{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#10: Intrinsic Semiconductors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.1, Page number 277"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The intrinsic carrier concentration at room temperature is 1.3889 *10**16 m^-3\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"ec=4*10**-4; #electrical conductivity of intrinsic silicon at room temperature(ohm^-1 m^-1)\n",
"me=0.14; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.04; #The hole mobility(m^2 V^-1 s^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"ni=ec/(e*(me+mh)); #The intrinsic carrier concentration at room temperature(m^-3)\n",
"\n",
"#Result\n",
"print \"The intrinsic carrier concentration at room temperature is\",round(ni/10**16,4),\"*10**16 m^-3\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.2, Page number 277"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The resistivity of intrinsic carrier is 0.4709 ohm m\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=2.37*10**19; #The intrinsic carrier density at room temperature(m^-3)\n",
"me=0.38; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.18; #The hole mobility(m^2 V^-1 s^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"r=1/(d*e*(me+mh)); #The resistivity of intrinsic carrier(ohm m)\n",
"\n",
"#Result\n",
"print \"The resistivity of intrinsic carrier is\",round(r,4),\"ohm m\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.3, Page number 277"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The intrinsic carrier density at room tepmerature is 5.04 *10**21 m^-3\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"r=2*10**-4; #the resistivity of In-Sb(ohm m)\n",
"me=6; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.2; #The hole mobility(m^2 V^-1 s^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"d=1/(r*e*(me+mh)); #The intrinsic carrier density at room tepmerature(m^-3)\n",
"\n",
"#Result\n",
"print \"The intrinsic carrier density at room tepmerature is\",round(d/10**21,2),\"*10**21 m^-3\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.4, Page number 278"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The electrical conductivity at room temperature is 1.4374 *10**-3 ohm^-1 m^-1\n",
"answer given in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=1.1*1.6*10**-19; #The energy gap of silicon(J)\n",
"me=0.48; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.13; #The hole mobility(m^2 V^-1 s^-1)\n",
"h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.11*10**-31; #mass of an electron\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"t=300; #temperature(K)\n",
"\n",
"#Calculation\n",
"ni=2*(2*math.pi*m*kb*t/h**2)**(3/2)*math.exp(-Eg/(2*kb*t)); #intrinsic carrier concentration(m^-3)\n",
"ec=ni*e*(me+mh); #The electrical conductivity at room temperature(ohm^-1 m^-1 *10^-3)\n",
"\n",
"#Result\n",
"print \"The electrical conductivity at room temperature is\",round(ec*10**3,4),\"*10**-3 ohm^-1 m^-1\"\n",
"print \"answer given in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.5, Page number 279"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The intrinsic carrier concentration is 1.983 *10**12 m^-3\n",
"The electrical conductivity at room temperature is 2.8239 *10**-7 ohm^-1 m^-1\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=1.43*1.6*10**-19; #The energy gap of intrinsic GaAs(J)\n",
"xe=0.85; #The electron mobility(m^2 V^-1 s^-1)\n",
"xh=0.04; #The hole mobility(m^2 V^-1 s^-1)\n",
"me=0.068*9.11*10**-31; #effective mass of electron(m)\n",
"mh=0.5*9.11*10**-31; #effective mass of hole(m)\n",
"h=6.625*10**-34; #Planck's constant(m^2 Kg/sec)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.11*10**-31; #mass of an electron(kg)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"t=300; #temperature(K)\n",
"\n",
"#Calculation\n",
"ni=2*(2*math.pi*kb*t/h**2)**(3/2)*(me*mh)**(3/4)*math.exp(-Eg/(2*kb*t)); #intrinsic carrier concentration(m^-3)\n",
"ec=ni*e*(xe+xh); #The electrical conductivity at room temperature(ohm^-1 m^-1)\n",
"\n",
"#Result\n",
"print \"The intrinsic carrier concentration is\",round(ni/10**12,3),\"*10**12 m^-3\"\n",
"print \"The electrical conductivity at room temperature is\",round(ec*10**7,4),\"*10**-7 ohm^-1 m^-1\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.6, Page number 279"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The position of the fermi level is 9.223086 *10**-20 J or 0.5764 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=1.12*1.6*10**-19; #Energy gap of Si semi conductor(J)\n",
"me=0.12*9.11*10**-31; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.28*9.11*10**-31; #The hole mobility(m^2 V^-1 s^-1)\n",
"t=300; #temperature of fermi level(K)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"m=9.11*10**-31; #mass of an electron(Kg)\n",
"\n",
"#Calculation\n",
"Ef=(Eg/2)+((3*kb*t/4)*math.log(mh/me)); #position of the fermi level(J)\n",
"\n",
"#Result\n",
"print \"The position of the fermi level is\",round(Ef*10**20,6),\"*10**-20 J or\",round(Ef/(1.6*10**-19),4),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.7, Page number 280"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Temperature of the fermi level shifted by 10% is 1115.127 K\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=1*1.6*10**-19; #Energy gap(J)\n",
"E=0.1*1.6*10**-19; #Fermi level is shifted by 10%(J)\n",
