For a Si photoconductor of length 5 μm, doped n -type at 10^15 cm^-3, calculate the change in c

step 1 In this question for the N -type silicon photoconductor, we have to find the thermal equilibrium

For a Si photoconductor of length 5 μm, doped n -type at...

For a Si photoconductor of length $5 \mu \mathrm{m}$, doped $\mathrm{n}$ -type at $10^{15} \mathrm{~cm}^{-3}$, calculate the change in current density when we shine light on the photoconductor under the following circumstances: We create $10^{20}$ electron-hole pairs $/ \mathrm{cm}^{3}-\mathrm{s}$ and carrier-recombination lifetimes, $\tau=0.1 \mu$ s. The applied voltage is $2.5 \mathrm{~V}$ across the photoconductor's length. How about if we increase the voltage to $2500 \mathrm{~V} ?$ The electron and hole mobilities are $1500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and $500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, respectively, in the ohmic region for electric fields below $10^{4} \mathrm{~V} / \mathrm{cm}$. For higher fields, electrons and holes have a saturation velocity of $10^{7} \mathrm{~cm} / \mathrm{s}$.

For a Si photoconductor of length $5 \mu \mathrm{m}$, doped $\mathrm{n}$ -type at $10^{15} \mathrm{~cm}^{-3}$, calculate the change in current density when we shine light on the photoconductor under the following circumstances: We create $10^{20}$ electron-hole pairs $/ \mathrm{cm}^{3}-\mathrm{s}$ and carrier-recombination lifetimes, $\tau=0.1 \mu$ s. The applied voltage is $2.5 \mathrm{~V}$ across the photoconductor's length. How about if we increase the voltage to $2500 \mathrm{~V} ?$ The electron and hole mobilities are $1500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and $500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$,
respectively, in the ohmic region for electric fields below $10^{4} \mathrm{~V} / \mathrm{cm}$. For higher fields, electrons and holes have a saturation velocity of $10^{7} \mathrm{~cm} / \mathrm{s}$.

Key Concepts

Photoconductivity

Photoconductivity is the phenomenon where a material's electrical conductivity increases when it is exposed to light, due to the generation of additional free charge carriers (electrons and holes) upon photon absorption. This is a key concept in understanding the operation of devices like photoconductors, where the response to light is harnessed for applications such as imaging or light sensing.

Carrier Generation Rate

The carrier generation rate describes the number of electron-hole pairs created per unit volume per unit time due to the absorption of photons. It is a crucial parameter that determines how many carriers are available for conduction, thereby affecting the overall current in a photoconductive material when illuminated.

Carrier-Recombination Lifetime

The carrier-recombination lifetime is the average period that the photo-generated charge carriers exist before they recombine. This lifetime influences the steady-state concentration of carriers in the material under continuous illumination and is pivotal in calculating the resulting conductivity and current density.

Carrier Mobility

Carrier mobility is a measure of how quickly charge carriers, both electrons and holes, can move through a semiconductor when subjected to an electric field. It directly affects the drift velocity of carriers and thus the current, making it essential for analyzing current conduction under illumination in the ohmic regime.

Saturation Velocity

Saturation velocity is the maximum velocity that charge carriers can attain in a semiconductor when subjected to high electric fields. Beyond a certain threshold electric field, the drift velocity of carriers no longer increases linearly with the field due to scattering and other effects, thus leading to a saturated current response.

Electric Field Regimes (Ohmic and Saturation Regions)

The behavior of charge carriers in a semiconductor can differ significantly depending on the applied electric field. In the ohmic region, carrier drift velocity increases linearly with the field (characterized by mobility), whereas in high electric fields the device enters the saturation regime where the carrier velocity approaches a constant saturation value. Understanding these regimes is key to predicting how the device will perform under different biases.

Current Density Calculation

The current density in a photoconductor is determined by the product of the charge carrier density (which itself depends on the generation rate and recombination lifetime), the charge of an electron, and the drift velocity of the carriers (which depends on both mobility and the applied electric field). This calculation is fundamental to the analysis and design of photoconductive devices under varying illumination and bias conditions.

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