In a p-n-p transistor emitter, doping is 5 ×10^18 / cm^3, base doping is 10^17 / cm^3, base widt

step 1 In this question we have to find the VBE and the collector current for two cases. First for case

In a p-n-p transistor emitter, doping is 5 ×10^18 / cm^3,...

In a p-n-p transistor emitter, doping is $5 \times 10^{18} / \mathrm{cm}^{3}$, base doping is $10^{17} / \mathrm{cm}^{3}$, base width is $0.985 \mu \mathrm{m}$, diffusion lengths for electrons and holes are the same at $10 \mu \mathrm{m}$. Assume $\tau_{p}=\tau_{n}=10^{-7} \mathrm{sec}$, find the emitter injection efficiency, the base transport factor, and the transistor gains if electron and hole mobility are 1250 and $450 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$, respectively.

Key Concepts

Emitter Injection Efficiency

Emitter injection efficiency is a measure of the proportion of carriers injected from the emitter that are the desired type (majority carriers of the base region) relative to the total injected carriers. It is determined by the ratio of the useful current (those carriers that contribute to conduction) to the total injection current across the emitter-base junction. This concept is critical in bipolar junction transistor design because a high injection efficiency indicates effective carrier injection that minimizes recombination losses and optimizes device performance.

Base Transport Factor

The base transport factor quantifies the fraction of minority carriers that, once injected from the emitter, successfully diffuse across the base to reach the collector without recombining. It depends on factors such as the base width, minority carrier lifetime, and diffusion length. A high base transport factor is essential for achieving high current gain in a transistor, as it ensures that most of the minority carriers contribute to the collector current.

Transistor Current Gain

The transistor current gain, often denoted as beta, represents the amplification capability of a bipolar junction transistor, defined as the ratio of the output collector current to the input base current. It is a product of the emitter injection efficiency and the base transport factor. This gain is a crucial parameter in the design and analysis of amplifiers and switching circuits, as it dictates how effectively the transistor can amplify a signal while taking into account carrier injection and transport properties.

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