path: root/Semiconductor_Devices_Basic_Principle_by_J._Singh/chapter3.ipynb

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  {

   "cells": [

    {

     "cell_type": "heading",

     "level": 1,

     "metadata": {},

     "source": [

      "Chapter3:CARRIER DYNAMICS IN SEMICONDUCTORS"

     ]

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.1:pg-95"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "mo = 9.1*10**-31 #initializing value of mass of electron\n",

      "me = 0.067*mo #initializing value of effective mass of GaAs\n",

      "u1=8500*10**(-4) #initializing value of mobility of pure GaAs\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "u2=5000*10**(-4) #initializing value of mobility of impure GaAs\n",

      "Tsc1 = (me*u1)/e\n",

      "print\"The relaxation time of pure GaAs is Tsc1 = \",\"{:.2e}\".format(Tsc1),\"s\"\n",

      "Tsc2 = (me*u2)/e\n",

      "print\"The relaxation time of impure GaAs is Tsc2= \"\"{:.2e}\".format(Tsc2),\"s\"\n",

      "#using Mathieson rule\n",

      "Tsc = ((1/Tsc2)-(1/Tsc1))**-1\n",

      "print\"The impurity related time is Tsc(imp)  = \",\"{:.2e}\".format(Tsc),\"s\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The relaxation time of pure GaAs is Tsc1 =  3.24e-13 s\n",

        "The relaxation time of impure GaAs is Tsc2= 1.91e-13 s\n",

        "The impurity related time is Tsc(imp)  =  4.63e-13 s\n"

       ]

      }

     ],

     "prompt_number": 1

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.2:pg-96"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "mo = 9.1*10**-31 #initializing value of mass of electron\n",

      "ml = 0.98*mo #initializing value of longitudinal mass\n",

      "mt = 0.19*mo #initializing value of transverse mass\n",

      "u=1500*10**(-4) #initializing value of mobility of pure silicon\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "Msig = 3*((2/mt)+(1/ml))**(-1)\n",

      "Tsc = u*Msig/e\n",

      "print\"The scattering time is ,Tsc= \",\"{:.2e}\".format(Tsc),\"s\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The scattering time is ,Tsc=  2.22e-13 s\n"

       ]

      }

     ],

     "prompt_number": 3

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.3:pg-96"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "un1=1000 #initializing value of mobility of electron of silicon\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "un2 = 8000.0 #initializing value of mobility of electron of GaAs\n",

      "up1 = 350.0 #initializing value of mobility of holes of silicon\n",

      "up2 = 400.0 #initializing value of mobility of holes of GaAs\n",

      "ndoped = (50.0/100)*10**17 #initializing value of electron density of doped semiconductor(50% of Nd=10**17 cm**-3)\n",

      "ni = 1.5*10**10 #initializing value of electron density of ionisation electron for silicon\n",

      "pdoped = (ni)**2/ndoped\n",

      "print\"The hole density of doped semiconductor is pdoped =  \",\"{:.2e}\".format(pdoped),\"cm**-3\"\n",

      "#pdoped can be neglected \n",

      "Sdoped = ndoped*e*un1\n",

      "print\"The conductivity of doped silicon is (sigma doped) Sdoped =\",round(Sdoped),\"ohmcm**-1\"\n",

      "p1 = 1.5*10**10 #initializing value of hole density for undoped silicon\n",

      "Sundoped = ni*e*un1+p1*e*up1\n",

      "print\"The conductivity of undoped silicon is (sigma undoped)Sundoped = \",\"{:.2e}\".format(Sundoped),\"ohmcm**-1\"\n",

      "Sdoped1 = ndoped*e*un2\n",

      "print\"The conductivity of doped GaAs is (sigma doped) Sdoped  = \",round(Sdoped1,1),\"ohmcm**-1\"\n",

      "p2 = 1.84*10**6 #initializing value of hole density for undoped GaAs\n",

      "ni1 = 1.84*10**6 #initializing value of electron density of ionisation electron for GaAs\n",

      "Sundoped = ni1*e*un2+p2*e*up1\n",

      "print\"The conductivity of undoped silicon is (sigma undoped) Sundoped  = \",\"{:.2e}\".format(Sundoped),\"ohmcm**-1\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The hole density of doped semiconductor is pdoped =   4.50e+03 cm**-3\n",

