From 4a1f703f1c1808d390ebf80e80659fe161f69fab Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb | 774 ++++++++++++++++++++++ 1 file changed, 774 insertions(+) create mode 100644 APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb (limited to 'APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb') diff --git a/APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb b/APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb new file mode 100644 index 00000000..ad04957e --- /dev/null +++ b/APPLIED_PHYSICS_by_M,_ARUMUGAM/Chapter_6a_1.ipynb @@ -0,0 +1,774 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#6(A): Semiconductors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.1, Page number 6.21" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "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 6.2, Page number 6.22" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "intrinsic conductivity is 1.434 *10**4 ohm-1 m-1\n", + "intrinsic resistivity is 0.697 *10**-4 ohm m\n", + "answer varies due to rounding off errors\n", + "number of germanium atoms per m**3 is 4.5 *10**28\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", + "sigmab=ni*e*(mew_e+mew_h); #intrinsic conductivity(ohm-1 m-1)\n", + "rhob=1/sigmab; #resistivity(ohm m)\n", + "n=Na*d/w; #number of germanium atoms per m**3\n", + "p=n/10**5; #boron density\n", + "sigma=p*e*mew_h;\n", + "rho=1/sigma;\n", + "\n", + "#Result\n", + "print \"intrinsic conductivity is\",round(sigma/10**4,3),\"*10**4 ohm-1 m-1\"\n", + "print \"intrinsic resistivity is\",round(rho*10**4,3),\"*10**-4 ohm m\"\n", + "print \"answer varies due to rounding off errors\"\n", + "print \"number of germanium atoms per m**3 is\",round(n/10**28,1),\"*10**28\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.3, Page number 6.23" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "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 6.4, Page number 6.24" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "intrinsic conductivity is 0.432 *10**-3 ohm-1 m-1 10.4\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\",sigma2\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 6.5, Page number 6.24" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "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\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.6, Page number 6.25" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)Concentration in N-type\n", + "n = 1.442 *10**24 m**-3\n", + "Hence p = 1.56 *10**8 m**-3\n", + "b)Concentration in P-type\n", + "p = 3.75 *10**24 m**-3\n", + "Hence n = 0.6 *10**8 m**-3\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "ni=1.5*10**16\n", + "mu_n=1300*10**-4\n", + "mu_p=500*10**-4\n", + "e=1.6*10**-19\n", + "sigma=3*10**4\n", + "\n", + "#Calculations\n", + "#Concentration in N-type\n", + "n1=sigma/(e*mu_n)\n", + "p1=ni**2/n1\n", + "#Concentration in P-type\n", + "p=sigma/(e*mu_p)\n", + "n2=(ni**2)/p\n", + "\n", + "#Result\n", + "print\"a)Concentration in N-type\"\n", + "print\"n =\",round(n1*10**-24,3),\"*10**24 m**-3\"\n", + "print\"Hence p =\",round(p1/10**8,2),\"*10**8 m**-3\"\n", + "print\"b)Concentration in P-type\"\n", + "print\"p =\",round(p/10**24,2),\"*10**24 m**-3\"\n", + "print\"Hence n =\",round(n2/10**8,1),\"*10**8 m**-3\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.7, Page number 6.26" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jx = 1000.0 ampere/m**2\n", + "Ey = 0.183 V/m\n", + "Vy = 1.83 mV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "i=10**-2\n", + "A=0.01*0.001\n", + "RH=3.66*10**-4\n", + "Bz=0.5\n", + "\n", + "#Calculations\n", + "Jx=i/A\n", + "Ey=RH*(Bz*Jx)\n", + "Vy=Ey*0.01\n", + "\n", + "#Result\n", + "print\"Jx =\",Jx,\"ampere/m**2\"\n", + "print\"Ey =\",round(Ey,3),\"V/m\"\n", + "print\"Vy =\",round(Vy*10**3,2),\"mV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.8, Page number 6.26" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position of fermi level = 0.5764 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Ev=0\n", + "Ec=1.12\n", + "k=1.38*10**-23\n", + "T=300\n", + "mh=0.28\n", + "mc=0.12\n", + "e=1.6*10**-19\n", + "#Calculations\n", + "Ef=((Ec+Ev)/2)+((3*k*T)/(4*e))*math.log(mh/mc)\n", + "\n", + "#Result\n", + "print\"Position of fermi level =\",round(Ef,4),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.9, Page number 6.26" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conductivity of intrinsic germanium at 300K = 2.24 ohm**-1 