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| author | hardythe1 | 2015-05-05 14:21:39 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-05-05 14:21:39 +0530 |
| commit | 435840cef00c596d9e608f9eb2d96f522ea8505a (patch) | |
| tree | 4c783890c984c67022977ca98432e5e4bab30678 /Applied_Physics/Chapter_09_Semiconductors_1.ipynb | |
| parent | aa1863f344766ca7f7c20a395e58d0fb23c52130 (diff) | |
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diff --git a/Applied_Physics/Chapter_09_Semiconductors_1.ipynb b/Applied_Physics/Chapter_09_Semiconductors_1.ipynb new file mode 100755 index 00000000..9ce2ea83 --- /dev/null +++ b/Applied_Physics/Chapter_09_Semiconductors_1.ipynb @@ -0,0 +1,782 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:c155cecc785c23bdccd0bf715c04d53d7788e1b590b4310d6af27c13ce7b97ac"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9:Semiconductors"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2 , Page no:272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "Eg=0.67; #in eV (Energy band gap)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "T1=298; #in K (room temperature)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "K=10; #ratio of number of electrons at different temperature\n",
+ "\n",
+ "#calculate\n",
+ "Eg=Eg*e; #changing unit from eV to Joule\n",
+ "#since ne=Ke*exp(-Eg/(2*k*T))\n",
+ "#and ne/ne1=exp(-Eg/(2*k*T))/exp(-Eg/(2*k*T1)) and ne/ne1=K=10\n",
+ "#therefore we have 10=exp(-Eg/(2*k*T))/exp(-Eg/(2*k*T1))\n",
+ "#re-arranging the equation for T, we get T2=1/((1/T1)-((2*k*log(10))/Eg))\n",
+ "T=1/((1/T1)-((2*k*math.log(10))/Eg)); #calculation of the temperature\n",
+ "\n",
+ "#result\n",
+ "print\"The temperature at which number of electrons in the conduction band of a semiconductor increases by a factor of 10 is T=\",round(T),\"K (roundoff error)\";\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The temperature at which number of electrons in the conduction band of a semiconductor increases by a factor of 10 is T= 362.0 K (roundoff error)\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.3 , Page no:272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ni=2.5E13; #in /cm^3 (intrinsic carrier density)\n",
+ "ue=3900; #in cm^2/(V-s) (electron mobilities)\n",
+ "uh=1900; #in cm^2/(V-s) (hole mobilities)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "l=1; #in cm (lenght of the box)\n",
+ "b=1;h=1; #in mm (dimensions of germanium rod )\n",
+ "\n",
+ "#calculate\n",
+ "ni=ni*1E6; #changing unit from 1/cm^3 to 1/m^3\n",
+ "ue=ue*1E-4; #changing unit from cm^2 to m^2\n",
+ "uh=uh*1E-4; #changing unit from cm^2 to m^2\n",
+ "sigma=ni*e*(ue+uh); #calculation of conductivity\n",
+ "rho=1/sigma; #calculation of resistivity\n",
+ "l=l*1E-2; #changing unit from mm to m for length\n",
+ "A=(b*1E-3)*(h*1E-3); #changing unit from mm to m for width and height and calculation of cross-sectional area\n",
+ "R=rho*l/A; #calculation of resistance\n",
+ "\n",
+ "#result\n",
+ "print\"The resistance of intrinsic germanium is R=\",'%.3E'%R,\"ohm\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The resistance of intrinsic germanium is R= 4.310E+03 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4 , Page no:273"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ne=2.5E19; #in /m^3 (electron density)\n",
+ "nh=2.5E19; #in /m^3 (hole density)\n",
+ "ue=0.36; #in m^2/(V-s) (electron mobilities)\n",
+ "uh=0.17; #in m^2/(V-s) (hole mobilities)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "#since ne=nh=ni, therefore we have \n",
