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Chapter 1: Problem 44

Find the applied reverse bias potential if the transition capacitance of a silicon diode is \(4 \mathrm{pF}\) but the no-bias level is \(10 \mathrm{pF}\) with \(n=1 / 3\) and \(V_{K}=0.7 \mathrm{~V}\).

Short Answer

Expert verified
The applied reverse bias potential is \(0.65 \mathrm{V}\).

Step by step solution

01

Understanding the concepts

The transition capacitance of a diode, also known as junction capacitance, relates to the variable capacitance of the diode junction. It depends on the diode's working state, whether it is forward biased or reverse biased. In reverse bias, the depletion region widens; therefore the capacitance decreases. The no-bias level refers to the capacitance when there is no bias applied, i.e., zero volts regime.
02

Applying the formula

We are going to use the formula for junction capacitance in reverse bias, which is: \(C_{t} = \frac{C_{0}}{(1 + \frac{V}{V_{k}})^n}\), where \(C_{t}\) is the transition capacitance, \(C_{0}\) is the no-bias level or zero-bias junction capacitance, \(V\) is the applied reverse-bias potential, \(V_{k}\) is the knee voltage, and \(n\) is the grading coefficient, ranging from 1/3 for a step junction to 1/2 for a linearly graded junction. For this problem, \(C_{t} = 4 \mathrm{pF}\), \(C_{0} = 10 \mathrm{pF}\), \(n=1/3\), and \(V_{k} = 0.7 \mathrm{V}\). We will solve for \(V\).
03

Substituting the given values

Now that we have the formula, we substitute the given values to get: \(4 = \frac{10}{(1 + \frac{V}{0.7})^{1/3}}\)
04

Solving for the unknown

With some algebraic manipulation, the equation above simplifies to: \((1 + \frac{V}{0.7})^{1/3} = 2.5\). After squaring both sides, we then get \(V = 2.45 \times 0.7 - 0.7 = 0.65 \mathrm{V}\)

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Most popular questions from this chapter

a. Determine the thermal voltage for a diode at a temperature of \(20^{\circ} \mathrm{C}\). b. For the same diode of part (a), find the diode current using Eq. 2 if \(I_{s}=40 \mathrm{nA}, n=2\) (low value of \(V_{D}\) ), and the applied bias voltage is \(0.5 \mathrm{~V}\).

Describe the difference between \(n\) -type and \(p\) -type semiconductor materials.

Determine the temperature coefficient of a 5-V Zener diode (rated \(25^{\circ} \mathrm{C}\) value) if the nominal voltage drops to \(4.8 \mathrm{~V}\) at a temperature of \(100{ }^{\circ} \mathrm{C}\).

Sketch the atomic structure of copper and discuss why it is a good conductor and how its structure is different from that of germanium, silicon, and gallium arsenide.

Describe the difference between donor and acceptor impurities.
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