In a Si base long p'n diode, the excess hole distribution...

In a Si base long p'n diode, the excess hole distribution due to optical excitation becomes $$ \delta p\left(x_{n}\right)=\left[p_{n} \cdot\left(e^{a V K T}-1\right)-g_{o p}, \frac{L_{p}^{2}}{D_{p}}\right] \cdot e^{-x_{n} / L_{p}}+g_{o p}, \frac{L_{p}^{2}}{D_{p}} $$ Suppose for such a device acceptor concentration is $10^{18} / \mathrm{cm}^{3}$, diffusion coefficient for holes is $10.36 \mathrm{~cm}^{2} / \mathrm{sec}$, mobility for holes is $400 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$, carrier lifetime = $10 \mathrm{~ns}$ and applied bias is $0.7 \mathrm{~V}$. Due to uniform illumination, $10^{20} / \mathrm{cm}^{3}$ EHP is generated. Now calculate the excess hole distribution for this long diode at a distance of twice the diffusion length from the junction at the $\mathrm{n}$ side.

In a Si base long p'n diode, the excess hole distribution due to optical excitation becomes
$$
\delta p\left(x_{n}\right)=\left[p_{n} \cdot\left(e^{a V K T}-1\right)-g_{o p}, \frac{L_{p}^{2}}{D_{p}}\right] \cdot e^{-x_{n} / L_{p}}+g_{o p}, \frac{L_{p}^{2}}{D_{p}}
$$
Suppose for such a device acceptor concentration is $10^{18} / \mathrm{cm}^{3}$, diffusion coefficient for holes is $10.36 \mathrm{~cm}^{2} / \mathrm{sec}$, mobility for holes is $400 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{sec}$, carrier lifetime = $10 \mathrm{~ns}$ and applied bias is $0.7 \mathrm{~V}$. Due to uniform illumination, $10^{20} / \mathrm{cm}^{3}$ EHP is generated. Now calculate the excess hole distribution for this long diode at a distance of twice the diffusion length from the junction at the $\mathrm{n}$ side.

Key Concepts

Diffusion Length

Diffusion length is the average distance that minority carriers travel before recombining. It is calculated from the diffusion coefficient and the carrier lifetime, and it sets the spatial scale for the exponential decay of the carrier concentration in the semiconductor. This concept is central to understanding how far excess carriers can influence the device behavior.

Excess Carrier Distribution

Excess carrier distribution describes how the additional carriers (electrons or holes) generated by external excitation (such as optical illumination) are spatially distributed in a semiconductor. It is typically characterized by exponential decay away from the generation region and depends on parameters like the diffusion coefficient, carrier lifetime, and the geometry of the device.

Minority Carrier Diffusion

Minority carrier diffusion refers to the process in which carriers in lower concentration (minority carriers) move from regions of high concentration to regions of low concentration. This movement is driven by concentration gradients and is accurately described by the diffusion equation, which is fundamental in predicting the behavior of carriers in p–n junction devices under non-equilibrium conditions.

Optical Carrier Generation

Optical carrier generation is the process by which electron-hole pairs are created in a semiconductor upon absorption of photons. This mechanism is crucial for optoelectronic devices, as it provides the extra carriers that modify the equilibrium conditions, leading to changes in the electrical characteristics of devices like photodiodes.

Carrier Recombination

Carrier recombination is the process where electrons and holes recombine, reducing the number of free carriers available in the semiconductor. The recombination rate, often expressed in terms of the carrier lifetime, is an important parameter as it influences the steady-state concentration of excess carriers and thereby affects the overall device performance.

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