(a) The room-temperature electrical conductivity of a silicon specimen is \(5.93 \times 10^{-3}\) \((\Omega \cdot \mathrm{m})^{-1} .\) The hole concentration is known to be \(7.0 \times 10^{17} \mathrm{~m}^{-3}\). Using the electron and hole mobilities for silicon in Table \(18.3\), compute the electron concentration. (b) On the basis of the result in part (a), is the specimen intrinsic, \(n\)-type extrinsic, or \(p\)-type extrinsic? Why?

Electrical conductivity in semiconductors is heavily influenced by the concentration of charge carriers, which are electrons and holes. Hole concentration refers to the number of 'holes', or absence of electrons, available for conduction in a semiconductor. A 'hole' can be thought of as a positive charge carrier; when an electron moves away from its position, it leaves behind a hole that can move around as adjacent electrons fill the gap, effectively causing the hole to move in the opposite direction.

In a pure, intrinsic semiconductor, such as undoped silicon or germanium, electrons and holes are created in pairs through thermal energy. However, doping the material with certain atoms can increase the hole concentration, leading to what is known as a p-type extrinsic semiconductor. The hole concentration is crucial for understanding the behavior of a semiconductor because it directly affects the material's ability to conduct electric current.

In the context of semiconductors, the term electron mobility is used to describe how quickly an electron can move through the semiconductor when an electric field is applied. It's a measure of the ease with which electrons can navigate through the lattice of atoms.

High electron mobility means that electrons can travel through the semiconductor with less resistance, resulting in higher electrical conductivity. The mobility of electrons is affected by a number of factors including impurities in the material, temperature, and the intrinsic properties of the semiconductor. Silicon, for instance, has lower electron mobility compared to some other materials like gallium arsenide, but it is favored in many applications due to its abundance and well-understood properties.

Moreover, it is important to note that electron mobility can be different from hole mobility, which represents the movement of holes in a semiconductor. Understanding both is key to analyzing and designing semiconductor devices.

A p-type extrinsic semiconductor is a material that has been 'doped' with atoms which have fewer valence electrons than the host atoms of the semiconductor. For example, silicon has four valence electrons, so doping it with atoms having three valence electrons, such as boron, creates deficiencies or 'holes' where a silicon electron has nothing to bond with.

This doping process increases the hole concentration in the material, making holes the majority charge carriers, whereas electrons become minority carriers. The result is a semiconductor with enhanced electrical conductivity due to the 'p-type' doping. When electric voltage is applied, holes move toward the negative terminal, and electrons toward the positive terminal, but since there are more holes, the current is primarily due to their movement, hence the name 'p-type'.

While hole concentration describes the density of vacant electron positions, electron concentration in a semiconductor measures the number of free electrons available for conduction. In an intrinsic (pure) semiconductor at thermal equilibrium, the number of free electrons is equal to the number of holes. However, doping a semiconductor with impurities can increase either the number of free electrons (n-type doping) or the number of holes (p-type doping).

The electron concentration has a critical impact on the semiconductor properties, such as conductivity and the behavior of semiconductor devices like diodes and transistors. Understanding both the electron and hole concentrations is essential for predicting how a semiconductor will perform in an electronic circuit.