A silicon pnp bipolar transistor at T=300 K has a B-E cross-sectional area of AB E-5 ×10^-4 cm

step 1 In this question we have to find these parameters for each case. So first, INC is given by this

A silicon pnp bipolar transistor at T=300 K has a B-E...

A silicon pnp bipolar transistor at $T=300 \mathrm{~K}$ has a $\mathrm{B}-\mathrm{E}$ cross-sectional area of $A_{\overline{B E}}-5 \times 10^{-4} \mathrm{~cm}^{2}$, neutral base width of $x_{B}-0.70 \mu \mathrm{m}$, a neutral emitter width of $x_{E}=0.50 \mu \mathrm{m}$, and uniform doping concentrations of $N_{E}=5 \times 10^{17} \mathrm{~cm}^{-3}$, $N_{B}=10^{16} \mathrm{~cm}^{-3}$, and $N_{C}=10^{15} \mathrm{~cm}^{-3} .$ Other transistor parameters are $D_{B}=10 \mathrm{~cm}^{2} / \mathrm{s}$ $D_{E}=15 \mathrm{~cm}^{2} / \mathrm{s}, \tau_{E 0}=\tau_{B 0}=5 \times 10^{-7} \mathrm{~s}$, and $\tau_{c 0}=2 \times 10^{-6} \mathrm{~s}$. The transistor is biased in the forward-active mode and the recombination factor is $\delta=0.995 .$ Determine the collector current for $(a) V_{E B}=0.550 \mathrm{~V},(b) I_{B}=0.80 \mu \mathrm{A}$, and (c) $I_{E}=125 \mu \mathrm{A}$.

A silicon pnp bipolar transistor at $T=300 \mathrm{~K}$ has a $\mathrm{B}-\mathrm{E}$ cross-sectional area of $A_{\overline{B E}}-5 \times 10^{-4} \mathrm{~cm}^{2}$, neutral base width of $x_{B}-0.70 \mu \mathrm{m}$, a neutral emitter width of $x_{E}=0.50 \mu \mathrm{m}$, and uniform doping concentrations of $N_{E}=5 \times 10^{17} \mathrm{~cm}^{-3}$, $N_{B}=10^{16} \mathrm{~cm}^{-3}$, and $N_{C}=10^{15} \mathrm{~cm}^{-3} .$ Other transistor parameters are $D_{B}=10 \mathrm{~cm}^{2} / \mathrm{s}$
$D_{E}=15 \mathrm{~cm}^{2} / \mathrm{s}, \tau_{E 0}=\tau_{B 0}=5 \times 10^{-7} \mathrm{~s}$, and $\tau_{c 0}=2 \times 10^{-6} \mathrm{~s}$. The transistor is
biased in the forward-active mode and the recombination factor is $\delta=0.995 .$ Determine the collector current for $(a) V_{E B}=0.550 \mathrm{~V},(b) I_{B}=0.80 \mu \mathrm{A}$, and
(c) $I_{E}=125 \mu \mathrm{A}$.

Key Concepts

Bipolar Junction Transistor (BJT) Operation

BJTs are three?terminal devices that operate by the injection of minority carriers from one region (emitter) across a junction into another region (base), where these carriers diffuse and are then collected by the third terminal (collector). Understanding their operation involves the analysis of charge injection, carrier transport across the base, and the resulting current amplification through the device’s inherent current gain.

Forward-Active Mode Biasing

In the forward-active mode, the emitter-base junction is forward biased while the collector-base junction is reverse biased. This biasing condition promotes efficient injection of carriers from the emitter into the base and minimizes the recombination losses in the base, which is crucial for achieving high current gains and accurate device performance predictions.

Minority Carrier Injection and Diffusion

The operation of BJTs in active mode relies on the injection of minority carriers (holes in a pnp transistor, electrons in an npn) from the heavily doped emitter into the lightly doped base. Once injected, these carriers diffuse across the base. The diffusion process is governed by the gradient of carrier concentration and is characterized by parameters such as the diffusion coefficient and the effective diffusion length.

Carrier Recombination and Lifetime

During their transit through the base, injected carriers can recombine via various mechanisms, which is quantified by the carrier lifetime. The extent of recombination affects the base transport factor and, consequently, the overall performance and current gain of the transistor. A recombination factor close to unity indicates minimal recombination losses, which is important for efficient device operation.

Current Relationships and Device Modeling

The relationship among the emitter, base, and collector currents is central to BJT behavior. Device models, including the Ebers-Moll model, provide mathematical frameworks that relate the voltages and currents of the BJT under different biasing conditions. These models incorporate exponential (diode-like) behavior of the junctions and account for factors such as recombination and carrier diffusion losses to predict collector currents under various operating conditions.

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