Consider a sample of n -type silicon with ND=10^21 / m^'. Determine the electron and hole densit

step 1 This is the problem number 20 and 12 and this problem is said that Consider a sample of n -type

Consider a sample of n -type silicon with ND=10^21 / m^'....

Consider a sample of $n$ -type silicon with $\mathrm{N}_{\mathrm{D}}=10^{21} / \mathrm{m}^{\prime}$. Determine the electron and hole densities al 300 $\mathrm{K}$. The intrinsic carrier concentration for silicon at $300 \mathrm{~K}$. is $9.8 \times 10^{17} \mathrm{~m}$

Key Concepts

Charge Neutrality

The principle of charge neutrality in semiconductors states that the total positive charge must balance the total negative charge. In an n-type semiconductor, the electron concentration increases due to the ionization of donor impurities, and the minority carrier (hole) concentration adjusts accordingly to maintain electrical neutrality.

Mass Action Law

The mass action law in semiconductor physics states that, at thermal equilibrium, the product of the electron and hole concentrations is constant and equal to the square of the intrinsic carrier concentration. This relationship (n·p = ni^2) is used to calculate the minority carrier concentration once the majority carrier concentration, typically approximated by the dopant density in heavily doped materials, is known.

Doping in Semiconductors

Doping is the process of intentionally introducing impurities into a semiconductor to modify its electrical properties. In an n-type semiconductor, donor impurities are added to increase the electron concentration, making electrons the majority carriers. This shift in carrier concentration affects the conductivity of the material by providing extra free electrons for electrical conduction.

Intrinsic Carrier Concentration

Intrinsic carrier concentration refers to the number of electron-hole pairs generated in a pure semiconductor due solely to thermal excitation at a given temperature. It is a fundamental property that depends on the bandgap and temperature of the material, and serves as a baseline against which the effects of doping are measured.

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