m**-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "ni=2.5*10**19\n", + "mu_e=0.38\n", + "mu_h=0.18\n", + "e=1.6*10**-19\n", + "\n", + "#Calculations\n", + "sigmai=ni*e*(mu_e+mu_h)\n", + "\n", + "#Result\n", + "print\"Conductivity of intrinsic germanium at 300K =\",round(sigmai,2),\"ohm**-1 m**-1\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.10, Page number 6.27" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conductivity = 1.1593 *10**-3 ohm**-1 m**-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "m=9.1*10**-31\n", + "k=1.38*10**-23\n", + "T=300\n", + "h=6.626*10**-34\n", + "Eg=1.1\n", + "e=1.6*10**-19\n", + "mu_e=0.48\n", + "mu_h=0.013\n", + "#Calculations\n", + "ni=2*((2*math.pi*m*k*T)/h**2)**(3/2)*math.exp(-(Eg*e)/(2*k*T))\n", + "sigma=ni*e*(mu_e+mu_h)\n", + " \n", + "#Result\n", + "print\"Conductivity =\",round(sigma*10**3,4),\"*10**-3 ohm**-1 m**-1\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.11, Page number 6.27" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p = 2.0 *10**23 m**-3\n", + "The electron concentration is given by n = 2.0 *10**9 m**-3\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Na=5*10**23\n", + "Nd=3*10**23\n", + "ni=2*10**16\n", + "#Calculations\n", + "p=((Na-Nd)+(Na-Nd))/2\n", + "\n", + "#Result\n", + "print\"p =\",p*10**-23,\"*10**23 m**-3\"\n", + "print\"The electron concentration is given by n =\",ni**2/p*10**-9,\"*10**9 m**-3\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.12, Page number 6.28" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rh = 3.7 *10**-6 C**-1 m**3\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Vh=37*10**-6\n", + "thick=1*10**-3\n", + "width=5\n", + "Iy=20*10**-3\n", + "Bz=0.5\n", + "\n", + "#Calculations\n", + "Rh=(Vh*width*thick)/(width*Iy*Bz)\n", + "\n", + "#Result\n", + "print\"Rh =\",round(Rh*10**6,1),\"*10**-6 C**-1 m**3\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.13, Page number 6.28" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Dn = 33.54 cm**2 s**-1\n", + "Dp = 12.9 cm**2 s**-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Vt=0.0258\n", + "mu_n=1300\n", + "mu_p=500\n", + "\n", + "#Calculations\n", + "Dn=Vt*mu_n\n", + "Dp=Vt*mu_p\n", + "\n", + "#Result\n", + "print\"Dn =\",Dn,\"cm**2 s**-1\"\n", + "print\"Dp =\",Dp,\"cm**2 s**-1\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.14, Page number 6.29" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The hole concentration 'p' = 1.125 *10**13 /m**3\n", + "'n'= Nd = 2.0 *10**19\n", + "Electrical Conductivity = 0.384 ohm**-1 m**-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "ni=1.5*10**16\n", + "Nd=2*10**19\n", + "e=1.602*100**-19\n", + "mu_n=0.12\n", + "\n", + "#Calculations\n", + "p=ni**2/Nd\n", + "E_c=e*Nd*mu_n\n", + "\n", + "#Result\n", + "print\"The hole concentration 'p' =\",round(p*10**-13,3),\"*10**13 /m**3\"\n", + "print\"'n'= Nd =\",round(Nd*10**-19),\"*10**19\"\n", + "print\"Electrical Conductivity =\",round(E_c*10**19,3),\"ohm**-1 m**-1\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.15, Page number 6.29" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mu_p= 1389.0 cm**2/V-s\n", + "n= 6.0355 *10**13/cm**3\n", + "p= 1.0355 *10**13/cm**3\n", + "J= 582.5 A/m**2\n", + "#Answer varies due to rounding of numbers\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N=1/60\n", + "e=1.6*10**-19\n", + "ni=2.5*10**13\n", + "b=5*10**13\n", + "E=2\n", + "\n", + "#Calculations\n", + "n=(b+math.sqrt(2*b**2))/2\n", + "mu_p=N/(3*e*ni)\n", + "mu_i=2*mu_p\n", + "np=ni**2\n", + "p=(ni**2)/n\n", + "e=1.6*10**-19\n", + "E=2\n", + "J=(e*E)*((n*mu_i)+(p*mu_p))\n", + "#Result\n", + "print\"mu_p=\",round(mu_p),\"cm**2/V-s\"\n", + "print\"n=\",round(n/10**13,4),\"*10**13/cm**3\"\n", + "print\"p=\",round(p*10**-13,4),\"*10**13/cm**3\"\n", + "print\"J=\",round(J*10**4,1),\"A/m**2\"\n", + "print\"#Answer varies due to rounding of numbers\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 6.16, Page number 6.30" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ni = 2.293 *10**19 /m**3\n", + "Drift velocity of holes 1900.0 ms**-1\n", + "Drift velocity of electrons= 3900.0 ms**-1\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "rho=47*10**-2\n", + "e=1.6*10**-19\n", + "mu_n=0.39\n", + "mu_p=0.19\n", + "E=10**4\n", + "\n", + "#Calculations\n", + "ni=1/(rho*e*(mu_n+mu_p))\n", + "Dh=mu_p*E\n", + "De=mu_n*E\n", + "\n", + "#Results\n", + "print\"ni =\",round(ni/10**19,3),\"*10**19 /m**3\"\n", + "print\"Drift velocity of holes\",Dh,\"ms**-1\"\n", + "print\"Drift velocity of electrons=\",De,\"ms**-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": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- cgit