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Chapter 1: Problem 18

Given a diode current of \(8 \mathrm{~mA}\) and \(n=1\), find \(I_{s}\) if the applied voltage is \(0.5 \mathrm{~V}\) and the temperature is room temperature \(\left(25^{\circ} \mathrm{C}\right)\).

Short Answer

Expert verified
The solution to the problem is the saturation current \(I_s\), which is found by substituting the given values into the rearranged Shockley's diode equation and performing the calculations. The specific value of \(I_s\) is found by calculating \(\frac{8 \times 10^{-3}}{e^{0.5/0.02586}-1}\).

Step by step solution

01

Convert parameters to standard units

The given current \(I\) is in milliamps (mA), so it needs to be converted to amps (A) by multiplying by \(10^{-3}\). Hence, \(I = 8 \times 10^{-3} A\). The temperature \(T\) which is given in Celsius should be converted to Kelvin by adding 273.15 to the Celsius value. Hence, \(T = 25 + 273.15 = 298.15 K\). The thermal voltage \(V_T\) can be calculated from the temperature by the equation \(V_T = k \times T/q\), where \(k\) is Boltzmann's constant \(1.38 \times 10^{-23} J/K\) and \(q\) is the elementary charge \(1.602 \times 10^{-19} C\) . Thus \(V_T = \frac{1.38 \times 10^{-23} \times 298.15}{1.602 \times 10^{-19}} = 0.02586 V\)
02

Substitute given values into Shockley's diode equation

For a diode, the Shockley diode equation is defined as \(I = I_s(e^{V/nV_T}-1)\). Here, we know \(I\), \(V\), \(n\), and \(V_T\), and we are expected to find \(I_s\). We can arrange the Shockley diode equation to determine \(I_s\): \(I_s = I/(e^{V/nV_T}-1)\). Substitute \(I = 8 \times 10^{-3} A\), \(V = 0.5 V\), \(n = 1\) and \(V_T = 0.02586 V\) into the equation to get \(I_s\).
03

Calculate the saturation current

After substituting the given values, the equation becomes \(I_s = \frac{8 \times 10^{-3}}{e^{0.5/0.02586}-1}\). Calculating this value will give us \(I_s\). This can be done by using a calculator and doing the exponentiation and subtraction first, then performing the division.

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