+ "ni=nh;\n",
+ "sigma=ni*e*(ue+uh); #calculation of conductivity\n",
+ "rho=1/sigma; #calculation of resistivity\n",
+ "\n",
+ "#result\n",
+ "print\"The conductivity of germanium is =\",round(sigma,2),\"/ohm-m\";\n",
+ "print\"The resistivity of germanium is =\",round(rho,2),\"ohm-m\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The conductivity of germanium is = 2.12 /ohm-m\n",
+ "The resistivity of germanium is = 0.47 ohm-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 , Page no:273"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ni=1.5E16; #in /m^3 (intrinsic carrier density)\n",
+ "ue=0.135; #in m^2/(V-s) (electron mobilities)\n",
+ "uh=0.048; #in m^2/(V-s) (hole mobilities)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "ND=1E23; #in atom/m^3 (doping concentration)\n",
+ "\n",
+ "#calculate\n",
+ "sigma_i=ni*e*(ue+uh); #calculation of intrinsic conductivity\n",
+ "sigma=ND*ue*e; #calculation of conductivity after doping\n",
+ "rho=ni**2/ND; #calculation of equilibrium hole concentration\n",
+ "\n",
+ "#result\n",
+ "print\"The intrinsic conductivity for silicon is =\",'%.3E'%sigma_i,\"S\";\n",
+ "print\"The conductivity after doping with phosphorus atoms is =\",'%.3E'%sigma,\"S\";\n",
+ "print\"The equilibrium hole concentration is =\",'%.3E'%rho,\"/m^3\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The intrinsic conductivity for silicon is = 4.392E-04 S\n",
+ "The conductivity after doping with phosphorus atoms is = 2.160E+03 S\n",
+ "The equilibrium hole concentration is = 2.250E+09 /m^3\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 , Page no:274"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ni=1.5E16; #in /m^3 (intrinsic carrier density)\n",
+ "ue=0.13; #in m^2/(V-s) (electron mobilities)\n",
+ "uh=0.05; #in m^2/(V-s) (hole mobilities)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "ne=5E20; #in /m^3 (concentration of donor type impurity)\n",
+ "nh=5E20; #in /m^3 (concentration of acceptor type impurity)\n",
+ "\n",
+ "#calculate\n",
+ "#part-i\n",
+ "sigma=ni*e*(ue+uh); #calculation of intrinsic conductivity\n",
+ "#part-ii\n",
+ "#since 1 donor atom is in 1E8 Si atoms, hence holes concentration can be neglected\n",
+ "sigma1=ne*e*ue; #calculation of conductivity after doping with donor type impurity\n",
+ "#part-iii\n",
+ "#since 1 acceptor atom is in 1E8 Si atoms, hence electron concentration can be neglected\n",
+ "sigma2=nh*e*uh; #calculation of conductivity after doping with acceptor type impurity\n",
+ "\n",
+ "#result\n",
+ "print\"The intrinsic conductivity for silicon is =\",'%.3E'%sigma,\"(ohm-m)^-1\";\n",
+ "print\"The conductivity after doping with donor type impurity is =\",sigma1,\"(ohm-m)^-1\";\n",
+ "print\"The conductivity after doping with acceptor type impurity is =\",sigma2,\"(ohm-m)^-1\";\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The intrinsic conductivity for silicon is = 4.320E-04 (ohm-m)^-1\n",
+ "The conductivity after doping with donor type impurity is = 10.4 (ohm-m)^-1\n",
+ "The conductivity after doping with acceptor type impurity is = 4.0 (ohm-m)^-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.7 , Page no:274"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ni=1E20; #in /m^3 (intrinsic carrier density)\n",
+ "ND=1E21; #in /m^3 (donor impurity concentration)\n",
+ "\n",
+ "#calculate\n",
+ "nh=ni**2/ND; #calculation of density of hole carriers at room temperature\n",
+ "\n",
+ "#result\n",
+ "print\"The density of hole carriers at room temperature is nh=\",nh,\"/m^3\";\n",