"me=1*9.11*10**-31; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=4*9.11*10**-31; #Effective mass of holes is 4 times that of electrons(m^2 V^-1 s^-1)\n",
"m=9.11*10**-31; #mass of an electron(kg)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"\n",
"#Calculation\n",
"T=4*E/(3*kb*math.log(4)); #The Temperature of the fermi level shifted by 10%(K)\n",
"\n",
"#Result\n",
"print \"The Temperature of the fermi level shifted by 10% is\",round(T,3),\"K\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.8, Page number 281"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The resistance of an intrinsic Ge rod is 4310 ohm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"l=1*10**-2; #length of the intrinsic Ge rod(m)\n",
"b=1*10**-3; #breadth of the intrinsic Ge rod(m)\n",
"t=1*10**-3; #thickness of the intrinsic Ge rod(m)\n",
"T=300; #temperature of the intrinsic Ge rod(K)\n",
"me=0.39; #The electron mobility(m^2 V^-1 s^-1)\n",
"mh=0.19; #The hole mobility(m^2 V^-1 s^-1)\n",
"ni=2.5*10**19; #intrinsic carrier conduction(m^3)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"\n",
"#Calculation\n",
"ec=ni*e*(me+mh); #The electrical conductivity at room temperature(ohm^-1 m^-1)\n",
"A=b*t; #area(m^2)\n",
"R=l/(ec*A); #The resistance of an intrinsic Ge rod(ohm)\n",
"\n",
"#Result\n",
"print \"The resistance of an intrinsic Ge rod is\",int(R),\"ohm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.9, Page number 281"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The ratio of conductiveness is 1.08 *10**5\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=1.2*1.6*10**-19; #The energy gap of intrinsic semiconductor(J)\n",
"T1=600; #Temperature(K)\n",
"T2=300; #Temperature(K)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"\n",
"#Calculation\n",
"x=math.exp((-Eg/(2*kb))*((1/T1)-(1/T2))); #The ratio of conductiveness\n",
"\n",
"#Result\n",
"print \"The ratio of conductiveness is\",round(x/10**5,2),\"*10**5\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.10, Page number 282"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The conductivity of Ge at T2 is 4.969895 ohm^-1 m^-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg=0.72*1.6*10**-19; #The band gap of Ge(J)\n",
"T1=293; #Temperature(K)\n",
"T2=313; #Temperature(K)\n",
"x1=2; #The conductivity of Ge at T1(ohm^-1 m^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"\n",
"#Calculation\n",
"x2=x1*math.exp((Eg/(2*kb))*((1/T1)-(1/T2))); #The ratio of conductiveness\n",
"\n",
"#Result\n",
"print \"The conductivity of Ge at T2 is\",round(x2,6),\"ohm^-1 m^-1\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.11, Page number 282"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The intrinsic carrier density of A to B is 1015\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Eg1=0.36; #The energy gap of intrinsic semiconductor A(eV)\n",
"Eg2=0.72; #The energy gap of intrinsic semiconductor B(eV)\n",
"T1=300; #Temperature of semiconductor A(K)\n",
"T2=300; #Temperature of semiconductor B(K)\n",
"m=9.11*10**-31; #mass of an electron(kg)\n",
"KT=0.026; #kt(eV)\n",
"\n",
"#Calculation\n",
"x=math.exp((Eg2-Eg1)/(2*KT)); #The intrinsic carrier density of A to B\n",
"\n",
"#Result\n",
"print \"The intrinsic carrier density of A to B is\",int(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.12, Page number 283"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The band gap of semiconductor is 5.5863 *10**-20 J or 0.349 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"T1=293; #Temperature(K)\n",
"T2=373; #Temperature(K)\n",
"x1=250; #The conductivity of semiconductor at T1(ohm^-1 m^-1)\n",
"x2=1100; #The conductivity of semiconductor at T2(ohm^-1 m^-1)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"\n",
"#Calculation\n",
"Eg=2*kb*math.log(x2/x1)*(T1*T2/(T2-T1)); #The band gap of semiconductor(J)\n",
"\n",
"#Result\n",
"print \"The band gap of semiconductor is\",round(Eg*10**20,4),\"*10**-20 J or\",round(Eg/(1.6*10**-19),3),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.13, Page number 284"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mobility of pure semi conductor is 0.08283 m^2 V^-1 s^-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"me=50; #The electron mobility of pure semi conductor(m^2 V^-1 s^-1)\n",
"t1=4.2; #temperature of pure semi conductor(K)\n",
"t2=300; #temperature(K)\n",
"\n",
"#Calculation\n",
"m=me*((t2**(-3/2))/(t1**(-3/2))); #mobility of pure semi conductor(m^2 V^-1 s^-1)\n",
"\n",
"#Result\n",
"print \"mobility of pure semi conductor is\",round(m,5),\"m^2 V^-1 s^-1\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 10.14, Page number 284"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The band gap of an intrinsic semi conductor is 1.183808 *10**-19 J or 0.7399 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"ec1=19.96; #The electrical conductivity of an intrinsic semi conductor(ohm^-1 m^-1)\n",
"ec2=79.44; #The increasing electrical conductivity of an intrinsic semi conductor(ohm^-1 m^-1)\n",
"t1=333; #temperature of an intrinsic semi conductor(K)\n",
"t2=373; #increasing temperature of an intrinsic semi conductor(K)\n",
"kb=1.38*10**-23; #Boltzmann's constant(m^2 Kg s^-2 k^-1)\n",
"\n",
"#Calculation\n",
"Eg=2*kb*math.log(ec2/ec1)*((t1*t2)/(t2-t1)); #The band gap of an intrinsic semi conductor(J)\n",
"\n",
"#Result\n",
"print \"The band gap of an intrinsic semi conductor is\",round(Eg*10**19,6),\"*10**-19 J or\",round(Eg/(1.6*10**-19),4),\"eV\""
]
}
],
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