{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter2 : Energy Bands and Charge Carriers in semiconductor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.1 Page No.58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability when the energy of the state is above 0.1 eV 0.02\n",
      "Probability when the energy of the state is below 0.1 eV 0.98\n"
     ]
    }
   ],
   "source": [
    "#Example 2.1\n",
    "#Find probability of an electronic state\n",
    "\n",
    "#Given\n",
    "dE1=0.1             #eV\n",
    "dE2=-0.1           #eV\n",
    "k=8.61*10**-5     #Boltzman constant\n",
    "T=300             #K\n",
    "\n",
    "#Calcualtion\n",
    "import math\n",
    "FE1=1/(1+math.exp(dE1/(k*T)))\n",
    "FE2=1/(1+math.exp(dE2/(k*T)))\n",
    "\n",
    "#Result\n",
    "print\"Probability when the energy of the state is above 0.1 eV\",round(FE1,2)\n",
    "print\"Probability when the energy of the state is below 0.1 eV\",round(FE2,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.2 Page No. 58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Temprature is 758.3 K\n"
     ]
    }
   ],
   "source": [
    "#Calculate the temprature at which there is 1 percent probability\n",
    "#that a state of 0.30 eV below the fermi energy level will not contain electrons.\n",
    "import math\n",
    "#Exa 2.2\n",
    "Ef=6.25         #EV  fermi energy level\n",
    "dE=-0.30        #eV\n",
    "k=8.61*10**-5    #Boltzman constant\n",
    "fE=0.99\n",
    "\n",
    "#calculation\n",
    "#From the probability formula fE=1/(1+math.exp(dE/(k*T)))\n",
    "T=(dE)/(k*math.log(1/fE-1))\n",
    "\n",
    "#result\n",
    "print\"The Temprature is\",round(T,1),\"K\" "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.3 Page No. 64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the fraction of total no. of electron is  8.85e-07\n"
     ]
    }
   ],
   "source": [
    "#Example 2.3\n",
    "#Determine the fraction of total no. of electron\n",
    "\n",
    "#Given\n",
    "Eg=0.72            #eV\n",
    "Ef=0.5*Eg\n",
    "dE=Eg-Ef           #eV\n",
    "k=8.61*10**-5     #Boltzman constant\n",
    "T=300             #K\n",
    "\n",
    "#Calcualtion\n",
    "import math\n",
    "N=1/(1+math.exp(dE/(k*T)))\n",
    "\n",
    "\n",
    "#Result\n",
    "print\"the fraction of total no. of electron is \",round(N,9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.4 Page No. 64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The wavwlength is 1.416 A\n"
     ]
    }
   ],
   "source": [
    "#Example 2.4\n",
    "#Calculate the wave length\n",
    "import math\n",
    "#Given\n",
    "E=300*1.602*10**-19            #eV Energy\n",
    "m=9.108*10**-31                #kg, mass of electron\n",
    "h=6.626*10**-34                #Planck constant\n",
    "\n",
    "#Calculation\n",
    "v=math.sqrt(2*E/m)\n",
    "lam=h*v/E\n",
    "\n",
    "#Result\n",
    "print\"The wavwlength is\",round(lam*10**10,3),\"A\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.5 Page No. 70"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ratio of electron to hole concentration :  1e+12\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.5\n",
    "#Find the ratio of electron to hole concentration ratio\n",
    "\n",
    "#given data\n",
    "ni=1.4*10**18\t\t\t#in atoms/m**3\n",
    "Nd=1.4*10**24\t\t\t#in atoms/m**3\n",
    "n=Nd\t\t\t\t#in atoms/m**3\n",
    "\n",
    "#Calculation\n",
    "p=ni**2/n\t\t\t#in atoms/m**3\n",
    "ratio=n/p\t\t\t#unitless\n",
    "\n",
    "#Result\n",
    "print\"Ratio of electron to hole concentration : \",round(ratio,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.7 Page no 74"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The magnitude of current is 0.24 A\n"
