A Si p-n-p transistor has the following properties at room...

A Si p-n-p transistor has the following properties at room temperature: $\tau_{n}=\tau_{p}=0.1 \mu \mathrm{s}$ $D_{n}=D_{p}=10 \mathrm{~cm}^{2} / \mathrm{s}$ $N_{E}=10^{19} \mathrm{~cm}^{-3}=$ emitter concentration $N_{B}=10^{16} \mathrm{~cm}^{-3}=$ base concentration $N_{C}=10^{16} \mathrm{~cm}^{-3}=$ collector concentration $W_{E}=$ emitter width $=3 \mu \mathrm{m}$ $W=$ metallurgical base width $=1.5 \mu \mathrm{m}=$ distance between base-emitter junction and base-collector junction $A=$ cross-sectional area $=10^{-5} \mathrm{~cm}^{2}$ Calculate the neutral base width $W_{b}$ for $V_{C B}=0$ and $V_{E B}=0.2 \mathrm{~V}$. Repeat for $0.6 \mathrm{~V}$

A Si p-n-p transistor has the following properties at room temperature:
$\tau_{n}=\tau_{p}=0.1 \mu \mathrm{s}$
$D_{n}=D_{p}=10 \mathrm{~cm}^{2} / \mathrm{s}$
$N_{E}=10^{19} \mathrm{~cm}^{-3}=$ emitter concentration
$N_{B}=10^{16} \mathrm{~cm}^{-3}=$ base concentration
$N_{C}=10^{16} \mathrm{~cm}^{-3}=$ collector concentration
$W_{E}=$ emitter width $=3 \mu \mathrm{m}$
$W=$ metallurgical base width $=1.5 \mu \mathrm{m}=$ distance between base-emitter junction and base-collector junction $A=$ cross-sectional area $=10^{-5} \mathrm{~cm}^{2}$
Calculate the neutral base width $W_{b}$ for $V_{C B}=0$ and $V_{E B}=0.2 \mathrm{~V}$. Repeat for $0.6 \mathrm{~V}$

Key Concepts

Quasi-Neutral (Neutral) Base Region

The quasi-neutral base region is the part of the base that lies outside the depletion regions at the junctions. In this region, the minority carriers diffuse and recombine without being immediately influenced by the built-in electric fields. The effective width of this region (the neutral base width) is crucial for high-speed transistor operation, as it determines the transit time of carriers through the base and thus the frequency response of the device.

Junction Biasing and Depletion Width Modulation

The application of external voltages (biasing) significantly impacts the widths of the depletion regions at the junctions. In a transistor, forward biasing the emitter–base junction injects carriers and modifies the depletion region extent on the lightly doped side. This modulation of the depletion width directly affects the effective neutral base width. Calculations of the neutral base width require subtracting the depletion width (which depends on the applied voltage and doping concentrations) from the total physical base width.

Bipolar Junction Transistor (BJT) Structure and Operation

A bipolar junction transistor consists of three regions (emitter, base, and collector) with alternating doping types. In the context of transistor analysis, understanding how the physical dimensions and junction properties (such as doping levels and applied voltages) influence its operation is essential. In particular, the effective (neutral) base width—which is the active region between the depletion layers—plays a critical role in determining the transport of minority carriers through the base and ultimately the gain and speed of the device.

Depletion Region in a p–n Junction

In a p–n junction, the depletion region is formed due to the diffusion of carriers across the junction, leaving behind charged ions. This region lacks free carriers and behaves as an insulator. Its width can change with the applied voltage, becoming narrower under reverse bias and wider under forward bias. In analyzing a transistor, it is important to account for how the depletion regions at the emitter–base and base–collector junctions consume part of the total metallurgical base width, thereby reducing the effective neutral base width available for carrier transport.

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