Question
(a) A silicon pn junction diode has the geometry shown in Figure $8.11$ in which the $\mathrm{n}$ region is "short" with a length $W_{n}=0.7 \mu \mathrm{m}$. The doping concentrations are $N_{a}=2 \times 10^{17} \mathrm{~cm}^{-3}$ and $N_{d}=2 \times 10^{15} \mathrm{~cm}^{-3} .$ The cross-sectional area is $A=10^{-3} \mathrm{~cm}^{2} .$ Determine (i) the maximum forward-bias voltage such that low injection is still valid, and ( $(i$ ) the resulting current at this forward-bias voltage. $(b)$ Repeat part $(a)$ if the doping concentrations are reversed such that $N_{a}=2 \times 10^{15} \mathrm{~cm}^{-3}$ and $N_{d}=2 \times 10^{17} \mathrm{~cm}^{-3}$
Step 1
Given that $L_p = 10 \mu m$, we can see that the length of the n region, $W_n = 0.7 \mu m$, is much less than $L_p$. Show more…
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The cross-sectional area of a silicon pn junction is $10^{-3} \mathrm{~cm}^{2} .$ The temperature of the diode is $T=300 \mathrm{~K}$, and the doping concentrations are $N_{d}=10^{16} \mathrm{~cm}^{-3}$ and $N_{a}=$ $8 \times 10^{15} \mathrm{~cm}^{-3} .$ Assume minority carrier lifetimes of $\tau_{n 0}=10^{-6} \mathrm{~s}$ and $\tau_{p 0}=10^{-7} \mathrm{~s}$. Calculate the total number of excess electrons in the $\mathrm{p}$ region and the total number of excess holes in the $\mathrm{n}$ region for $(a) V_{a}=0.3 \mathrm{~V},(b) V_{a}=0.4 \mathrm{~V}$, and $(c) V_{a}=0.5 \mathrm{~V}$.
A long silicon pn junction photodiode has the following parameters at $T=300 \mathrm{~K}$ : $N_{a}=10^{16} \mathrm{~cm}^{-3}, N_{d}=2 \times 10^{15} \mathrm{~cm}^{-3}, D_{p}=10 \mathrm{~cm}^{2} / \mathrm{s}, D_{n}=25 \mathrm{~cm}^{2} / \mathrm{s}, \tau_{p 0}=10^{-7} \mathrm{~s}$ and $\tau_{n 0}=5 \times 10^{-7} \mathrm{~s}$. The cross-sectional area of the diode is $A=10^{-3} \mathrm{~cm}^{2}$. Assume that a reverse-biased voltage of 5 volts is applied and that a uniform generation rate for electron-hole pairs of $G_{L}=10^{21} \mathrm{~cm}^{-3} \mathrm{~s}^{-1}$ exists throughout the entire photodiode. (a) Determine the prompt component of photocurrent. (b) Find the steady-state excess carrier concentrations in the $\mathrm{p}$ and $\mathrm{n}$ regions far from the junction. ( $c$ ) Determine the total steady-state photocurrent.
A one-sided $\mathrm{p}^{+} \mathrm{n}$ silicon diode has doping concentrations of $N_{a}=5 \times 10^{17} \mathrm{~cm}^{-s}$ and $N_{d}=8 \times 10^{15} \mathrm{~cm}^{-3}$. The minority carrier lifetimes are $\tau_{n 0}=10^{-7} \mathrm{~s}$ and $\tau_{p 0}=8 \times$ $10^{-8} \mathrm{~s}$. The cross-sectional area is $A=2 \times 10^{-4} \mathrm{~cm}^{2}$. Calculate the $(a)$ reverse-biased saturation current, and $(b)$ the forward-bias current at (i) $V_{a}=0.45 \mathrm{~V}$, (ii) $V_{a}=0.55 \mathrm{~V}$, and (iii) $V_{a}=0.65 \mathrm{~V}$.
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