**In this article, we will draw characteristic curves of a diode at different temperatures.**

From the following equation, it is evident that the thermal voltage and the reverse saturation current of a diode depend on the temperature.

$i={{I}_{s}}\left[ {{e}^{\left( {}^{v}/{}_{n{{V}_{T}}} \right)}}-1 \right]\text{ }\cdots \text{ (1)}$

I_{S} is reverse saturation current or leakage current,

n is an empirical constant between 1 and 2,

V_{T} is thermal voltage, given by

$\begin{matrix} {{V}_{T}}=\frac{kT}{q} & \cdots & (2) \\\end{matrix}$

k is Boltzmann’s constant = 1.38×10^{−23} J / ^{o}K,

q is the electronic charge = 1.6×10^{−19} Coulombs,

T is the absolute temperature in ^{o}K

At room temperature (25 ^{o}C), the thermal voltage is about 25.7 mV.

The reverse saturation current *I _{s}* of a diode increases by 7.2%/

^{0}C for germanium as well as for silicon material. The reverse saturation current can be expressed as:

$\begin{matrix} {{I}_{s}}({{T}_{2}})={{I}_{s}}({{T}_{1}}){{e}^{\left[ {{k}_{s}}({{T}_{2}}-{{T}_{1}}) \right]}} & \cdots & (3) \\\end{matrix}$

Where

\[{{k}_{s}}=0.072/{}^{o}C\]

And T_{1} and T_{2} represent different temperatures.

**Example:**

Saturation current of a diode at 25^{o}C=10^{-12} A

Emission Constant=1.9

Let’s plot the v-i curves at the following temperatures: *T*_{1} = 0 ^{0}C, *T*_{2} = 100 ^{0}C using Matlab:

% Temperature effects on diode characteristics clear all;close all;clc %%Parameters and Formulation Part k_Boltz = 1.38e-23; % Boltzman Constant q_Electron = 1.6e-19; % q is the electron charge T1 = 273 + 0; %Temperature Conversion to Kelvin Scale T2 = 273 + 100; %Temperature Conversion to Kelvin Scale l_saturation1 = 1.0e-12; % Saturation Current k_saturation = 0.072; % Saturation Constant l_saturation2 = l_saturation1*exp(k_saturation*(T2-T1)); % Saturation Current mentioned in (3) in text V_diode = 0.45:0.01:0.7; % Voltage Sampling l_T1 = l_saturation1*exp(q_Electron*V_diode/(k_Boltz*T1)); % Diode Current at T1 l_T2 = l_saturation2*exp(q_Electron*V_diode/(k_Boltz*T2)); % Diode Current at T2 %% Plotting the Results plot(V_diode,l_T1,'r',V_diode,l_T2,'g') axis([0.45,0.75,0,10]) title('Diode I-V Curve at two Temperatures') xlabel('Voltage (V)') ylabel('Current (A)')

**Results:**

Fig.1: Diode Characteristic Curves