+ "#Note: answer in the book is wrong due to printing mistake"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The density of hole carriers at room temperature is nh= 1e+19 /m^3\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8 , Page no:275"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "M=72.6; #atomic mass of germanium\n",
+ "P=5400; #in Kg/m^3 (density)\n",
+ "ue=0.4; #in m^2/V-s (mobility of electrons)\n",
+ "uh=0.2; #in m^2/V-s (mobility of holes)\n",
+ "Eg=0.7; #in eV (Band gap)\n",
+ "m=9.1E-31; #in Kg (mass of electron)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "T=300; #in K (temperature)\n",
+ "h=6.63E-34; #in J/s (Planck\u2019s constant)\n",
+ "pi=3.14; #value of pi used in the solution\n",
+ "e=1.6E-19; #in C(charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "Eg=Eg*e; #changing unit from eV to J\n",
+ "ni=2*(2*pi*m*k*T/h**2)**(3/2)*math.exp(-Eg/(2*k*T));\n",
+ "sigma=ni*e*(ue+uh);\n",
+ "\n",
+ "#result\n",
+ "print\"The intrinsic carrier density for germanium at 300K is ni=\",'%.3E'%ni,\"/m^3\";\n",
+ "print\"The conductivity of germanium is=\",round(sigma,3),\"(ohm-m)^-1\";\n",
+ "print \"NOTE: The answer in the textbook is wrong\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The intrinsic carrier density for germanium at 300K is ni= 3.334E+19 /m^3\n",
+ "The conductivity of germanium is= 3.201 (ohm-m)^-1\n",
+ "NOTE: The answer in the textbook is wrong\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.9 , Page no:275"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "rho1=4.5; #in ohm-m (resistivity at 20 degree Celcius)\n",
+ "rho2=2.0; #in ohm-m (resistivity at 32 degree Celcius)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "T1=20; T2=32; #in degree Celcius (two temperatures)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "T1=T1+273; #changing unit from degree Celius to K\n",
+ "T2=T2+273; #changing unit from degree Celius to K\n",
+ "#since sigma=e*u*C*T^(3/2)*exp(-Eg/(2*k*T))\n",
+ "#therefore sigma1/sigma2=(T1/T2)^3/2*exp((-Eg/(2*k)*((1/T1)-(1/T2))\n",
+ "#and sigma=1/rho \n",
+ "#therefore we have rho2/rho1=(T1/T2)^3/2*exp((-Eg/(2*k)*((1/T1)-(1/T2))\n",
+ "#re-arranging above equation for Eg, we get Eg=(2*k/((1/T1)-(1/T2)))*((3/2)*log(T1/T2)-log(rho2/rho1))\n",
+ "Eg=(2*k/((1/T1)-(1/T2)))*((3/2)*math.log(T1/T2)-math.log(rho2/rho1));\n",
+ "Eg1=Eg/e;#changing unit from J to eV\n",
+ "\n",
+ "#result\n",
+ "print\"The energy band gap is Eg=\",'%.3E'%Eg,\"J\";\n",
+ "print\"\\t\\t\\t =\",round(Eg1,3),\"eV\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The energy band gap is Eg= 1.543E-19 J\n",
+ "\t\t\t = 0.964 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.10 , Page no:276"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "rho=2300; #in ohm-m (resistivity of pure silicon)\n",
+ "ue=0.135; #in m^2/V-s (mobility of electron)\n",
+ "uh=0.048; #in m^2/V-s (mobility of electron)\n",
+ "Nd=1E19; #in /m^3 (doping concentration)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "#since sigma=ni*e*(ue+uh) and sigma=1/rho\n",
+ "#therefore ni=1/(rho*e*(ue+uh))\n",
+ "ni=1/(rho*e*(ue+uh)); #calculation of intrinsic concentration\n",
+ "ne=Nd; #calculation of electron concentration\n",
+ "nh=ni**2/Nd; #calculation of hole concentration\n",
+ "sigma=ne*ue*e+nh*uh*e; #calculation of conductivity\n",
+ "rho=1/sigma; #calculation of resistivity\n",
+ "\n",
+ "#result\n",
+ "print\"The electron concentration is ne=\",ne,\"/m^3\";\n",