     ]
    }
   ],
   "source": [
    "#Example 2.7\n",
    "#Calculate the magnitude of current\n",
    "\n",
    "#Given\n",
    "n=10**24          #Electron density\n",
    "e=1.6*10**-19     #Electron charge\n",
    "v=0.015           #m/s drift velocity\n",
    "A=10**-4            #m**2 area\n",
    "\n",
    "#Calculation\n",
    "I=n*e*v/A\n",
    "\n",
    "#Result\n",
    "print\"The magnitude of current is\",round(I/10**8,2),\"A\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.8 Page No. 74"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relaxation time in sec :  4.004e-14 s\n",
      "Resistivity of conductor in ohm-m :  1.531e-08 ohm m\n",
      "velocity of electron with fermi energy is  1390707.0 m/s\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.8\n",
    "#calculate (i) Relaxation time (ii)Resistivity of conductor (iii) velocity of electron \n",
    "\n",
    "#given data\n",
    "Ef=5.5\t\t\t#in eV\n",
    "MUe=7.04*10**-3\t\t#in m**2/V-s\n",
    "n=5.8*10**28\t\t#in m**-3\n",
    "e=1.6*10**-19\t\t#constant\n",
    "m=9.1*10**-31\t\t#in Kg\n",
    "\n",
    "#calculation\n",
    "#part (i)\n",
    "import math\n",
    "tau=MUe*m/e\t\t#in sec\n",
    "rho=1/(n*e*MUe)\t\t#in ohm-m\n",
    "vF=math.sqrt(2*Ef*1.6*10**-19/m)\n",
    "\n",
    "#Result\n",
    "print\"Relaxation time in sec : \",tau,\"s\"\n",
    "print\"Resistivity of conductor in ohm-m : \",round(rho,11),\"ohm m\"\n",
    "print\"velocity of electron with fermi energy is \",round(vF,0),\"m/s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.9 Page No. 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NO. of free electrons are 8.49e+28\n",
      "mobility of  electrons is 0.004 m**2/Vs\n"
     ]
    }
   ],
   "source": [
    "#Example 2.9\n",
    "#Find (i)the valence electrons per unit volume (ii) mobility\n",
    "\n",
    "#Given\n",
    "rho=1.73*10**-8       #resistivity\n",
    "Tav=2.42*10**-14      #Average Time\n",
    "e=1.6*10**-19\t\t#constant\n",
    "m=9.1*10**-31\t\t#in Kg\n",
    "\n",
    "#Calculation\n",
    "n=m/(e**2*Tav*rho)\n",
    "mu=(e*Tav)/m\n",
    "\n",
    "#Result\n",
    "print\"NO. of free electrons are\",round(n,-26)\n",
    "print\"mobility of  electrons is\",round(mu,3),\"m**2/Vs\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.10 page No. 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relaxation time in sec :  3.95e-14 s\n",
      "velocity of electron with fermi energy is  0.7 m/s\n"
     ]
    }
   ],
   "source": [
    "#Example 2.10\n",
    "#calculate Relaxation time and drift velocity\n",
    "\n",
    "Ef=100\t\t\t#in V/m Applied electric field\n",
    "n=6*10**28\t\t#in m**-3\n",
    "e=1.6*10**-19\t\t#constant electronic charge\n",
    "m=9.1*10**-31\t\t#in Kg  mass of electron\n",
    "rho=1.5*10**-8      #Density\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "tau=m/(n*e**2*rho)\t\t#in sec\n",
    "vF=e*Ef*tau/m\n",
    "\n",
    "#Result\n",
    "print\"Relaxation time in sec : \",round(tau,16),\"s\"\n",
    "print\"velocity of electron with fermi energy is \",round(vF,1),\"m/s\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.11 Page No.75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Charge density is 1.133e+29 m**-3\n",
      "current density is 1160000.0 A/m**2\n",
      "curret flowing is 3.644 A\n",
      "electron drift velocityis 6.4e-05 m/s\n"
     ]
    }
   ],
   "source": [
    "#Exampl 2.11\n",
    "#Determine charge density, current density ,Current flowing in the wire, Electron drift velocity\n",
    "\n",
    "#Given\n",
    "d=0.002             #m, diameter of pipe\n",
    "s=5.8*10**7         #Conductivity S/m\n",
    "mu=0.0032            #m**2/Vs, Electron mobility\n",
