{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 4: Junction Properties" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_10: Forward_biasing_voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.10\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "I_o = 2.4 * 10^-14;\n", "I = 1.5;// in mA\n", "I=I*10^-3;// in A\n", "Eta = 1;\n", "V_T = 26;// in mV\n", "V_T= V_T*10^-3;// in V\n", "v =log((I + I_o)/I_o) * V_T;// in V\n", "disp(v,'The forward biasing voltage across the junction in V is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_11: Theoretical_diode_current.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.11\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "I_o = 10;// in nA\n", "// I = I_o * ((e^(v/(Eta * V_T))) - 1)\n", "// e^(v/(Eta * V_T)<< 1, so neglecting it\n", "I = I_o * (-1);// in nA\n", "disp(I,'The Diode current in nA is ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_12: Diode_dynamic_resistance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.12\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "R = 4.5;// in ohm\n", "I = 44.4;// in mA\n", "I=I*10^-3;// in A\n", "V = R * I;// in V\n", "Eta = 1;\n", "V_T = 26;//in mV\n", "V_T=V_T*10^-3;// in V\n", "I_o = I/((%e^(V/(Eta * V_T))) -1);// in A\n", "// At\n", "V = 0.1;// in V\n", "r_f = (Eta * V_T)/(I_o * ((%e^(V/(Eta * V_T)))-1));// in ohm\n", "disp(r_f,'The diode dynamic resistance in Ω is');\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_13: Q_point.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.13\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "V_D = 10;// in V\n", "// V_S = i*R_L + V_D\n", "V_S = V_D;// in V (i * R_L = 0)\n", "disp(V_S,'when diode is OFF, the voltage in volts is : ');\n", "R_L = 250;// in ohm\n", "I = V_S/R_L;// in A\n", "disp(I*10^3,'when diode is ON, the current in mA is');\n", "V_D= 0:0.1:10;// in V\n", "I= (V_S-V_D)/R_L*1000;// in mA\n", "plot(V_D,I)\n", "xlabel('V_D in volts');\n", "ylabel('Current in mA')\n", "title('DC load line');\n", "disp('DC load line shown in figure')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_14: AC_resistance_of_a_Ge_diode.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.14\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "V = 0.25;// in V\n", "I_o = 1.2;// in µA\n", "I_o = I_o * 10^-6;// in A\n", "V_T = 26;// in mV\n", "V_T = V_T * 10^-3;// in V\n", "Eta = 1;\n", "r = (Eta * V_T)/(I_o * (%e^(V/(Eta * V_T))));// in ohm\n", "disp(r,'The ac resistance of the diode in ohm is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_15: Junction_potential.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.15\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "t = 4.4 * 10^22;// in total number of atoms/cm^3\n", "n = 1 * 10^8;// number of impurity\n", "N_A = t/n;// in atoms/cm^3\n", "N_A = N_A * 10^6;// in atoms/m^3\n", "N_D = N_A * 10^3;// in atoms/m^3\n", "V_T = 26;// in mV\n", "V_T = V_T * 10^-3;// in V\n", "n_i = 2.5 * 10^19;// in /cm^3\n", "V_J = V_T * log((N_A * N_D)/(n_i)^2);// in V\n", "disp(V_J,'The junction potential in V is')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_16: Dynamic_resistance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.16\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "Eta = 1;\n", "I_o = 30;// in MuA\n", "I_o = I_o * 10^-6;// in A\n", "v = 0.2;// in V\n", "K = 1.381 * 10^-23;// in J/degree K \n", "T = 125;// in °C\n", "T = T + 273;// in K\n", "q = 1.6 * 10^-19;// in C\n", "V_T = (K*T)/q;// in V\n", "r_f = (Eta * V_T)/(I_o * (%e^(v/(Eta * V_T))));// in ohm\n", "disp(r_f,'The forward dynamic