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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 2: Semiconductor Physics"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_1: calculate_mobility_of_electro.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_1,pg 2-47\n",
+"\n",
+"ro=1.72*10^-8 //resistivity of Cu\n",
+"\n",
+"s=1/ro //conductivity of Cu\n",
+"\n",
+"n=10.41*10^28 //no of electron per unit volume\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"u=s/(n*e)\n",
+"\n",
+"printf('mobility of electron in Cu =')\n",
+"\n",
+"disp(u)\n",
+"\n",
+"printf('m^2/volt-sec')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_2: calculate_Resistivity_of_Cu.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_2,pg 2-47\n",
+"\n",
+"m=63.5 //atomic weight\n",
+"\n",
+"u=43.3 //mobility of electron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"N=6.02*10^23 //Avogadro's number\n",
+"\n",
+"d=8.96 //density\n",
+"\n",
+"Ad=N*d/m //Atomic density\n",
+"\n",
+"n=1*Ad\n",
+"\n",
+"ro=1/(n*e*u)\n",
+"\n",
+"printf('Resistivity of Cu =')\n",
+"\n",
+"disp(ro)\n",
+"\n",
+"printf('ohm-cm')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_3: calculate_Resistivity_of_Ge.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_3,pg 2-47\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"ne=2.5*10^19 //density of carriers\n",
+"\n",
+"nh=ne //for intrinsic semiconductor\n",
+"\n",
+"ue=0.39 //mobility of electron\n",
+"\n",
+"uh=0.19 //mobility of hole\n",
+"\n",
+"s=ne*e*ue+nh*e*uh //conductivity of Ge\n",
+"\n",
+"ro=1/s //resistivity of Ge\n",
+"\n",
+"printf('Resistivity of Ge =')\n",
+"\n",
+"disp(ro)\n",
+"\n",
+"printf('ohm-m')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_5: calculate_Ratio_between_conductivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_5,pg 2-48\n",
+"\n",
+"Eg=1.2 //energy gap\n",
+"\n",
+"T1=600 //temperature\n",
+"\n",
+"T2=300 //temperature\n",
+"\n",
+"//since ue>>uh for intrinsic semiconductor\n",
+"\n",
+"//s=ni*e*ue\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant\n",
+"\n",
+"s=%s\n",
+"\n",
+"s1=s*exp((-Eg)/(2*K*T1))\n",
+"\n",
+"s2=s*exp((-Eg)/(2*K*T2))\n",
+"\n",
+"m=(s1/s2)\n",
+"\n",
+"printf('Ratio between conductivity =')\n",
+"\n",
+"disp(m)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_6: calculate_conductivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_6,pg 2-49\n",
+"\n",
+"c=5*10^28 //concentration of Si atoms\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"u=0.048 //mobility of hole\n",
+"\n",
+"s=4.4*10^-4 //conductivity of Si\n",
+"\n",
+"//since millionth Si atom is replaced by an indium atom\n",
+"\n",
+"n=c*10^-6\n",
+"\n",
+"sp=u*e*n //conductivity of resultant\n",
+"\n",
+"printf('conductivity =')\n",
+"\n",
+"disp(sp)\n",
+"\n",
+"printf('mho/m')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.21_7: calculate_hole_concentration_and_mobility.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_21_7,pg 2-49\n",
+"\n",
+"m=28.1 //atomic weight of Si\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"N=6.02*10^26 //Avogadro's number\n",
+"\n",
+"d=2.4*10^3 //density of Si\n",
+"\n",
+"p=0.25 //resistivity\n",
+"\n",
+"//no. of Si atom/m^3\n",
+"\n",
+"Ad=N*d/m //Atomic density\n",
+"\n",
+"//impurity level is 0.01 ppm i.e. 1 atom in every 10^8 atoms of Si\n",
+"\n",
+"n=Ad/10^8 //no of impurity atoms\n",
+"\n",
+"//since each impurity produce 1 hole\n",
+"\n",
+"nh=n\n",
+"\n",
+"printf('1) hole concentration =')\n",
+"\n",
+"disp(n)\n",
+"\n",
+"printf('holes/m^3')\n",
+"\n",
+"up=1/(e*p*nh)\n",
+"\n",
+"printf(' 2) mobility =')\n",
+"\n",
+"disp(up)\n",
+"\n",
+"printf('m^2/volt.sec') "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.22_1: calculate_probability_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_22_1,pg 2-50\n",