    "e=1.6*10**-19\t\t#constant electronic charge\n",
    "m=9.1*10**-31\t\t#in Kg  mass of electron\n",
    "E=0.02               #V/m Electric field\n",
    "\n",
    "#Calculation\n",
    "import math\n",
    "#From eq 2.62\n",
    "n=s/(e*mu)\n",
    "J=s*E\n",
    "I=J*(math.pi*d**2/4.0)\n",
    "v=mu*E\n",
    "\n",
    "#Result\n",
    "print\"Charge density is\",round(n,-26),\"m**-3\"\n",
    "print\"current density is\",round(J,6),\"A/m**2\"\n",
    "print\"curret flowing is\",round(I,3),\"A\"\n",
    "print\"electron drift velocityis\",round(v,6),\"m/s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.12 page no 76"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The drift velocity is  20.0 m/s\n",
      "Time taken by the electron is 5e-07 s\n"
     ]
    }
   ],
   "source": [
    "#example 2.12\n",
    "#calculate the drift velocity and time\n",
    "\n",
    "#Given\n",
    "rho=0.5        #ohm-m Resistivity\n",
    "J=100          #A/m**2 Current density\n",
    "mue=0.4        #m**2/Vs Electron mobility\n",
    "d=10*10**-6    #m distance\n",
    "\n",
    "#calculation\n",
    "Ve=mue*J*rho\n",
    "t=d/Ve\n",
    "\n",
    "#Result\n",
    "print\"The drift velocity is \",Ve,\"m/s\"\n",
    "print\"Time taken by the electron is\",round(t,8),\"s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.13 Page No.76"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Concentration of electron is 4.45e+16 /cm**3\n",
      "Concentration of holes is 14040000000.0 /cm**3\n"
     ]
    }
   ],
   "source": [
    "#Example 2.13\n",
    "#Calculate drift velocity and time\n",
    "\n",
    "#Given\n",
    "e=1.6*10**-19\t\t#constant electronic charge\n",
    "m=9.1*10**-31\t\t#in Kg  mass of electron\n",
    "rho=0.039             #ohm-cm resistivity\n",
    "mu=3600               #cm**2/Vs  Carrier mobility\n",
    "ni=2.5*10**13\n",
    "\n",
    "#Calculation \n",
    "Nd=(1/(rho*e*mu))\n",
    "n=Nd\n",
    "p=(ni**2/n)\n",
    "\n",
    "#Result\n",
    "print\"Concentration of electron is\",round(n,-14),\"/cm**3\"\n",
    "print\"Concentration of holes is\",round(p,0),\"/cm**3\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.14 page No 76"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Concentration of electrons is 4.41e+14 atoms/cm**3\n",
      "Concentration of holes is 1.42e+12 atoms/cm**3\n",
      "Conductivity of N-type germanium 26.8 /ohm-m\n"
     ]
    }
   ],
   "source": [
    "#Example 2.14\n",
    "#Determine concentration of holes and electrons\n",
    "\n",
    "#Given\n",
    "rho=5.32              #kg/m**3, density\n",
    "Aw=72.6               #kg/K kmol atomic weight\n",
    "ni=2.5*10**13\n",
    "di=10**8              #Donor impurity\n",
    "e=1.6*10**-19         #Electronic charge\n",
    "mue=0.38              #m**/Vs\n",
    "muh=0.18               #m**/Vs\n",
    "\n",
    "#CAlculation\n",
    "N=6.023*10**23*rho/Aw       #No 0f germanium atoms per cm**3\n",
    "Nd=N/di\n",
    "n=Nd\n",
    "p=(ni**2/n)\n",
    "s=n*e*mue*10**4\n",
    "\n",
    "#Result\n",
    "print\"Concentration of electrons is\",round(n,-12),\"atoms/cm**3\"\n",
    "print\"Concentration of holes is\",round(p,-10),\"atoms/cm**3\"\n",
    "\n",
    "if n > p:\n",
    "    \n",
    "    print\"Conductivity of N-type germanium\",round(s*100,1),\"/ohm-m\" \n",
    "else:\n",
    "    print \"Calculate p-type germanium conductivity\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.15 Page no.79"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Density of electrons is 2.29e+19 /m**3\n",
      "Drift velocity for electrons 3900.0 m/s\n",
      "Drift velocity for holes 1900.0 m/s\n"
     ]
    }
   ],
   "source": [
    "#Example 2.15\n",
