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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7: Tunnelling phenomena"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.1: Transmission_coefficient_for_an_oxide_layer.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex7.1: Pg 235 (2005)\n",
+"clc; clear;\n",
+"c = 3e+08; // Velocity of light, m/s\n",
+"m_e = 511e+03/(c^2); // Mass of electron, eV\n",
+"U = 3.00; // Ground state energy neglecting E, eV\n",
+"h_cross = (1.973e+03)/c; // Reduced planck's constant, eV\n",
+"alpha = sqrt(2*m_e*U)/h_cross;\n",
+"L = 50; // Thickness of the layer, angstrom\n",
+"T = 1/(1+1/4*10^2/(7*3)*sinh(alpha*L)^2);\n",
+"printf('\nThe transmission coefficient for the layer thickness of');\n",
+"printf('\n%2d angstrom = %5.3e', L, T);\n",
+"L = 10; // // Thickness of the layer, angstrom\n",
+"T = 1/(1+1/4*10^2/(7*3)*sinh(alpha*L)^2);\n",
+"printf('\n%2d angstrom = %5.3e', L, T);\n",
+"\n",
+"// Result\n",
+"// The transmission coefficient for the layer thickness of\n",
+"// 50 angstrom = 9.628e-39\n",
+"// 10 angstrom = 6.573e-08 "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.2: Tunnelling_current_through_an_oxide_layer.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex7.2: Pg 236 (2005)\n",
+"clc; clear;\n",
+"e = 1.60e-19; // Electrc charge, C\n",
+"i = 1.00e-03; // Electron current, A\n",
+"N = i/e; // Electrons per second\n",
+"T = 0.657e-07; // Fraction of electrons transmitted\n",
+"T_e = N*T; // Number of electrons transmitted per second\n",
+"T_i = T_e*e; // Transmitted current, A\n",
+"printf('\nThe transmitted current through the oxide layer = %4.1f pA', T_i*1e+12);\n",
+"\n",
+"// Result\n",
+"// The transmitted current through the oxide layer = 65.7 pA "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.5: Tunnelling_in_a_parallel_plate_capacitor.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex7.5: Pg 241 (2005)\n",
+"clc; clear;\n",
+"epsilon_c = 5.5e+10; // Characteristic field strength, V/m\n",
+"epsilon = 1.0e+09; // Electric field, V/m\n",
+"f = 1.0e+30; // Collision frequency, s(-1)cm(-2)\n",
+"lamda = f*exp(-epsilon_c/epsilon); // Electron emission rate, electrons/sec\n",
+"e = 1.60e-19; // Electrc charge, C\n",
+"I = lamda*e; // Tunelling current, A\n",
+"printf('\nTunelling current in parallel plate capacitor = %4.2f pA', I/1e-12);\n",
+"printf('\n');\n",
+"\n",
+"// Result\n",
+"// Tunelling current in parallel plate capacitor = 0.21 pA"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 7.6: Estimating_halflives_of_Thorium_and_Polonium.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Scilab code Ex7.6: Pg 244 (2005)\n",
+"clc; clear;\n",
+"Z_T = 88; // Atomic number of daughter nucleus\n",
+"E_T = 4.05e+06; // Energy of ejected alphas, eV\n",
+"R = 9.00e-15; // Nuclear radius, m\n",
+"r_o = 7.25e-15; // Bohr radius, m\n",
+"E_o = 0.0993e+06; // Energy analogous to the Rydberg in Atomic Physics \n",
+"T_T = exp(-4*%pi*Z_T*sqrt(E_o/E_T) + 8*sqrt((Z_T*R)/r_o)); // Transmission factor in case of Thorium\n",
+"f = 1e+21; // Frequency of collisions, Hz\n",
+"lamda_T = f*T_T; // Decay rate in case of Thorium, s^(-1)\n",
+"t_T = 0.693/lamda_T; // Half-life time of Thorium, s\n",
+"Z_P = 82; // Atomic number of daughter nucleus\n",
+"E_P = 8.95e+06; // Energy of ejected alphas, eV\n",
+"R = 9.00e-15; // Nuclear radius, m\n",
+"r_o = 7.25e-15; // Bohr radius, m\n",
+"E_o = 0.0993e+06; // Energy unit, eV\n",
+"T_P = exp(-4*%pi*Z_P*sqrt(E_o/E_P) + 8*sqrt((Z_P*R)/r_o)); // Transmission factor in case of Polonium\n",
+"f = 1e+21; // Frequency of collisions, Hz\n",
+"lamda_P = f*T_P; // Decay rate in case of Thorium, s^(-1)\n",
+"t_P = 0.693/lamda_P; // Half-life time of Polonium, s\n",
+"\n",
+"printf('\nHalf-life time of Thorium = %3.1e s = %3.1e yrs', t_T, t_T/(365*24*60*60));\n",
+"printf('\nHalf-life time of Polonium = %3.1e s', t_P);\n",
+"\n",
+"// Result\n",
+"// Half-life time of Thorium = 5.3e+17 s = 1.7e+10 yrs\n",
+"// Half-life time of Polonium = 8.4e-10 s "
+ ]
+ }
+],
+"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
+}