(a) A Si p^+-n junction 10^-2 cm^2 in area has Nd=10^15 cm^-3 doping on the n side. Calculate

step 1 In this question, we have to find the minimum end region width such that the avalan breakdown oc

(a) A Si p^+-n junction 10^-2 cm^2 in area has Nd=10^15...

(a) $\mathrm{A}$ Si $\mathrm{p}^{+}-\mathrm{n}$ junction $10^{-2} \mathrm{~cm}^{2}$ in area has $N_{d}=10^{15} \mathrm{~cm}^{-3}$ doping on the $\mathrm{n}$ side. Calculate the junction capacitance with a reverse bias of $10 \mathrm{~V}$. (b) An abrupt $\mathrm{p}^{+}-\mathrm{n}$ junction is formed in $\mathrm{Si}$ with a donor doping of $N_{d}=10^{15} \mathrm{~cm}^{-3} .$ What is the depletion region thickness $W$ just prior to avalanche breakdown?

(a) $\mathrm{A}$ Si $\mathrm{p}^{+}-\mathrm{n}$ junction $10^{-2} \mathrm{~cm}^{2}$ in area has $N_{d}=10^{15} \mathrm{~cm}^{-3}$ doping on the $\mathrm{n}$ side. Calculate the junction capacitance with a reverse bias of $10 \mathrm{~V}$.
(b) An abrupt $\mathrm{p}^{+}-\mathrm{n}$ junction is formed in $\mathrm{Si}$ with a donor doping of $N_{d}=10^{15} \mathrm{~cm}^{-3} .$ What is the depletion region thickness $W$ just prior to avalanche breakdown?

Key Concepts

Avalanche Breakdown

Avalanche breakdown is a phenomenon where, under high reverse biases, the electric field in the depletion region becomes strong enough to accelerate carriers to energies that can ionize atoms through impact ionization. This leads to a multiplication of carriers, resulting in a sudden increase in current. Understanding avalanche breakdown is essential for designing devices to avoid uncontrolled conduction or to exploit it in applications like avalanche photodiodes.

Junction Capacitance

The junction capacitance of a p-n junction under reverse bias is determined by the width of the depletion region, which acts like a dielectric in a parallel-plate capacitor. As the reverse bias increases, the depletion width widens and the capacitance decreases. This capacitance is crucial for high-frequency applications and impacts the speed and performance of semiconductor devices.

p-n Junction

A p-n junction is formed by joining p-type and n-type semiconductor materials, creating a boundary where mobile charge carriers (holes and electrons) diffuse and recombine. This results in the formation of a depletion region with built-in electric fields that are crucial for a wide range of semiconductor device operations, including rectification, amplification, and switching.

Depletion Region (Space?Charge Region)

The depletion region is a zone around the p-n junction that is depleted of mobile carriers due to recombination, leaving behind charged dopant ions. This region widens under reverse bias, and its width is a key parameter that influences several device characteristics, such as the junction capacitance and the breakdown voltage.

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