    "#Calculate the density and drift velocity\n",
    "\n",
    "#Given\n",
    "e=1.6*10**-19         #Electronic charge\n",
    "mue=0.39              #m**/Vs\n",
    "muh=0.19               #m**/Vs\n",
    "rhoi=0.47              #ohm-m, intrinsic resistivity\n",
    "E=10**4                #Electric field\n",
    "\n",
    "#Calculation\n",
    "sigmai=1/rhoi\n",
    "ni=sigmai/(e*(mue+muh))\n",
    "Vn=mue*E\n",
    "Vh=muh*E\n",
    "\n",
    "#Result\n",
    "print\"Density of electrons is\",round(ni,-17),\"/m**3\"\n",
    "print\"Drift velocity for electrons\",round(Vn,0),\"m/s\"\n",
    "print\"Drift velocity for holes\",round(Vh,0),\"m/s\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.16 page No.80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intrinsic conductivity of Ge is  0.0224 ohm-cm**-1\n",
      "Conductivity of N type Ge semiconductor is 2.68 ohm-cm**-1\n"
     ]
    }
   ],
   "source": [
    "#Example 2.16\n",
    "#Calculate conductivity\n",
    "\n",
    "#Given\n",
    "i=10**7            #IMpurity in Ge atom\n",
    "ni=2.5*10**13      #/cm**3\n",
    "N=4.4*10**22       #No. of atoms of Ge\n",
    "mue=3800            #cm**2/Vs\n",
    "muh=1800            #cm**2/Vs\n",
    "e=1.6*10**-19       #Electronic charge\n",
    "E=400               #Electric field\n",
    "\n",
    "#Calculation\n",
    "sigmai=ni*e*(mue+muh)\n",
    "Nd=N/i\n",
    "n=Nd\n",
    "p=ni**2/(Nd)\n",
    "sigman=e*Nd*mue\n",
    "\n",
    "print\"Intrinsic conductivity of Ge is \",sigmai,\"ohm-cm**-1\"\n",
    "print\"Conductivity of N type Ge semiconductor is\",round(sigman,2),\"ohm-cm**-1\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.17 Page No. 80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(i)Electron drift velocity is  152.0 m/s\n",
      "   hole drift velocity is  72.0 m/s\n",
      "(ii)Intrinsic Conductivity of Ge is 2.24 ohm-m**-1\n",
      "(iii)The total current is  5.376 mA\n"
     ]
    }
   ],
   "source": [
    "#Example 2.17\n",
    "#(i)Electron drift velocity & hole drift velocity .\n",
    "#(ii)Intrinsic Conductivity of Ge,(iii)The total current .\n",
    "\n",
    "#Given\n",
    "V=10              #Volt\n",
    "l=0.025           #m, length\n",
    "w=0.004           #m width\n",
    "t=0.0015         #m thickness\n",
    "\n",
    "ni=2.5*10**19      #/cm**3\n",
    "mue=0.38               #m**2/Vs\n",
    "muh=0.18               #m**2/Vs\n",
    "e=1.6*10**-19           #Electronic charge\n",
    "E=400              #Electric field\n",
    "\n",
    "#Calculation\n",
    "E=V/l\n",
    "Ve=mue*E\n",
    "Vh=muh*E\n",
    "sigmai=ni*e*(mue+muh)\n",
    "I=sigmai*E*w*t\n",
    "\n",
    "#Result\n",
    "print\"(i)Electron drift velocity is \",Ve,\"m/s\"\n",
    "print\"   hole drift velocity is \",Vh,\"m/s\"\n",
    "print\"(ii)Intrinsic Conductivity of Ge is\",sigmai,\"ohm-m**-1\"\n",
    "print\"(iii)The total current is \",I*1000,\"mA\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.18 page no.80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ratio of electrons to holes drift velocity is  1.0\n"
     ]
    }
   ],
   "source": [
    "#Example 2.18\n",
    "#What is ratio of electrons to holes\n",
    "\n",
    "#Given\n",
    "Ie=3/4.0           #Current due to electron\n",
    "Ih=1-Ie            #Current due to holes\n",
    "Vh=1               #Hole velocity\n",
    "Ve=3                #Electron velocity 3 times the hole velocity\n",
    "\n",
    "#ccalculation\n",
    "R=(Ie*Vh/(Ih*Ve))\n",
    "\n",
    "#Result\n",
    "print\"The ratio of electrons to holes drift velocity is \",R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.19 Page No.81"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diffusion constant of electron is  43.99 (in cm**2/s)\n",