+"\n",
+"t=27 //temp in degree \n",
+"\n",
+"T=t+273 //temp in kelvin\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant in eV\n",
+"\n",
+"Eg=1.12 //Energy band gap\n",
+"\n",
+"//For intrensic semiconductor (Ec-Ev)=Eg/2\n",
+"\n",
+"//let (Ec-Ev)=m\n",
+"\n",
+"m=Eg/2\n",
+"\n",
+"a=(m/(K*T))\n",
+"\n",
+"//probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n",
+"\n",
+"p=1/(1+exp(a))\n",
+"\n",
+"\n",
+"printf('probability of an electron being thermally excited to conduction band=')\n",
+"\n",
+"disp(p)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.22_2: calculate_probability_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_22_2,pg 2-50\n",
+"\n",
+"T=300 //temp in kelvin\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant in eV\n",
+"\n",
+"m=0.012 //energy level(Ef-E)\n",
+"\n",
+"a=(m/(K*T))\n",
+"\n",
+"//probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n",
+"\n",
+"p=1/(1+exp(a))\n",
+"\n",
+"p1=1-p\n",
+"\n",
+"printf('probability of an energy level not being occupied by an electron=')\n",
+"\n",
+"disp(p1)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.22_3: calculate_probability_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_22_3,pg 2-51\n",
+"\n",
+"t=20 //temp in degree \n",
+"\n",
+"T=t+273 //temp in kelvin\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant in eV\n",
+"\n",
+"Eg=1.12 //Energy band gap\n",
+"\n",
+"//For intrensic semiconductor (Ec-Ev)=Eg/2\n",
+"\n",
+"//let (Ec-Ev)=m\n",
+"\n",
+"m=Eg/2\n",
+"\n",
+"a=(m/(K*T))\n",
+"\n",
+"//probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n",
+"\n",
+"p=1/(1+exp(a))\n",
+"\n",
+"\n",
+"printf('probability of an electron being thermally excited to conduction band=')\n",
+"\n",
+"disp(p)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.22_4: calculate_energy_for_different_probability.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_22_4,pg 2-51\n",
+"\n",
+"T=300 //temp in kelvin\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant in eV\n",
+"\n",
+"Eg=2.1 //Energy band gap\n",
+"\n",
+"//probability f(Ec)=1/(1+exp((Ec-Ev)/(K*T))\n",
+"\n",
+"m=K*T\n",
+"\n",
+"//for f(E)=0.99\n",
+"\n",
+"p1=0.99\n",
+"\n",
+"b=1-1/p1\n",
+"\n",
+"a=log(b) //a=(E-2.1)/m\n",
+"\n",
+"E=2.1+m*a\n",
+"\n",
+"printf('1) Energy for which probability is 0.99=')\n",
+"\n",
+"disp(real(E))\n",
+"\n",
+"printf('eV')\n",
+"\n",
+"//for f(E)=0.01\n",
+"\n",
+"p2=0.01\n",
+"\n",
+"b2=1-1/p2\n",
+"\n",
+"a1=log(b2) //a=(E-2.1)/m\n",
+"\n",
+"E1=2.1+m*a1\n",
+"\n",
+"printf('2)Energy for which probability is 0.01=')\n",
+"\n",
+"disp(real(E1))\n",
+"\n",
+"printf('eV')\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_1: calculate_Potential_barrier_for_Ge.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_1,pg 2-52\n",
+"\n",
+"ni=2.4*10^19 //density of intrensic semiconductor\n",
+"\n",
+"n=4.4*10^28 //no atom in Ge crystal\n",
+"\n",
+"Nd=n/10^6 //density\n",
+"\n",
+"Na=Nd\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"T=300 //temerature at N.T.P.\n",
+"\n",
+"K=1.38*10^-23 //Boltzman constant\n",
+"\n",
+"Vo=(K*T/e)*log(Na*Nd/(ni^2))\n",
+"\n",
+"printf('Potential barrier for Ge =')\n",
+"\n",
+"disp(Vo)\n",
+"\n",
+"printf('Volts')\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_2: calculate_Hall_voltage.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_2,pg 2-52\n",
+"\n",
+"B=0.6 //magnetic field\n",
+"\n",
+"d=5*10^-3 //distancebetween surface\n",
+"\n",
+"J=500 //current density\n",
+"\n",
+"Nd=10^21 //density\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"Vh=(B*J*d)/(Nd*e) //due to Hall effect\n",
+"\n",
+"printf('Hall voltage =')\n",
+"\n",
+"disp(Vh)\n",
+"\n",
+"printf('Volts')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_3: calculate_Hall_voltage.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_3,pg 2-53\n",