+ "print\"The hole concentration is nh=\",'%.3E'%nh,\"/m^3\";\n",
+ "print\"The resistivity of the specimen is =\",round(rho,3),\"ohm-m\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The electron concentration is ne= 1e+19 /m^3\n",
+ "The hole concentration is nh= 2.205E+13 /m^3\n",
+ "The resistivity of the specimen is = 4.63 ohm-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.11 , Page no:276"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "uh=1900; #in cm^2/V-s (mobility of electron)\n",
+ "Na=2E17; #in /m^3 (acceptor doping concentration)\n",
+ "e=1.6E-19; #in C(charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "uh=uh*1E-4; #changing unit from cm^2/V-s to m^2/V-s\n",
+ "Na=Na*1E6; #changing unit from 1/cm^3 to 1/m^3\n",
+ "nh=Na; #hole concentration \n",
+ "#since sigma=ne*ue*e+nh*uh*e and nh>>ne\n",
+ "#therefore sigma=nh*uh*e\n",
+ "sigma=nh*uh*e; #calculation of conductivity\n",
+ "\n",
+ "#result\n",
+ "print\"The conductivity of p-type Ge crystal is =\",sigma,\"/ohm-m (roundoff error)\";\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The conductivity of p-type Ge crystal is = 6080.0 /ohm-m (roundoff error)\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.12 , Page no:277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ue=0.19; #in m^2/V-s (mobility of electron)\n",
+ "T=300; #in K (temperature)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "e=1.6E-19; #in C(charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "Dn=ue*k*T/e; #calculation of diffusion co-efficient\n",
+ "\n",
+ "#result\n",
+ "print\"The diffusion co-efficient of electron in silicon is Dn=\",'%.3E'%Dn,\"m^2/s\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The diffusion co-efficient of electron in silicon is Dn= 4.916E-03 m^2/s\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.13 , Page no:277"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "Eg=0.4; #in eV (Band gap of semiconductor)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "T1=0; #in degree Celcius (first temperature)\n",
+ "T2=50; #in degree Celcius (second temperature)\n",
+ "T3=100; #in degree Celcius (third temperature)\n",
+ "e=1.602E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "T1=T1+273; #changing temperature form Celcius to Kelvin\n",
+ "T2=T2+273; #changing temperature form Celcius to Kelvin\n",
+ "T3=T3+273; #changing temperature form Celcius to Kelvin\n",
+ "Eg=Eg*e; #changing unit from eV to Joule\n",
+ "#Using F_E=1/(1+exp(Eg/2*k*T))\n",
+ "F_E1=1/(1+math.exp(Eg/(2*k*T1))); #calculation of probability of occupation of lowest level at 0 degree Celcius\n",
+ "F_E2=1/(1+math.exp(Eg/(2*k*T2))); #calculation of probability of occupation of lowest level at 50 degree Celcius\n",
+ "F_E3=1/(1+math.exp(Eg/(2*k*T3))); #calculation of probability of occupation of lowest level at 100 degree Celcius\n",
+ "\n",
+ "#result\n",
+ "print\"The probability of occupation of lowest level in conduction band is\";\n",
+ "print\"\\t at 0 degree Celcius, F_E=\",'%.3E'%F_E1,\"eV\";\n",
+ "print\"\\t at 50 degree Celcius, F_E=\",'%.3E'%F_E2,\"eV\";\n",
+ "print\"\\t at 100 degree Celcius, F_E=\",'%.3E'%F_E3,\"eV\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The probability of occupation of lowest level in conduction band is\n",
+ "\t at 0 degree Celcius, F_E= 2.025E-04 eV\n",
+ "\t at 50 degree Celcius, F_E= 7.550E-04 eV\n",
+ "\t at 100 degree Celcius, F_E= 1.976E-03 eV\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.14 , Page no:278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "Eg=1.2; #in eV (Energy band gap)\n",