        "The conductivity of doped silicon is (sigma doped) Sdoped = 8.0 ohmcm**-1\n",

        "The conductivity of undoped silicon is (sigma undoped)Sundoped =  3.24e-06 ohmcm**-1\n",

        "The conductivity of doped GaAs is (sigma doped) Sdoped  =  64.0 ohmcm**-1\n",

        "The conductivity of undoped silicon is (sigma undoped) Sundoped  =  2.46e-09 ohmcm**-1\n"

       ]

      }

     ],

     "prompt_number": 10

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.4:pg-97"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "un1=1000 #initializing value of mobility of electron of silicon\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "un2 = 400.0 #initializing value of mobility of electron of GaAs\n",

      "up1 = 350.0 #initializing value of mobility of holes of silicon\n",

      "up2 = 8000.0 #initializing value of mobility of holes of GaAs\n",

      "ni = 1.5*10**10 #initializing value of electron density of ionisation electron\n",

      "nmax = 2.78*10**19 #initializing value of maximum electron density for silicon\n",

      "nmax1 = 7.72*10**18 #initializing value of maximum electron density for GaAs\n",

      "Smax = nmax*e*un1\n",

      "print\"The maximum conductivity for silicon is (sigma max) Smax =  \",\"{:.2e}\".format(Smax),\"ohmcm**-1\"\n",

      "Smax1 = nmax1*e*un2\n",

      "print\"The maximum conductivity of GaAs is (sigma max) Smax=\",\"{:.1e}\".format(Smax1),\"ohmcm**-1\"\n",

      "Smin = ni*e*((un1*sqrt(up1/un1))+(up1*sqrt(un1/up1)))\n",

      "print\"The minimum conductivity of silicon is (sigma min)Smin = \"\"{:.1e}\".format(Smin),\"ohmcm**-1\"\n",

      "ni1 = 1.84*10**6 #initializing value of electron density of ionisation electron for GaAs\n",

      "Smin1 = ni1*e*((un2*sqrt(up2/un2))+(up2*sqrt(un2/up2)))\n",

      "print\"The minimum conductivity of GaAs is (sigma min)Smin1 =\",\"{:.2e}\".format(Smin1),\"ohmcm**-1\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The maximum conductivity for silicon is (sigma max) Smax =   4.45e+03 ohmcm**-1\n",

        "The maximum conductivity of GaAs is (sigma max) Smax= 4.9e+02 ohmcm**-1\n",

        "The minimum conductivity of silicon is (sigma min)Smin = 2.8e-06 ohmcm**-1\n",

        "The minimum conductivity of GaAs is (sigma min)Smin1 = 1.05e-09 ohmcm**-1\n"

       ]

      }

     ],

     "prompt_number": 24

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.5:pg-98"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "mo = 9.1*10**-31 #initializing value of mass of electron\n",

      "me = 0.26*mo #initializing value of conductivity mass of silicon\n",

      "v1=1.4*10**(6) #initializing value of velocity of silicon electron at 300K\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "v2=1.0*10**(7) #initializing value of velocity of silicon electron at 300K\n",

      "F1= 1000 #initializing value of electric field \n",

      "F2= 100000 #initializing value of electric field \n",

      "u1 = v1/(F1*10**4)\n",

      "print\"The mobility for electrons in silicon (1 kV/cm) is u1=\",\"{:.2e}\".format(u1),\"m**2/V.s\"\n",

      "u2 = v2/(F2*10**4)\n",

      "print\"The mobility for electrons in silicon (100 kV/cm) is u2=\",\"{:.2e}\".format(u2),\"m**2/V.s\"\n",

      "Tsc1 = (me*u1)/e\n",

      "print\"The relaxation time of electrons in silicon at 1kV/cm is Tsc1=\",\"{:.2e}\".format(Tsc1),\"s\"\n",

      "Tsc2 = (me*u2)/e\n",

      "print\"The relaxation time of electrons in silicon at 100kV/cm is Tsc2 =\",\"{:.2e}\".format(Tsc2),\"s\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The mobility for electrons in silicon (1 kV/cm) is u1= 1.40e-01 m**2/V.s\n",

