T * math.log(ND * NA/ni**2)\n",
"\n",
"#Result\n",
"\n",
"print \"Potential barrier is \",round(Vo,2),\" eV.\"\n",
"\n",
"#Unit in the book should be eV instead of V."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.23 , Page Number 83"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R1 is 250.0 ohm.\n",
"R2 is 40.0 ohm.\n",
"R3 is 10.0 Mega-ohm.\n"
]
}
],
"source": [
"#Variables\n",
"\n",
"ID1 = 2.0 * 10**-3 #Diode current1 (in Ampere)\n",
"VD1 = 0.5 #Diode voltage1 (in volts)\n",
"ID2 = 20.0 * 10**-3 #Diode current2 (in Ampere)\n",
"VD2 = 0.8 #Diode voltage2 (in volts)\n",
"ID3 = -1.0 * 10**-6 #Diode current3 (in Ampere)\n",
"VD3 = -10.0 #Diode voltage3 (in volts)\n",
"\n",
"#Calculation\n",
"\n",
"R1 = VD1 / ID1 #Resistance1 (in ohm)\n",
"R2 = VD2 / ID2 #Resistance2 (in ohm)\n",
"R3 = VD3 / ID3 #Resistance3 (in ohm)\n",
"\n",
"#Result\n",
"\n",
"print \"R1 is \",R1,\" ohm.\\nR2 is \",R2,\" ohm.\\nR3 is \",R3 * 10**-6,\" Mega-ohm.\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.24 , Page Number 83"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fraction of the total number of electrons in the conduction band at 300 K is 8.85 e-7 .\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variables\n",
"\n",
"k = 8.61 * 10**-5 #Boltzmann constant (in electron-volt per kelvin)\n",
"T = 300.0 #Temperature (in kelvin)\n",
"EG = 0.72 #Energy band gap (in electron-volt) \n",
"\n",
"#Calculation\n",
"\n",
"EF = 1.0/2 * EG #Fermi level (in electron-volt)\n",
"ncbyn = 1/(1 + math.exp((EG-EF)/(k*T))) #Ratio\n",
"\n",
"#Result\n",
"\n",
"print \"Fraction of the total number of electrons in the conduction band at 300 K is \",round(ncbyn*pow(10,7),2),\"e-7 .\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.25 , Page Number 83"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Since electron concentration 5.32 e+16 is more than hole concentration 1.33 e+16 .Therefore , Si is of n-type.\n"
]
}
],
"source": [
"import math\n",
"\n",
"#Variables\n",
"\n",
"Ao = 4.83 * 10**21 #Constant\n",
"T = 300.0 #Temperature (in kelvin)\n",
"EG = 1.1 #Energy level (in electron-volt)\n",
"kT = 0.026 #Product of k and T (in electron-volt)\n",
"ND = 5.0 * 10**15 #Donor concentration (in per cubic-meter) \n",
"NA = 2.0 * 10**16 #Acceptor concentration (in per cubic-meter) \n",
"\n",
"#Calculation\n",
"\n",
"ni = Ao * T**1.5 * math.exp(-EG/(2*kT)) #Intrinsic concentration (in per cubic-meter)\n",
"h = ni**2 / NA #Hole concentration (in per cubic-meter)\n",
"n = ni**2 / ND #Electron concentration (in per cubic-meter)\n",
"\n",
"#Result\n",
"\n",
"print \"Since electron concentration\",round(n*10**-16,2),\"e+16 is more than hole concentration \",round(h*10**-16,2),\"e+16 .Therefore , Si is of n-type.\"\n",
"\n",
"#Slight variations due to higher precision."
]
}
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