resistance in ohm is');\n", "r_f1 = (Eta * V_T)/(I_o * (%e^(-(v)/(Eta * V_T))));// in ohm\n", "disp(r_f1*10^-3,'The Reverse dynamic resistance in kΩ is');\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_17: Space_charge_capacitance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.17\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "q = 1.6 * 10^-19;// in C\n", "N_A = 3 * 10^20;// in /m^3\n", "A = 1;// in µm^2\n", "A = A * 10^-6;// in m^2\n", "V = -10;// in V\n", "V_J = 0.25;// in V\n", "V_B = V_J - V;// in V\n", "epsilon_o = 8.854;// in pF/m\n", "epsilon_o = epsilon_o * 10^-12;// in F/m\n", "epsilon_r = 16;\n", "epsilon = epsilon_o * epsilon_r;\n", "W = sqrt((V_B * 2 * epsilon)/(q * N_A));// in m \n", "disp(W*10^6,'The width of depletion layer in µm is');\n", "C_T = (epsilon * A)/W;// in pF\n", "disp(C_T*10^12,'the space charge capacitance in pF is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_18: Barrier_capacitance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.18\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "W = 2 * 10^-4;// in cm\n", "W = W * 10^-2;// in m\n", "A = 1;// in mm^2\n", "A = A * 10^-6;// in m^2\n", "epsilon_r = 16;\n", "epsilon_o = 8.854 * 10^-12;// in F/m\n", "epsilon = epsilon_r * epsilon_o;\n", "C_T = (epsilon * A)/W;// in F\n", "disp(C_T*10^12,'The barrier capacitance in pF is');\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_19: Diameter.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.19\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "C_T = 100;// in pF\n", "C_T=C_T*10^-12;// in F\n", "epsilon_r = 12;\n", "epsilon_o = 8.854 * 10^-12;// in F/m\n", "epsilon = epsilon_r * epsilon_o;\n", "Rho_p = 5;// in ohm-cm\n", "Rho_p = Rho_p * 10^-2;// in ohm-m\n", "V_j = 0.5;// in V\n", "V = -4.5;// in V\n", "Mu_p = 500;// in cm^2\n", "Mu_p = Mu_p * 10^-4;// in m^2\n", "Sigma_p = 1/Rho_p;// in per ohm-m\n", "qN_A = Sigma_p/ Mu_p;\n", "V_B = V_j - V;\n", "W = sqrt((V_B * 2 * epsilon)/qN_A);// in m\n", "//C_T = (epsilon * A)/W;\n", "A = (C_T * W)/ epsilon;// in m\n", "D = sqrt(A * (4/%pi));// in m\n", "D = D * 10^3;// in mm\n", "disp(D,'The diameter in mm is');\n", " " ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_1: Contact_difference_of_potential.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// EXa 4.16.1\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "t = 4.4 * 10^22;// total number of Ge atoms/cm^3\n", "n = 1 * 10^8;// number of impurity atoms\n", "N_A = t/n;// in atoms/cm^3\n", "N_A = N_A * 10^6;// in atoms/m^3\n", "N_D = N_A * 10^3;// in atoms/m^3\n", "n_i = 2.5 * 10^13;// in atoms/cm^3\n", "n_i = n_i * 10^6;// in atoms/m^3\n", "V_T = 26;//in mV\n", "V_T= V_T*10^-3;// in V\n", "V_J = V_T * log((N_A * N_D)/(n_i)^2);// in V\n", "disp(V_J,'The contact potential in V is');\n", "// Part (b)\n", "t = 5* 10^22;// total number of Si atoms/cm^3\n", "N_A = t/n;// in atoms/cm^3\n", "N_A = N_A * 10^6;// in atoms/m^3\n", "N_D = N_A * 10^3;// in atoms/m^3\n", "n_i = 1.5 * 10^10;// in atoms/cm^3\n", "n_i = n_i * 10^6;// in atoms/m^3\n", "V_T = 26;//in mV\n", "V_T= V_T*10^-3;// in V\n", "V_J = V_T * log((N_A * N_D)/(n_i)^2);// in V\n", "disp(V_J,'The contact potential in V is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_20: Temperature_of_junction.