        "The mobility for electrons in silicon (100 kV/cm) is u2= 1.00e-02 m**2/V.s\n",

        "The relaxation time of electrons in silicon at 1kV/cm is Tsc1= 2.07e-13 s\n",

        "The relaxation time of electrons in silicon at 100kV/cm is Tsc2 = 1.48e-14 s\n"

       ]

      }

     ],

     "prompt_number": 13

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.6:pg-99"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "v2=1.0*10**(7) #initializing value of saturation velocity of GaAs device\n",

      "F= 5000 #initializing value of average electric field in GaAs device\n",

      "L= 2*10**(-4) #initializing value of length of GaAs device \n",

      "u = 8000 #initializing value of low field mobility\n",

      "v1 = u*F\n",

      "print\"The average velocity of electrons is v = \",\"{:.2e}\".format(v1),\"cm/s\"\n",

      "Ttr1 = L/v1\n",

      "print\"The transit time of electrons through the device is Ttr1 =\"\"{:.2e}\".format(Ttr1),\"s\"\n",

      "Ttr2 = L/v2\n",

      "print\"The transit time of electrons using saturation velocity through the device is Ttr2 = \",\"{:.2e}\".format(Ttr2),\"s\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The average velocity of electrons is v =  4.00e+07 cm/s\n",

        "The transit time of electrons through the device is Ttr1 =5.00e-12 s\n",

        "The transit time of electrons using saturation velocity through the device is Ttr2 =  2.00e-11 s\n"

       ]

      }

     ],

     "prompt_number": 14

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.7:pg-103"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "h=1.05*10**-34 #initializing value of reduced plancks constant or dirac constant or h-bar\n",

      "mo = 9.1*10**-31 #initializing value of mass of electron\n",

      "me1 = 0.065*9.1*10**-31 #initializing value of electron mass of GaAs\n",

      "me2 = 0.02*9.1*10**-31 #initializing value of electron mass of InAs\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "Eg1 = 1.5*1.6*10**-19 #initializing value of valence bandedge energy of GaAs\n",

      "Eg2 = 0.4052*1.6*10**-19 #initializing value of valence bandedge energy of InAs\n",

      "F= 2*10**7 #initializing value of applied electric field \n",

      "T1 = math.exp(-(4*sqrt(2*me1)*(Eg1)**(3/2))/(3*e*h*F))\n",

      "print\"The tunneling probability in GaAs is T1 =\",round(T1,1)\n",

      "T2 = math.exp(-(4*sqrt(2*me2)*(Eg2)**(3/2))/(3*e*h*F))\n",

      "print\"The tunneling probability in InAs is T2 =\",\"{:.2e}\".format(T2)\n",

      "#NOTE: The tunneling probability in GaAs is approximately given zero in the textbook"

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The tunneling probability in GaAs is T1 = 0.0\n",

        "The tunneling probability in InAs is T2 = 0.00e+00\n"

       ]

      }

     ],

     "prompt_number": 19

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.8:pg-106"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "L =10**-4 #initializing value of length\n",

      "Dn =220 #initializing value of electron diffusion coefficient\n",

      "#n(x) = 10**16*exp(-(x/L)) cm**-3\n",

      "#Derivative of n(x) for x =0 is  10**16/L\n",

      "dn_by_dx =10**16/L #initializing value of derivative of n(x) for x=0\n",

      "Jn_diff = e*Dn*dn_by_dx\n",

      "print\"The diffusion current density is Jn_diff =\",\"{:.1e}\".format(Jn_diff),\"A/cm**2\"\n",

      "# Note : due to different precisions taken by me and the author ... my answer differ "

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The diffusion current density is Jn_diff = 3.5e+03 A/cm**2\n"

       ]

      }

     ],

     "prompt_number": 7

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "\n",

      "Ex3.9:pg-109"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "v1=1.4*10**(4) #initializing value of velocity of electrons in silion at 1kV/cm\n",

      "v2=7*10**(4) #initializing value of velocity of electrons in silion at 10kV/cm\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "kbT = 0.026 #initializing value of kbT at 300K\n",