      "Diffusion constant of hole is  6.47 (in cm**2/s)\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.19\n",
    "#Find the diffusion coefficients of electrons and holes\n",
    "\n",
    "#given data\n",
    "e=1.6*10**-19\t\t\t#in coulamb\n",
    "T=300\t\t\t\t#in Kelvin\n",
    "MUh=0.025\t\t\t#in m**2/V-s\n",
    "MUe=0.17\t\t\t#in m**2/V-s\n",
    "k=1.38*10**-23\t\t\t#in J/K\n",
    "De=MUe*k*T/e\t\t\t#in cm**2/s\n",
    "Dh=MUh*k*T/e\t\t\t#in cm**2/s\n",
    "\n",
    "#Result\n",
    "print\"Diffusion constant of electron is \",round(De*10000,2),\"(in cm**2/s)\"\n",
    "print\"Diffusion constant of hole is \",round(Dh*10000,2),\"(in cm**2/s)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.20 Page no. 81                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The intrinsic carries concentration is  1.76e+16 /m**3\n",
      "The conductivity of Si is  0.00054 S/m\n"
     ]
    }
   ],
   "source": [
    "#Example 2.20\n",
    "#Find intrinsic carries cncentration and conductivity\n",
    "import math\n",
    "#Given\n",
    "N=3*10**25          #No of atoms\n",
    "e=1.6*10**-19\n",
    "Eg=1.1*e         #eV\n",
    "k=1.38*10**-23   #j/k  boltzman's constant\n",
    "T=300            #K\n",
    "mue=0.14\n",
    "muh=0.05\n",
    "\n",
    "#Calculation\n",
    "ni=N*math.exp(-Eg/(2*k*T))\n",
    "sigma=ni*e*(mue+muh)\n",
    "\n",
    "#Result\n",
    "print\"The intrinsic carries concentration is \",round(ni,-14),\"/m**3\"\n",
    "print\"The conductivity of Si is \",round(sigma,5),\"S/m\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.21 Page No.84"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The effective density is 4.6e+25 /m**3\n"
     ]
    }
   ],
   "source": [
    "#Example 2.21\n",
    "#Find the effective density\n",
    "\n",
    "#Given\n",
    "a=1.5        #a=me/mo\n",
    "T=300     #K\n",
    "\n",
    "#calculation\n",
    "#from eq. 2.29\n",
    "Nc=4.82*10**21*(a)**(1.5)*T**(1.5)\n",
    "\n",
    "#Result\n",
    "print\"The effective density is\",round(Nc,-23),\"/m**3\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.22 page no. 84"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The intrinsic concentration of charge carrier is 2.27e+18 /m**3\n"
     ]
    }
   ],
   "source": [
    "#Example 2.22\n",
    "#Calculate the intrinsic concentration\n",
    "\n",
    "#Given\n",
    "a=0.07          #a=me/mo\n",
    "b=0.4            #b=mh/mo\n",
    "T=300           #K\n",
    "Eg=0.7          #eV\n",
    "k=8.62*10**-5   # Boltzman constant\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "#From eq 2.101\n",
    "ni=math.sqrt(2.33*10**43*(a*b)**(1.5)*T**3*math.exp(-Eg/(k*T)))\n",
    "\n",
    "#Result\n",
    "print\"The intrinsic concentration of charge carrier is\",round(ni,-16),\"/m**3\"\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.23 Page no. 85"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The absolute temprature is 0.14 K\n"
     ]
    }
   ],
   "source": [
    "#Example 2.23\n",
    "#Find the value of absolute temprature\n",
    "\n",
    "#Given\n",
    "C=5*10**28            #atom/m**3, concentration of Si atoms\n",
    "DL=2*10**8            #Doping level \n",
    "m=1\n",
    "me=m\n",
    "#calculation\n",
    "Nd=C/DL\n",
    "nc=Nd\n",
    "T=((nc/(4.82*10**21))*(m/me)**(1.5))**(2/3.0)\n",
    "\n",
    "#Result\n",
    "print\"The absolute temprature is\",round(T,2),\"K\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.24 Page No. 85"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The effective density at temprature 300 K is 3.2e+20 /m**3\n",
      "The effective density at temprature 400 K is 8.98e+21 /m**3\n"
     ]
    }
   ],