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.20\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "q = 1.6 * 10^-19;// in C\n", "Mu_p = 500;// in cm^2/V-sec\n", "Rho_p = 3.5;// in ohm-cm\n", "Mu_n = 1500;// in cm^2/V-sec\n", "Rho_n = 10;// in ohm-cm\n", "N_A = 1/(Rho_p * Mu_p * q);// in /cm^3\n", "N_D = 1/(Rho_n * Mu_n * q);// in /cm^3\n", "V_J = 0.56;// in V\n", "n_i = 1.5 * 10^10;// in /cm^3\n", "V_T = V_J/log((N_A * N_D)/(n_i)^2);// in V\n", "// V_T = T/11600\n", "T = V_T * 11600;// in K\n", "T = T - 273;// in °C\n", "disp(T,'The Temperature of junction in °C is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_21: Voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.21\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "V_T = 26;// in mV\n", "V_T = V_T * 10^-3;// in V\n", "Eta = 1;\n", "// I = -90% for Io, so\n", "IbyIo= 0.1;\n", "// I = I_o * ((e^(v/(Eta * V_T)))-1)\n", "V = log(IbyIo) * V_T;// in V\n", "disp(V,'The reverse bias voltage in volts is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_22: Reverse_saturation_current.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.22\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "R = 5;// in ohm\n", "I = 50;// in mA\n", "I=I*10^-3;// in A\n", "V = R * I;// in V\n", "Eta = 1;\n", "V_T = 26;// in mV\n", "V_T=V_T*10^-3;// in V\n", "I_o = I/((%e^(V/(Eta * V_T))) - 1);// in A\n", "disp(I_o*10^6,'Reverse saturation current in µA is');\n", "v1 = 0.2;// in V\n", "r = (Eta * V_T)/(I_o * (%e^(v1/(Eta * V_T))));// in ohm\n", "disp(r,'Dynamic resistance of the diode in Ω is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_2: Height_of_the_potential_energy_barrier.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.2\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "V_T = 26;// in mV\n", "V_T=V_T*10^-3;// in V\n", "n_i = 2.5 * 10^13;\n", "Sigma_p = 1;\n", "Sigma_n = 1;\n", "Mu_n = 3800;\n", "q = 1.6 * 10^-19;// in C\n", "Mu_p = 1800;\n", "N_A = Sigma_p/(2* q * Mu_p);// in /cm^3\n", "N_D = Sigma_n /(q * Mu_n);// in /cm^3\n", "V_J = V_T * log((N_A * N_D)/(n_i)^2);// in V\n", "disp(V_J,'For Ge the height of the energy barrier in V is');\n", "// For Si p-n juction\n", "n_i = 1.5 * 10^10;\n", "Mu_n = 1300;\n", "Mu_p = 500;\n", "N_A = Sigma_p/(2* q * Mu_p);// in /cm^3\n", "N_D = Sigma_n /(q * Mu_n);// in /cm^3\n", "V_J = V_T * log((N_A * N_D)/(n_i)^2);// in V\n", "disp(V_J,'For Si p-n junction the height of the energy barrier in V is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_3: Forward_current.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 4.16.3\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "Eta = 1;\n", "V_T = 26;// in mV\n", "V_T= V_T*10^-3;// in V\n", "// I = I_o * (%e^(V/(Eta*V_T)) - 1) and I = -(0.9) * I_o;\n", "V= log(1-0.9)*V_T;// in V\n", "disp(V,'The voltage in volts is : ')\n", "// Part (ii)\n", "V1=0.05;// in V\n", "V2= -0.05;// in V\n", "ratio= (%e^(V1/(Eta*V_T))-1)/(%e^(V2/(Eta*V_T))-1)\n", "disp(ratio,'The ratio of the current for a forward bias to reverse bias is : ')\n", "// Part (iii)\n", "Io= 10;// in µA\n", "Io=Io*10^-3;// in mA\n", "//For \n", "V=0.1;// in V\n", "I = Io * (%e^(V/(Eta*V_T)) - 1);// in mA\n", "disp(I,'For V=0.1 V , the value of I in mA is : ')\n", "//For \n", "V=0.2;// in V\n", "I = Io * (%e^(V/(Eta*V_T)) - 1);// in mA\n", "disp(I,'For V=0.2 V , the value of I in mA is : ')\n", "//For \n", "V=0.3;// in V\n", "I = Io * (%e^(V/(Eta*V_T)) - 1);// in mA\n", "disp(I*10^-3,'For V=0.3 V , the value of I in A is : ')\n", "disp('From three value of I, for small rise in forward voltage, the diode current increase rapidly')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_4: Anticipated_factor.