      "F1= 10**5 #initializing value of applied electric field\n",

      "F2= 10**6 #initializing value of applied electric field \n",

      "D1 = (v1*kbT*1.6*10**-19)/(e*F1)\n",

      "print\"The diffusion coefficient is ,D(1kV/cm)=\",\"{:.2e}\".format(D1),\"m**2/s\"\n",

      "D2 = (v2*kbT*1.6*10**-19)/(e*F2)\n",

      "print\"The diffusion coefficient is ,D(10kV/cm)=\",\"{:.2e}\".format(D2),\"m**2/s\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The diffusion coefficient is ,D(1kV/cm)= 3.64e-03 m**2/s\n",

        "The diffusion coefficient is ,D(10kV/cm)= 1.82e-03 m**2/s\n"

       ]

      }

     ],

     "prompt_number": 2

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.10:pg-111"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "Nc=2.8*10**(19)\n",

      "Nv=1.04*10**(19)\n",

      "#NOTE: Ec-Ev = forbidden band gap energy = Eg\n",

      "Eg = 1.1\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "kbT = 0.026 #initializing value of kbT at 300K\n",

      "n= 10**17\n",

      "p= 10**17\n",

      "Efn_minus_Efp = Eg+(kbT*(log(p/Nv)+log(n/Nc)))\n",

      "print\"The difference in the quasi fermi level is ,Efn_minus_Efp=\",\"{:.2e}\".format(Efn_minus_Efp),\"eV\"\n",

      "n= 10**15\n",

      "p= 10**15\n",

      "Efn_minus_Efp = Eg+(kbT*(log(p/Nv)+log(n/Nc)))\n",

      "print\"The difference in the quasi fermi level is ,Efn_minus_Efp=\",\"{:.2e}\".format(Efn_minus_Efp),\"eV\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The difference in the quasi fermi level is ,Efn_minus_Efp= 8.33e-01 eV\n",

        "The difference in the quasi fermi level is ,Efn_minus_Efp= 5.93e-01 eV\n"

       ]

      }

     ],

     "prompt_number": 26

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.11:pg-118"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "alpha1=(-10**(4)) #initializing value of absorption coefficient near the bandedges of GaAs\n",

      "alpha2=(-10**(3)) #initializing value of absorption coefficient near the bandedges of Si\n",

      "Iabs_by_Iinc = 0.9 #initializing value of amount of light absorbed\n",

      "L1 = (1.0/alpha1)*log(1-(Iabs_by_Iinc))\n",

      "print\"The thickness of a sample GaAs is ,L =\",\"{:.2e}\".format(L1),\"cm\"\n",

      "L2 = (1.0/alpha2)*log(1-(Iabs_by_Iinc))\n",

      "print\"The thickness of a sample Si is ,L = \",\"{:.2e}\".format(L2),\"cm\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The thickness of a sample GaAs is ,L = 2.30e-04 cm\n",

        "The thickness of a sample Si is ,L =  2.30e-03 cm\n"

       ]

      }

     ],

     "prompt_number": 5

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.12:pg-118"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "alpha=(3*10**(3)) #initializing value of absorption coefficient near the bandedges of GaAs\n",

      "p=(10**(3)) #initializing value of power density that impringes on GaAs\n",

      "Tr = 1.5*1.6*10**-19 #initializing value of photon energy\n",

      "d = 10**-3 #initializing value of photon energy\n",

      "Rg1 = (alpha*p)/Tr\n",

      "print\"The carrier generation rate at the surface is ,Rg(0)= \",\"{:.2e}\".format(Rg1),\"cm**-3s**-1\"\n",

      "Rg2 = (alpha*p*exp(-3))/Tr\n",

      "print\"The carrier generation rate at the depth of 10 um is ,Rg(10) =\",\"{:.2e}\".format(Rg2),\"cm**-3s**-1\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The carrier generation rate at the surface is ,Rg(0)=  1.25e+25 cm**-3s**-1\n",

        "The carrier generation rate at the depth of 10 um is ,Rg(10) = 6.22e+23 cm**-3s**-1\n"

       ]

      }

     ],

     "prompt_number": 6

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.13:pg-120"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "mo = 9.1*10**-31  #initializing value of mass of electron\n",

