Calculate the junction capacitance of a pn junction.

Consider the same pn junction as that in Example 7.3. Again assume that $V_{R}=5 \mathrm{~V}$ .

Question

Calculate the junction capacitance of a pn junction.

Consider the same pn junction as that in Example 7.3. Again assume that [latex]V_{R}=5 \mathrm{~V}[/latex].

Accepted Answer

The junction capacitance is found from Equation (7.42) as

[latex]\begin{array}{c}C^{\prime}=\left\{\frac{e \epsilon_{s} N_{a} N_{d}}{2\left(V_{b i}+V_{R} ight)\left(N_{a}+N_{d} ight)} ight\}^{1 / 2} \ \end{array}[/latex] (7.42)

[latex]\begin{array}{c}C^{\prime}=\left\{\frac{\left(1.6 imes 10^{-19} ight)(11.7)\left(8.85 imes 10^{-14} ight)\left(10^{16} ight)\left(10^{15} ight)}{2(0.635+5)\left(10^{16}+10^{15} ight)} ight\}^{1 / 2}\end{array}[/latex]

or

[latex]C^{\prime}=3.66 imes 10^{-9} \mathrm{~F} / \mathrm{cm}^{2}[/latex]

If the cross-sectional area of the pn junction is, for example, [latex]A=10^{-4} \mathrm{~cm}^{2}[/latex], then the total junction capacitance is

[latex]C=C^{\prime} \cdot A=0.366 imes 10^{-12} \mathrm{~F}=0.366 \mathrm{pF}[/latex]

Comment

The value of junction capacitance is usually in the [latex]\mathrm{pF}[/latex], or smaller, range.

Question 7.5: Calculate the junction capacitance of a pn junction. Conside...

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