+ "k=1.38E-23; #in J/K (Boltzmann\u2019s constant)\n",
+ "T1=600; T2=300; #in K (two temperatures)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "Eg=Eg*e; #changing unit from eV to Joule\n",
+ "#since sigma is proportional to exp(-Eg/(2*k*T))\n",
+ "#therefore ratio=sigma1/sigma2=exp(-Eg/(2*k*((1/T1)-(1/T2))));\n",
+ "ratio= math.exp((-Eg/(2*k))*((1/T1)-(1/T2))); #calculation of ratio of conductivity at 600K and at 300K\n",
+ "\n",
+ "#result\n",
+ "print\"The ratio of conductivity at 600K and at 300K is =\",'%.3E'%ratio;"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The ratio of conductivity at 600K and at 300K is = 1.085E+05\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.15 , Page no:278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "ue=0.39; #in m^2/V-s (mobility of electron)\n",
+ "n=5E13; #number of donor atoms\n",
+ "ni=2.4E19; #in atoms/m^3 (intrinsic carrier density)\n",
+ "l=10; #in mm (length of rod)\n",
+ "a=1; #in mm (side of square cross-section)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "l=l*1E-3; #changing unit from mm to m\n",
+ "a=a*1E-3; #changing unit from mm to m\n",
+ "A=a**2; #calculation of cross-section area\n",
+ "Nd=n/(l*A); #calculation of donor concentration\n",
+ "ne=Nd; #calculation of electron density\n",
+ "nh=ni**2/Nd; #calculation of hole density\n",
+ "#since sigma=ne*e*ue+nh*e*ue and since ne>>nh\n",
+ "#therefore sigma=ne*e*ue\n",
+ "sigma=ne*e*ue; #calculation of conductivity\n",
+ "rho=1/sigma; #calculation of resistivity\n",
+ "R=rho*l/A; #calculation of resistance \n",
+ "\n",
+ "#result\n",
+ "print\"The electron density is ne=\",ne,\"/m^3\";\n",
+ "print\"The hole density is nh=\",nh,\"/m^3\";\n",
+ "print\"The conductivity is =\",sigma,\"/ohm-m\";\n",
+ "print\"The resistance is R=\",round(R),\"ohm\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The electron density is ne= 5e+21 /m^3\n",
+ "The hole density is nh= 1.152e+17 /m^3\n",
+ "The conductivity is = 312.0 /ohm-m\n",
+ "The resistance is R= 32.0 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.16 , Page no:279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "RH=3.66E-4; #in m^3/C (Hall coefficient)\n",
+ "rho=8.93E-3; #in ohm-m (resistivity)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "u=RH/rho; #calculation of mobility\n",
+ "n=1/(RH*e); #calculation of density\n",
+ "\n",
+ "#result\n",
+ "print\"The mobility is u=\",round(u,4),\"m^2/(V-s)\";\n",
+ "print\"The density is n=\",'%.3E'%n,\"/m^3\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The mobility is u= 0.041 m^2/(V-s)\n",
+ "The density is n= 1.708E+22 /m^3\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.17 , Page no:279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#given\n",
+ "RH=3.66E-4; #in m^3/C (Hall coefficient)\n",
+ "rho=8.93E-3; #in ohm-m (resistivity)\n",
+ "e=1.6E-19; #in C (charge of electron)\n",
+ "\n",
+ "#calculate\n",
+ "nh=1/(RH*e); #calculation of density of charge carrier\n",
+ "uh=1/(rho*nh*e); #calculation of mobility of charge carrier\n",
+ "\n",
+ "#result\n",
+ "print\"The density of charge carrier is nh=\",'%.3E'%nh,\"/m^3\";\n",
+ "print\"The mobility of charge carrier is uh=\",round(uh,4),\"m^2/(V-s)\";"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The density of charge carrier is nh= 1.708E+22 /m^3\n",
+ "The mobility of charge carrier is uh= 0.041 m^2/(V-s)\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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