   "source": [
    "#Example 2.24\n",
    "#Determine the effective density\n",
    "\n",
    "#Given\n",
    "T1=300.0          #K temprature\n",
    "T2=400.0\n",
    "k=1.38*10**-23  #J/k\n",
    "m=1.25*9.107*10**-31\n",
    "h=6.625*10**-34\n",
    "dE=0.3           #eV\n",
    "k_=8.62*10**-5\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "nc1=2*(2*math.pi*m*k*T1/(h**2))**(1.5)\n",
    "n1=nc1*math.exp(-(0.3/(k_*T1)))\n",
    "\n",
    "nc2=2*(2*math.pi*m*k*T2/(h**2))**(1.5)\n",
    "n2=nc2*math.exp(-(0.3/(k_*T2)))\n",
    "\n",
    "#result\n",
    "print\"The effective density at temprature 300 K is\",round(n1,-19),\"/m**3\"\n",
    "print\"The effective density at temprature 400 K is\",round(n2,-19),\"/m**3\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.25 Page no.86"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is -0.0079 eV\n"
     ]
    }
   ],
   "source": [
    "#example 2.25\n",
    "#determine the position of intrinsic fermi level\n",
    "import math\n",
    "#Given\n",
    "T=300.0\n",
    "k=8.62*10**-5  #J/k\n",
    "m=9.107*10**-31\n",
    "me=0.6*m\n",
    "mh=0.4*m\n",
    "\n",
    "\n",
    "#calculation\n",
    "dE=-3*k*T*math.log((me/mh)**(1))/4.0   #dE=Ef-Emidgap\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE,4),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.26 Page no 86"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is 0.3912 eV\n"
     ]
    }
   ],
   "source": [
    "#example 2.26\n",
    "#determine the position of intrinsic fermi level\n",
    "\n",
    "#Given\n",
    "T=300.0\n",
    "Eg=0.72      #eV Energy gap\n",
    "k=8.62*10**-5  #J/k\n",
    "me=1\n",
    "mh=5.0\n",
    "\n",
    "#calculation\n",
    "#from   Ef=Ec-kTlog(nc/Nd)\n",
    "import math\n",
    "dE=(Eg/2.0)-3*k*T*math.log(me/mh)/4.0 #dE=Ef-Emidgap\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE,4),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.27 Page no 87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is 0.28 eV\n"
     ]
    }
   ],
   "source": [
    "#example 2.27\n",
    "#determine the position of intrinsic fermi level\n",
    "\n",
    "#Given\n",
    "T1=300.0\n",
    "T2=350\n",
    "Eg=0.24        #eV Energy gap\n",
    "\n",
    "#calculation\n",
    "#from   Ef=Ev+kTlog(nc/Nd)\n",
    "import math\n",
    "dE=(T2/T1)*Eg\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE,4),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.28 Page no.88"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is 0.36 eV\n"
     ]
    }
   ],
   "source": [
    "#Example 2.28\n",
    "#determine the position of intrinsic fermi level\n",
    "\n",
    "#Given\n",
    "T1=300.0\n",
    "T2=400\n",
    "Eg=0.27        #eV Energy gap\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "dE=(T2/T1)*Eg\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE,4),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.29 page no.88"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is 0.258 eV\n"
     ]
    }
   ],
   "source": [
    "##Example 2.29\n",
    "#determine the position of intrinsic fermi level\n",
    "\n",
    "#Given\n",
    "dE1=0.3        #eV Energy gap\n",
    "kT=0.026       #eV\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "x=math.exp(-dE1/kT)    #x=Nd/nc\n",
    "y=5           #y=Nd2/Nd1\n",
    "dE2=-math.log(y)*kT+dE1\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE2,3),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.30 Page no.89"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The position of fermi level is 0.36 eV\n"
     ]
    }
   ],
   "source": [
    "##Example 2.30\n",
    "#determine the position of intrinsic fermi level\n",
    "\n",
    "#Given\n",
    "dE1=0.39        #eV Energy gap\n",
