An n -type Si sample with Nd=10^15 cm^-3 is steadily illuminated such that gop =10^21 EHP / cm^

step 1 In this question we have to find the generation current density. So it is the integral from 0 to

An n -type Si sample with Nd=10^15 cm^-3 is steadily...

An $\mathrm{n}$ -type Si sample with $N_{d}=10^{15} \mathrm{~cm}^{-3}$ is steadily illuminated such that $g_{\text {op }}=10^{21} \mathrm{EHP} / \mathrm{cm}^{3}-\mathrm{s}$. If $\tau_{n}=\tau_{p}=1 \mu \mathrm{s}$ for this excitation, calculate the separation in the quasi-Fermi levels, $\left(F_{n}-F_{p}\right)$. Draw a band diagram such as Fig. 4-11.

Key Concepts

Semiconductor Band Diagram

A semiconductor band diagram graphically illustrates the energy levels of the conduction and valence bands, as well as the positions of the quasi-Fermi levels under both equilibrium and non-equilibrium conditions. This diagram is essential for visualizing electronic transitions, understanding carrier distributions, and analyzing device behavior under various excitations.

Quasi-Fermi Levels

In non-equilibrium conditions, such as during illumination, the electron and hole populations can no longer be described by a single Fermi level. Instead, separate quasi-Fermi levels develop for electrons and holes, with the separation between them serving as an indicator of the degree of non-equilibrium and the extent of carrier injection.

Excess Carrier Concentration

Excess carrier concentration represents the additional electrons and holes generated by external excitations beyond the equilibrium doping level. It plays a significant role in the dynamic behavior of carriers in the semiconductor, influencing parameters such as conductivity and the quasi-Fermi level separation.

Steady-State Carrier Generation and Recombination

Under continuous external excitation, such as illumination, carriers are generated at a constant rate and simultaneously recombine. In a steady state, the rate of generation equals the rate of recombination, establishing fixed excess carrier concentrations that are crucial for determining the material's non-equilibrium properties.

N-type Semiconductor

An n-type semiconductor is one that has been doped with donor impurities, which introduce additional electrons into the conduction band. This makes electrons the majority carriers, directly influencing the conduction properties of the material and its response under optical or electrical excitations.

Carrier Lifetime

Carrier lifetime refers to the average time that an excited electron or hole exists before recombining. It is a critical parameter in determining the steady-state concentration of excess carriers under external excitations, thereby affecting the separation between the quasi-Fermi levels.

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