      "m = 0.27*mo #initializing value of effective mass of silicon\n",

      "kb = (1.38*10**-23) #initializing value of boltzman constant\n",

      "T1 = 300.0 #initializing value of temperature\n",

      "T2 = 77.0 #initializing value of temperature\n",

      "vth1=(sqrt((3*kb*T1)/(m)))*100\n",

      "print\"The thermal velocity of the electron at 300K is ,vth(300K)=\",\"{:.0e}\".format(vth1),\"cms**-1\"\n",

      "vth2=(sqrt((3*kb*T2)/(m)))*100\n",

      "print\"The thermal velocity of the electron at 77K is ,vth(77K)=\",\"{:.0e}\".format(vth2),\"cms**-1\"\n",

      "sigma=10**(-14) #initializing value of cross-section\n",

      "Nt = 10**15 #initializing value of impurity density\n",

      "Tnr1 = (1.0/(sigma*Nt*vth1))\n",

      "print\"The electron trapping time is ,Tnr1 =\",\"{:.2e}\".format(Tnr1),\"s\"\n",

      "Tnr2 = (sigma*Nt*vth2)\n",

      "print\"The electron trapping time is ,Tnr2 = \",\"{:.0e}\".format(Tnr2),\"s\"\n",

      "#NOTE: in the Textbook the author has taken the approximated value for Vth thermal velocity\\\n",

      "# NOTE: these approximated values of velocity affects the value of electron trapping time\n",

      "# in the Textbook the answer of Tnr2 is wrong."

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The thermal velocity of the electron at 300K is ,vth(300K)= 2e+07 cms**-1\n",

        "The thermal velocity of the electron at 77K is ,vth(77K)= 1e+07 cms**-1\n",

        "The electron trapping time is ,Tnr1 = 4.45e-09 s\n",

        "The electron trapping time is ,Tnr2 =  1e+08 s\n"

       ]

      }

     ],

     "prompt_number": 45

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.14:pg-125"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "KbT = 1.38*(10**-23)*300 #initializing value of kbT at 300K\n",

      "mu=0.4 #initializing value of mobility of p-type GaAs\n",

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "Dn = (mu*KbT)/e\n",

      "print\"The diffusion constant using einstein relation is Dn =\",\"{:.2e}\".format(Dn),\"m**2/s\"\n",

      "T = 0.6*10**-9 #initializing value of recombination time\n",

      "Ln = sqrt(Dn*T)\n",

      "print\"The diffusion length of p type GaAs is Ln =\",\"{:.1e}\".format(Ln),\"m\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The diffusion constant using einstein relation is Dn = 1.03e-02 m**2/s\n",

        "The diffusion length of p type GaAs is Ln = 2.5e-06 m\n"

       ]

      }

     ],

     "prompt_number": 13

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Ex3.16:pg-126"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "e = 1.6*10**-19 #initializing value of charge of electron\n",

      "KbT = 0.026 #initializing value of kbT at 300K\n",

      "sigma=10 #initializing value of conductivity\n",

      "mu_n=1100 #initializing value of mobility of electrons\n",

      "mu_p=400 #initializing value of mobility of holes\n",

      "Nd = 10**17 #initializing value of doping\n",

      "n = sigma/(e*mu_n)\n",

      "print\"The carrier concentration in n type material is n =\",\"{:.2e}\".format(n),\"cm**-3\"\n",

      "# the answer in textbook is given in %\n",

      "#The excess drops by 50% once light is off using this fact in below equation\n",

      "T = -1/log(.5)\n",

      "print\"The recombination time is T = \",\"{:.2e}\".format(T),\"micro-sec\"\n",

      "Dp = mu_p*kbT\n",

      "print\"The diffusion constant is Dp = \",\"{:.2e}\".format(Dp),\"cm**2/s\"\n",

      "Lp = sqrt(Dp*T*10**-6)\n",

      "print\"The diffusion length is Lp =  \",\"{:.2e}\".format(Lp),\"m\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "The carrier concentration in n type material is n = 5.68e+16 cm**-3\n",

        "The recombination time is T =  1.44e+00 micro-sec\n",

        "The diffusion constant is Dp =  1.04e+01 cm**2/s\n",

        "The diffusion length is Lp =   3.87e-03 m\n"

       ]

      }

     ],

     "prompt_number": 12

    }

   ],

   "metadata": {}

  }

 ]

}