We shine 10^17 photons / cm^2-s which are all absorbed near the surface x=0 of a p-type semicond

step 1 In this question we have to find the electron concentration at x1, which is 20 microns for silic

We shine 10^17 photons / cm^2-s which are all absorbed near...

We shine $10^{17}$ photons $/ \mathrm{cm}^{2}-\mathrm{s}$ which are all absorbed near the surface $x=0$ of a p-type semiconductor, raising the temperature of the sample to $500 \mathrm{~K}$. If the minority carrier lifetime is $200 \mathrm{~ns}$ in this material, electron mobility is $2000 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, and hole mobility is $500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, calculate the electron diffusion current density 20 microns from the surface.

Key Concepts

Carrier Diffusion

Carrier diffusion is the process by which charge carriers move from regions of high concentration to regions of low concentration driven by a concentration gradient. In semiconductors, this process is critical for understanding how minority carriers, such as electrons in p-type materials, spread within the material after being generated.

Fick's Law

Fick's Law describes how particles diffuse, stating that the flux of carriers is proportional to the negative gradient of their concentration. In the context of semiconductors, this law underpins the derivation of the diffusion current density, linking the spatial derivative of the carrier concentration with the measurable current.

Einstein Relation

The Einstein relation establishes a connection between the diffusion coefficient and the mobility of charge carriers in a semiconductor. It shows that the diffusion coefficient is proportional to the carrier mobility and thermal voltage (kT/q), thus linking the random thermal motion of carriers with their drift under an electric field.

Minority Carrier Lifetime

Minority carrier lifetime is the average time that a minority carrier exists before recombining with a majority carrier. This parameter is crucial in determining how far carriers can diffuse before recombination, directly influencing phenomena such as diffusion length and the resultant current densities in semiconductor devices.

Optical Generation of Carriers

Optical generation of carriers involves the absorption of photons leading to the creation of electron-hole pairs in a semiconductor. The photon flux and absorption characteristics determine the generation rate, which in turn affects the spatial distribution of carrier concentration near the illuminated surface.

Diffusion Length

Diffusion length is the average distance that a carrier can travel before recombination, typically calculated as the square root of the product of the diffusion coefficient and the minority carrier lifetime. This length scale is pivotal for understanding how injected carriers spread within the semiconductor and influences the design and performance of semiconductor devices.

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