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 4.16.4\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "// Part (i)\n", "T1= 25;// in °C\n", "T2= 80;// in °C\n", "// Formula Io2= Io1*2^((T2-T1)/10)\n", "AntiFactor= 2^((T2-T1)/10);\n", "disp(round(AntiFactor),'Anticipated factor for Ge is : ')\n", "// Part (ii)\n", "T1= 25;// in °C\n", "T2= 150;// in °C\n", "AntiFactor= 2^((T2-T1)/10);\n", "disp(round(AntiFactor),'Anticipated factor for Si is : ')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_5: Leakage_resistance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 4.16.5\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "I=5;// in µA\n", "V=10;// in V\n", "T1= 0.11;// in °C^-1\n", "T2= 0.07;// in °C^-1\n", "// Io+I_R=I (i)\n", "// dI_by_dT= dIo_by_dT (ii)\n", "// 1/Io*dIo_by_dT = T1 and 1/I*dI_by_dT = T2, So\n", "Io= T2*I/T1;// in µA\n", "I_R= I-Io;// in µA\n", "R= V/I_R;// in MΩ\n", "disp(R,'The leakage resistance in MΩ is : ')" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_6: Dynamic_resistance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 4.16.6\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "Eta = 1;\n", "T = 125;// in °C\n", "T = T + 273;// in K\n", "V_T = 8.62 * 10^-5 * 398;// in V\n", "I_o = 30;// in µA\n", "I_o= I_o*10^-6;// in A\n", "v = 0.2;// in V\n", "r_f = (Eta * V_T)/(I_o * %e^(v/(Eta* V_T)));// in ohm\n", "disp(r_f,'The dynamic resistance in the forward direction in ohm is ');\n", "r_r = (Eta * V_T)/(I_o * %e^(-v/(Eta* V_T)));// in ohm\n", "disp(r_r*10^-3,'The dynamic resistance in the reverse direction in kohm is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_7: Barrier_capacitance.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.7\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "epsilon = 16/(36 * %pi * 10^11);// in F/cm\n", "A = 1 * 10^-2;\n", "W = 2 * 10^-4;\n", "C_T = (epsilon * A)/W;// in F\n", "disp(C_T*10^12,'The barrier capacitance in pF is');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_8: Width_of_the_depletion_layer.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 4.16.8\n", "clc;\n", "clear;\n", "close;\n", "//Given data\n", "A = 1;// in mm^2\n", "A = A * 10^-6;// in m^2\n", "N_A = 3 * 10^20;// in atoms/m^3\n", "q = 1.6 *10^-19;// in C\n", "V_o = 0.2;// in V\n", "epsilon_r=16;\n", "epsilon_o= 8.854*10^-12;// in F/m\n", "epsilon=epsilon_r*epsilon_o;\n", "// Part (a)\n", "V=-10;// in V\n", "// V_o - V = 1/2*((q * N_A )/epsilon) * W^2\n", "W = sqrt(((V_o - V) * 2 * epsilon)/(q * N_A));// m\n", "C_T1 = (epsilon * A)/W;// in F\n", "disp(W*10^6,'The width of the depletion layer for an applied reverse voltage of 10V in µm is ');\n", "// Part (b)\n", "V=-0.1;// in V\n", "W = sqrt(((V_o - V) * 2 * epsilon)/(q * N_A));// m\n", "C_T2 = (epsilon * A)/W;// in F\n", "disp(W*10^6,'The width of the depletion layer for an applied reverse voltage of 0.1V in µm is ');\n", "// Part (c)\n", "V=0.1;// in V\n", "W = sqrt(((V_o - V) * 2 * epsilon)/(q * N_A));// m\n", "disp(W*10^6,'The width of the depletion layer for an applied for a forward bias of 0.1V in µm is ');\n", "// Part (d)\n", "disp(C_T1*10^12,'The space charge capacitance for an applied reverse voltage of 10V in pF is');\n", "disp(C_T2*10^12,'The space charge capacitance for an applied reverse voltage of 0.1V in pF is');\n", "\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 4.16_9: Current_in_the_junction.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "// Exa 4.16.9\n", "clc;\n", "clear;\n", "close;\n", "// Given data\n", "I_o = 1.8 * 10^-9;// A\n", "v = 0.6;// in V\n", "Eta = 2;\n", "V_T = 26;// in mV\n", "V_T=V_T*10^-3;// in V\n", "I = I_o *(%e^(v/(Eta * V_T)));// in A\n", "disp(I*10^3,'The current in the junction in mA is');" ] } ], "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 }