On a Si sample, incident light is at t=0 uniformly, which...

On a Si sample, incident light is at $t=0$ uniformly, which generates excess carriers for $t>0$. The generation rate for carriers is $6 \times 10^{22} / \mathrm{cm}^{3}$. Sample is doped with $2 \times 10^{17} / \mathrm{cm}^{3}$ As atoms. Determine the conductivity of the sample at $t=5 \mathrm{~ms}$. Find the separation of quasi Fermi levels at $300 \mathrm{~K}$.

Key Concepts

Excess Carrier Generation

Excess carrier generation refers to the process by which additional electrons and holes are created in a semiconductor due to external excitation (such as light absorption), beyond the equilibrium concentration determined by doping. This process is crucial in understanding how devices like photodetectors and solar cells respond to illumination, as it directly increases the number of mobile charge carriers available for conduction.

Conductivity in Semiconductors

Conductivity in semiconductors depends on both the concentration and mobility of charge carriers (electrons and holes). Under external excitation, such as light, additional carriers are generated, altering the overall conductivity. Understanding the transient changes in conductivity requires accounting for both the equilibrium carriers provided by doping and the excess carriers produced by generation events.

Doping in Semiconductors

Doping is the introduction of impurity atoms into a semiconductor to modify its electrical properties by providing extra charge carriers. For example, adding donor atoms creates an n-type material with a higher concentration of electrons. This base level of carriers both sets the equilibrium conductivity and interacts with excess carriers generated by external stimuli, affecting the device’s overall response.

Quasi-Fermi Levels

Under non-equilibrium conditions, separate quasi-Fermi levels can be defined for electrons and holes. These levels represent the effective chemical potentials for each type of carrier when the system is not in thermal equilibrium. The separation of the quasi-Fermi levels indicates the degree of non-equilibrium and is critical in analyzing carrier distributions, recombination processes, and device operation under illumination.

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