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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 8: Semiconductor Physics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 1, Page number 8.19"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of electron hole pairs is 2.32 *10**16 per cubic metre\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",
"ni1=2.5*10**19; #number of electron hole pairs\n",
"T1=300; #temperature(K)\n",
"Eg1=0.72*1.6*10**-19; #energy gap(J)\n",
"k=1.38*10**-23; #boltzmann constant\n",
"T2=310; #temperature(K)\n",
"Eg2=1.12*1.6*10**-19; #energy gap(J)\n",
"\n",
"#Calculation\n",
"x1=-Eg1/(2*k*T1);\n",
"y1=(T1**(3/2))*math.exp(x1);\n",
"x2=-Eg2/(2*k*T2);\n",
"y2=(T2**(3/2))*math.exp(x2);\n",
"ni=ni1*(y2/y1); #number of electron hole pairs\n",
"\n",
"#Result\n",
"print \"number of electron hole pairs is\",round(ni/10**16,2),\"*10**16 per cubic metre\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 2, Page number 8.20"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"intrinsic conductivity is 2.016 ohm-1 metre-1\n",
"intrinsic resistivity is 0.496 ohm metre\n",
"number of germanium atoms per m**3 is 4.5 *10**28\n",
"new value of conductivity is 1.434 *10**4 ohm-1 metre-1\n",
"new value of resistivity is 0.697 *10**-4 ohm metre\n",
"answer for new values given in the book varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"w=72.6; #atomic weight\n",
"d=5400; #density(kg/m**3)\n",
"Na=6.025*10**26; #avagadro number\n",
"mew_e=0.4; #mobility of electron(m**2/Vs)\n",
"mew_h=0.2; #mobility of holes(m**2/Vs)\n",
"e=1.6*10**-19;\n",
"m=9.108*10**-31; #mass(kg)\n",
"ni=2.1*10**19; #number of electron hole pairs\n",
"Eg=0.7; #band gap(eV)\n",
"k=1.38*10**-23; #boltzmann constant\n",
"h=6.625*10**-34; #plancks constant\n",
"T=300; #temperature(K)\n",
"\n",
"#Calculation\n",
"sigma=ni*e*(mew_e+mew_h); #intrinsic conductivity(ohm-1 m-1)\n",
"rho=1/sigma; #resistivity(ohm m)\n",
"n=Na*d/w; #number of germanium atoms per m**3\n",
"p=n/10**5; #boron density\n",
"sigman=p*e*mew_h; #new value of conductivity(ohm-1 metre-1)\n",
"rhon=1/sigman; #new value of resistivity(ohm metre)\n",
"\n",
"#Result\n",
"print \"intrinsic conductivity is\",sigma,\"ohm-1 metre-1\"\n",
"print \"intrinsic resistivity is\",round(rho,3),\"ohm metre\"\n",
"print \"number of germanium atoms per m**3 is\",round(n/10**28,1),\"*10**28\"\n",
"print \"new value of conductivity is\",round(sigman/10**4,3),\"*10**4 ohm-1 metre-1\"\n",
"print \"new value of resistivity is\",round(rhon*10**4,3),\"*10**-4 ohm metre\"\n",
"print \"answer for new values given in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 3, Page number 8.21"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"charge carrier density is 2 *10**22 per m**3\n",
"electron mobility is 0.035 m**2/Vs\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=1.6*10**-19;\n",
"RH=3.66*10**-4; #hall coefficient(m**3/coulomb)\n",
"sigma=112; #conductivity(ohm-1 m-1)\n",
"\n",
"#Calculation\n",
"ne=3*math.pi/(8*RH*e); #charge carrier density(per m**3)\n",
"mew_e=sigma/(e*ne); #electron mobility(m**2/Vs)\n",
"\n",
"#Result\n",
"print \"charge carrier density is\",int(ne/10**22),\"*10**22 per m**3\"\n",
"print \"electron mobility is\",round(mew_e,3),\"m**2/Vs\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 4, Page number 8.21"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"intrinsic conductivity is 0.432 *10**-3 ohm-1 m-1\n",
"conductivity during donor impurity is 10.4 ohm-1 m-1\n",
"conductivity during acceptor impurity is 4 ohm-1 m-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"mew_e=0.13; #mobility of electron(m**2/Vs)\n",
"mew_h=0.05; #mobility of holes(m**2/Vs)\n",
"e=1.6*10**-19;\n",
"ni=1.5*10**16; #number of electron hole pairs\n",
"N=5*10**28;\n",
"\n",
"#Calculation\n",
"sigma1=ni*e*(mew_e+mew_h); #intrinsic conductivity(ohm-1 m-1)\n",
"ND=N/10**8;\n",
"n=ni**2/ND;\n",
"sigma2=ND*e*mew_e; #conductivity(ohm-1 m-1)\n",
"sigma3=ND*e*mew_h; #conductivity(ohm-1 m-1)\n",
"\n",
"#Result\n",
"print \"intrinsic conductivity is\",round(sigma1*10**3,3),\"*10**-3 ohm-1 m-1\"\n",
"print \"conductivity during donor impurity is\",sigma2,\"ohm-1 m-1\"\n",
"print \"conductivity during acceptor impurity is\",int(sigma3),\"ohm-1 m-1\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 5, Page number 8.22"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conductivity is 4.97 mho m-1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=1.6*10**-19;\n",
"Eg=0.72; #band gap(eV)\n",
"k=1.38*10**-23; #boltzmann constant\n",
"T1=293; #temperature(K)\n",
"T2=313; #temperature(K)\n",
"sigma1=2; #conductivity(mho m-1)\n",
"\n",
"#Calculation\n",
"x=(Eg*e/(2*k))*((1/T1)-(1/T2));\n",
"y=round(x/2.303,3);\n",
"z=round(math.log10(sigma1),3);\n",
"log_sigma2=y+z;\n",
"sigma2=10**log_sigma2; #conductivity(mho m-1)\n",
"\n",
"#Result\n",
"print \"conductivity is\",round(sigma2,2),\"mho m-1\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