+"\n",
+"Rh=6*10^-7 //Hall coefficient\n",
+"\n",
+"B=1.5 //magnetic field\n",
+"\n",
+"I=200 //current in strip\n",
+"\n",
+"W=1*10^-3 //thickness of strip\n",
+"\n",
+"Vh=Rh*(B*I)/W //due to Hall effect\n",
+"\n",
+"printf('Hall voltage =')\n",
+"\n",
+"disp(Vh)\n",
+"\n",
+"printf('Volt')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_4: calculate_Resistivity_of_P_type_silico.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_4,pg 2-53\n",
+"\n",
+"Rh=2.25*10^-5 //Hall coefficient\n",
+"\n",
+"u=0.025 //mobility of hole\n",
+"\n",
+"r=Rh/u\n",
+"\n",
+"printf('Resistivity of P type silicon =')\n",
+"\n",
+"disp(r)\n",
+"\n",
+"printf('ohm-m')\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_5: calculate_hall_voltage_hall_coefficient_and_hall_angle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_5,pg 2-53\n",
+"\n",
+"B=0.55 //magnetic field\n",
+"\n",
+"d=4.5*10^-3 //distancebetween surface\n",
+"\n",
+"J=500 //current density\n",
+"\n",
+"n=10^20 //density\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"Rh=1/(n*e) //Hall coefficient\n",
+"\n",
+"Vh=Rh*B*J*d //Hall voltage\n",
+"\n",
+"printf(' 1) Hall voltage =')\n",
+"\n",
+"disp(Vh)\n",
+"\n",
+"printf('Volts')\n",
+"\n",
+"printf(' 2) Hall coefficient =')\n",
+"\n",
+"disp(Rh)\n",
+"\n",
+"printf('m^3/C')\n",
+"\n",
+"u=0.17 //mobility of electrom\n",
+"\n",
+"m=atan(u*B)\n",
+"\n",
+"a=m*180/%pi //conversion randian into degree\n",
+"\n",
+"printf(' 3) Hall angle =')\n",
+"\n",
+"disp(a)\n",
+"\n",
+"printf('degree')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_6: calculate_density_and_mobility.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_6,pg 2-54\n",
+"\n",
+"Rh=3.66*10^-4 //Hall coefficient\n",
+"\n",
+"r=8.93*10^-3 //resistivity \n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"//Hall coefficient Rh=1/(n*e)\n",
+"\n",
+"n=1/(Rh*e) //density\n",
+"\n",
+"printf(' 1) density(n) =')\n",
+"\n",
+"disp(n)\n",
+"\n",
+"printf('/m^3')\n",
+"\n",
+"u=Rh/r //mobility of electron\n",
+"\n",
+"printf(' 2) mobility (u) =')\n",
+"\n",
+"disp(u)\n",
+"\n",
+"printf('m^2/v-s')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.23_7: calculate_Hall_voltage.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_23_7,pg 2-55\n",
+"\n",
+"B=0.2 //magnetic field\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"ue=0.39 //mobility of electron\n",
+"\n",
+"l=0.01 //length\n",
+"\n",
+"A=0.001*0.001 //cross section area of bar\n",
+"\n",
+"V=1*10^-3 //Applied voltage\n",
+"\n",
+"d=0.001 //sample of width \n",
+"\n",
+"r=1/(ue*e) //resistivity\n",
+"\n",
+"R=r*l/A //resistance of Ge bar\n",
+"\n",
+"//using ohm's law\n",
+"\n",
+"I=V/R\n",
+"\n",
+"Rh=r*ue //hall coefficient\n",
+"\n",
+"//using formulae for hall effect\n",
+"\n",
+"J=I/A //current density\n",
+"\n",
+"Vh=Rh*B*J*d\n",
+"\n",
+"printf('Hall voltage =')\n",
+"\n",
+"disp(Vh)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.24_1: calculate_fermi_level.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-2,Example2_24_1,pg 2-55\n",
+"\n",
+"x1=0.4 //difference between fermi level and conduction band(Ec-Ef)\n",
+"\n",
+"T=300 //temp in kelvin\n",
+"\n",
+"K=8.62*10^-5 //Boltzman constant in eV\n",
+"\n",
+"//ne=N*e^(-(Ec-Ef)/(K*T))\n",
+"\n",
+"//ne is no of electron in conduction band\n",
+"\n",
+"//since concentration of donor electron is doubled\n",
+"\n",
+"a=2 //ratio of no of electron\n",
+"\n",
+"//let x2 be the difference between new fermi level and conduction band(Ec-Ef')\n",
+"\n",
+"x2=-log(a)*(K*T)+x1 //arranging equation ne=N*e^(-(Ec-Ef)/(K*T))\n",
+"\n",
+"printf('Fermi level will be shifted towards conduction band by')\n",
+"\n",
+"disp(x2)\n",
+"\n",
+"printf('eV')"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2025-07-04 18:29:08 +0000