An electric field of 100 V / m is applied to a sample of n-type semiconductor whose Hall coeffi

step 1 In this question, an electric field is applied and this is suppose N type semiconductor an elect

An electric field of 100 V / m is applied to a sample of...

An electric field of $100 \mathrm{~V} / \mathrm{m}$ is applied to a sample of n-type semiconductor whose Hall coefficient is $0.0125 \mathrm{~m}^{1} \mathrm{C}$. Determine the current density in the sample, assuming the electron mobility to be $0.36$ Ans. $2880 \mathrm{~A} / \mathrm{m}^{2} \mathrm{f}$ $m^{2} v^{-1} x^{-1}$

Key Concepts

Hall Coefficient

The Hall coefficient is a parameter that arises when a magnetic field is applied perpendicular to the current flow in a semiconductor, creating a transverse voltage known as the Hall voltage. It is inversely proportional to the product of the charge carrier concentration and the elementary charge, and its sign indicates the type of predominant charge carriers. In semiconductor physics, it is used to determine the carrier density and assess whether the material is n-type or p-type.

Electron Mobility

Electron mobility represents how quickly electrons can move through a semiconductor material when subjected to an electric field. It reflects the ease with which electrons can navigate the crystal lattice and is influenced by scattering mechanisms such as impurities, phonons, and defects. High mobility indicates that electrons can move more freely, contributing to higher electrical conductivity in the material.

Charge Carrier Concentration

Charge carrier concentration is the number of free charge carriers (electrons in n-type or holes in p-type semiconductors) per unit volume of the material. It is a critical factor in determining the electrical properties of the semiconductor, including its conductivity. The carrier concentration in n-type semiconductors can be inferred from the Hall coefficient, as it is mathematically related through the inverse relationship with the product of the carrier charge and density.

Electric Field

The electric field is a vector field representing the force per unit charge acting on charged particles. In the context of semiconductors, it is responsible for driving the charge carriers (electrons or holes) through the material, initiating a drift current. This field is fundamental in understanding how voltage differences result in the movement of carriers, leading to measurable current densities.

Current Density

Current density is a measure of electric current flow per unit cross-sectional area within a conductor or semiconductor. It quantifies how much charge passes through a given area in a specified time and is directly related to the carrier concentration, charge of the carriers, their mobility, and the applied electric field. It is a key concept in determining the performance and efficiency of electronic devices.

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