A Si p-n junction with cross-sectional area A=0.001 cm^2 is formed with Na=10^15 cm^-3 and Nd=

step 1 In this question we have to find the electron diffusion current density, the whole drift current

A Si p-n junction with cross-sectional area A=0.001 cm^2 is...

A Si $\mathrm{p}-\mathrm{n}$ junction with cross-sectional area $A=0.001 \mathrm{~cm}^{2}$ is formed with $N_{a}=10^{15} \mathrm{~cm}^{-3}$ and $N_{d}=10^{20} \mathrm{~cm}^{-3} .$ Calculate: (a) Contact potential, $V_{0}$. (b) Space-charge width at equilibrium (zero bias). (c) Current with a forward bias of $0.7 \mathrm{~V}$. Assume that the current is diffusion dominated. Assume $\mu_{n}=1500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}, \mu_{p}=450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, and $\tau_{n}=\tau_{q}=2.5 \mathrm{~ms}$. Which carries most of the current, electrons or holes, and why? If you wanted to double the electron current, what should you do?

A Si $\mathrm{p}-\mathrm{n}$ junction with cross-sectional area $A=0.001 \mathrm{~cm}^{2}$ is formed with $N_{a}=10^{15} \mathrm{~cm}^{-3}$ and $N_{d}=10^{20} \mathrm{~cm}^{-3} .$ Calculate:
(a) Contact potential, $V_{0}$.
(b) Space-charge width at equilibrium (zero bias).
(c) Current with a forward bias of $0.7 \mathrm{~V}$. Assume that the current is diffusion dominated. Assume $\mu_{n}=1500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}, \mu_{p}=450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, and
$\tau_{n}=\tau_{q}=2.5 \mathrm{~ms}$. Which carries most of the current, electrons or holes, and why? If you wanted to double the electron current, what should you do?

Key Concepts

Carrier Mobility and Diffusion Coefficients

Carrier mobility reflects how quickly electrons or holes can move through a semiconductor under an electric field, while the diffusion coefficient quantifies the spread of carriers due to a concentration gradient. Through the Einstein relation, these quantities are interrelated, and differences in mobility between electrons and holes directly influence the magnitude of their contributions to the diffusion current.

Minority Carrier Injection

In a forward-biased p-n junction, minority carriers are injected into the opposite region where they are in low concentration, making them the dominant carriers contributing to the current. The effectiveness of this injection depends on factors such as the equilibrium minority carrier concentrations (which are influenced by doping levels), diffusion constants, and carrier lifetimes. This concept explains why one type of carrier may contribute more significantly to current flow in an asymmetrically doped junction and informs strategies to modify current levels, such as adjusting doping concentrations or improving carrier lifetimes.

Diffusion-Dominated Current in p-n Junctions

Under forward bias, a p-n junction conducts mainly through diffusion of minority carriers injected across the junction. This diffusion current is governed by the concentration gradient of the injected carriers, their diffusion coefficients, and their lifetimes in the respective regions. The analysis of this current is essential for understanding the device’s I-V characteristics in regimes where recombination is minimal.

p-n Junction Fundamentals

A p-n junction is formed when p-type and n-type semiconductor materials are joined, resulting in a region where free carriers diffuse and recombine. This leads to the development of an electric field that opposes further diffusion, thereby creating a built?in potential. Understanding the behavior of majority and minority carriers in this system is crucial for analyzing device operation under various biasing conditions.

Built-in (Contact) Potential

The built-in, or contact, potential is the voltage difference established across a p-n junction at equilibrium due to the diffusion of carriers from high concentration to low concentration regions. It is determined by the difference in Fermi levels of the p-type and n-type materials and can be calculated using thermal voltage and doping concentrations, reflecting the energy barrier for carrier movement.

Depletion Region and Depletion Approximation

The depletion region, also known as the space-charge region, is where mobile charge carriers are swept out, leaving behind fixed ionized donors and acceptors. Its width is determined using the depletion approximation, which simplifies Poisson’s equation by assuming complete depletion of free carriers in this region. This concept is key for understanding the electric field profile and junction capacitance in semiconductor devices.

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