The doping profile of a NPN BJT is given in the figure below. Estimate the emitter injection efficiency assuming the minority carrier diffusion coefficient for the base and emitter are the same.

[ans]

Question

The doping profile of a NPN BJT is given in the figure below. Estimate the emitter injection efficiency  assuming the minority carrier diffusion coefficient for the base and emitter are the same.

[ans]

BlackTom AI · Accepted Answer

Examining the prompt, we are asked to estimate the emitter injection efficiency for a BJT using the given doping profile, with the note that the minority carrier diffusion coefficients in base and emitter are equal.

First, recall what emitter injection efficiency means in the context of BJT operation. It quantifies how effectively carriers injected from the emitter contribute to the forward-active current, relative to leakage or minority carrier flow. In simple analyses, the injection efficiency is strongly influenced by the relative dopant concentrations on the emitter and base sides, as well as the material parameters that govern carrier transport.

Here, we are given a doping profile diagram with labeled regions: the emitter dopant concentration (N_D in the emitter region), the base dopant concentration (N_A in the base region), and the emitter- and base-side carrier transport properties. Since the minority carrier diffusion coefficients for base and emitter are assumed equal, the ratio of injected currents is primarily controlled by the dopant concentrations, because diffusion and recombination properties scale similarly on both sides when D is the same.

Option-by-option analysis (even though no explicit option list is shown, we consider the reasoning framework that would be used):

- If an option suggests a very high emitter injection efficiency (close to 1): This would occur when the emitter is much more heavily doped than the base, or when the emitter-to-base carrier transport favors emitter injection strongly. In the given diagram, the emitter region is doped with N_D that appears to be significantly lower than the base dopant concentration N_A (the emitter bar is much shorter in the vertical scale than the base bar). If the emitter were far more heavily doped than the base, we would expect η_E to approach 1; the observed diagram, however, shows the base being relatively heavily doped compared to the emitter, which tends to reduce η_E rather than maximize it. So a near-unity value would be questionable under the depicted profile.

- If an option suggests a modest-to-high emitter injection efficiency (e.g., around 0.9): This aligns with a scenario where even though the emitter is not the heaviest doped region, the emitter-base junction still favors electron injection from the emitter into the base due to the typical band structure and the difference in minority carrier concentrations at the junction, combined with equal diffusion coefficients. Given standard approximations in Ebers–Mlood-like analyses, such a value can be obtained when the emitter doping is sufficiently high relative to the base in the region near the junction and the transport properties are balanced by the equal D assumption. The figure’s relative scale between emitter (low doping) and base (higher doping) in a way that yields a large fraction of the emitter carriers contributing to forward current is consistent with η_E in the vicinity of ~0.9, recognizing that this is an approximate, order-of-magnitude estimate rather than a precise calculation.

- If an option suggests a very small emitter injection efficiency (much less than 0.5): This would occur if the base were extremely heavily doped relative to the emitter, or if the emitter–base junction were configured in a way that severely impeded emitter injection (e.g., large asymmetry or unintended barrier). The provided diagram does not indicate such an extreme asymmetry; the base is doped more than the emitter but not by orders of magnitude that would drive η_E far below 0.5 in a typical equal-D scenario.

- If an option asserts that diffusion coefficients being equal makes η_E independent of doping levels: This is a misconception. While having D_E = D_B simplifies the transport comparison, the emitter injection efficiency still depends on the relative dopant concentrations (and the resulting quasi-Fermi level alignment) because these determine how effectively carriers are injected across the emitter–base junction. Equal D does not erase the influence of NA vs ND on η_E.

In summary, the approach to estimating η_E from the given profile rests on comparing the emitter and base dopant concentrations near the junction and applying the equal-D simplification to relate diffusion-driven transport to injection efficiency. The resulting estimate in this scenario lands in a high but not unity range, consistent with a number around 0.9, reflecting substantial emitter contribution to forward current while acknowledging the base doping is not negligible.

EESM5200 (L2) Part I: Topic 13 - BJT Physical Structure and Switching

The doping profile of a NPN BJT is given in the figure below. Estimate the emitter injection efficiency assuming the minority carrier diffusion coefficient for the base and emitter are the same. [ans]

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