    "kT=0.026        #eV\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "x=math.exp(-dE1/kT)    #x=NA1/nV\n",
    "y=3           #y=NA2/NA1\n",
    "dE2=((dE1/kT)-math.log(y))*kT\n",
    "\n",
    "\n",
    "#Result\n",
    "print\"The position of fermi level is\",round(dE2,2),\"eV\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.31 Page no.91"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The electron density is 6.25e+22 /m**3\n",
      "The mobility is 1e-04 /m**3\n"
     ]
    }
   ],
   "source": [
    "#example 2.31\n",
    "#Determine electron density and mobility\n",
    "\n",
    "#Given\n",
    "rho=1       #ohm-m Resistivity\n",
    "Rh=100.0       #cm**3/coulomb\n",
    "e=1.6*10**-19\n",
    "\n",
    "#calculation\n",
    "con=1/rho   #Conductivity\n",
    "R=1/Rh      #Charge density\n",
    "ED=R*10**6/e\n",
    "mu=con/(R*10**6)\n",
    "\n",
    "#Result\n",
    "print\"The electron density is\",ED,\"/m**3\"\n",
    "print\"The mobility is %.e\"%mu,\"/m**3\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.32 Page no. 92"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hall Voltage is 22.8 micro V\n"
     ]
    }
   ],
   "source": [
    "#Example 2.32\n",
    "#Calculate Hall Voltage\n",
    "\n",
    "#Given\n",
    "w=0.1      #m width\n",
    "t=0.01     #m thickness\n",
    "F=0.6       #T, field\n",
    "Rh=3.8*10**-4  #Hall Coefficient\n",
    "I=10        #mA\n",
    "\n",
    "#calculation\n",
    "Vh=(Rh*F*I/w)\n",
    "\n",
    "#Result\n",
    "print\"Hall Voltage is\",Vh*1000,\"micro V\"\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.33 Page No. 92"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Magnitude of hall voltage is 76.0 mV\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.33\n",
    "#What is magnitude of Hall Voltage\n",
    "\n",
    "#given data\n",
    "e=1.6*10**-19\t\t\t#in coulamb\n",
    "ND=10**17\t\t\t#in cm**-3\n",
    "Bz=0.1\t\t\t\t#in Wb/m**2\n",
    "w=4\t\t\t\t#in mm\n",
    "d=4\t\t\t\t#in mm\n",
    "Ex=5\t\t\t\t#in V/cm\n",
    "MUe=3800\t\t\t#in cm**2/V-s\n",
    "\n",
    "#calculation\n",
    "v=MUe*Ex\t\t\t#in cm/s\n",
    "v=v*10**-2\t\t\t#in m/s\n",
    "VH=Bz*v*d\t\t\t#in mV\n",
    "\n",
    "#Result\n",
    "print\"Magnitude of hall voltage is\",VH,\"mV\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.34 Page No.92"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Magnitude of hall voltage is  3.0 mV\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.34\n",
    "#What is magnitude of hall voltage\n",
    "\n",
    "#given data\n",
    "e=1.6*10**-19\t\t\t#in coulamb\n",
    "ND=10**21\t\t\t#in m**-3\n",
    "Bz=0.2\t\t\t\t#in T\n",
    "d=4\t\t\t\t#in mm\n",
    "d=d*10**-3\t\t\t#in meter\n",
    "J=600\t\t\t\t#in A/m**2\n",
    "n=ND\t\t\t\t#in m**-3\n",
    "\n",
    "#calculation\n",
    "#formula : VH*w/(B*I)=1/(n*e)\n",
    "VH=Bz*J*d/(n*e)\t\t\t#in V\n",
    "\n",
    "#Result\n",
    "print\"Magnitude of hall voltage is \",VH*10**3,\"mV\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 2.35 Page No."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hall angle is 1.0709 degree\n"
     ]
    }
   ],
   "source": [
    "#Exa 2.35\n",
    "#Calculate hall angle\n",
    "\n",
    "#given data\n",
    "e=1.6*10**-19\t\t\t#in coulamb\n",
    "rho=0.00912\t\t\t#in ohm-m\n",
    "B=0.48\t\t\t\t#in Wb/m**2\n",
    "RH=3.55*10**-4\t\t\t#in m**3-coulamb**-1\n",
    "SIGMA=1/rho\t\t\t#in (ohm=m)**-1\n",
    "\n",
    "#calculation\n",
    "import math\n",
    "THETAh=math.atan(SIGMA*B*RH)\t#in Degree\n",
    "\n",
    "#result\n",
    "print\"Hall angle is\",round(THETAh*180/3.14,4),\"degree\""
   ]
  }
 ],
 "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}