An n-type Si sample is doped at 10^15 cm^-3. We shine light on it to create EHPs at 10^19 cm^-

step 1 In this question you have to find the type of the material whether it is n -pipe or p -type and

An n-type Si sample is doped at 10^15 cm^-3. We shine light...

An n-type Si sample is doped at $10^{15} \mathrm{~cm}^{-3}$. We shine light on it to create EHPs at $10^{19} \mathrm{~cm}^{-3} / \mathrm{s}$. What is the steady state concentration of minority carriers, if the lifetime is $100 \mathrm{~ns}$ ? How long does it take for the hole concentration to drop $10 \%$, after the light is switched off? How long for the hole concentration to reach a value that is $10 \%$ higher than the thermal equilibrium value?

Key Concepts

Exponential Decay and Time Constant

After an external excitation such as light is removed, the excess carriers decay exponentially toward equilibrium due to recombination. The time constant for this exponential decay is the carrier lifetime. This concept is essential for understanding and calculating the temporal response of a semiconductor device, such as the time required for the carrier concentration to drop by a given percentage.

Carrier Generation

This concept refers to the creation of electron?hole pairs in a semiconductor, which can be induced by external stimuli such as light. When a semiconductor is illuminated, photons with sufficient energy excite electrons from the valence band to the conduction band, producing free charge carriers that are in excess of the equilibrium concentrations.

Carrier Recombination

Carrier recombination is the process by which free electrons and holes recombine, effectively annihilating each other. This loss mechanism is characterized by a parameter known as the carrier lifetime, which represents the average time an excess carrier exists before recombining. Recombination processes are critical in determining the steady state and transient behavior of carrier populations in semiconductors.

Steady-State Carrier Concentration

In a semiconductor under continuous illumination, a steady state is reached when the rate of carrier generation equals the rate of recombination. This balance determines the excess concentration of minority carriers during operation. The steady state condition is fundamental to the operation of photonic and electronic devices since it sets the working point for the device’s response to external stimuli.

Thermal Equilibrium Carrier Concentration

Thermal equilibrium carrier concentration refers to the intrinsic balance between electrons and holes in a semiconductor in the absence of external excitation. For doped semiconductors, the majority carriers dominate the equilibrium concentration, while the minority carriers are determined by factors such as the law of mass action. Understanding this equilibrium condition is important when evaluating the impact of external voltage, light, or doping on the semiconductor properties.

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