The resistance of a metal increases with increasing temperature, while the resistance of a semiconductor decreases. Why the difference?

Electrical conductivity is a measure of how well a material can accommodate the flow of electric current. This property is primarily based on the presence and movement of charge carriers, which are typically electrons or holes (places where an electron is missing). In a conductive material, these charge carriers can move freely when an electric field is applied.

However, the conductivity of a material isn't constant; it changes with varying conditions, such as temperature. Metals, for example, contain a sea of delocalized electrons that can move easily, making them good conductors. As temperature rises, the increased atomic vibrations interfere with electron movement, resulting in higher resistance and lower conductivity. In semiconductors, increased temperature can elevate more electrons to a state where they can participate in conduction, improving conductivity. By understanding these behaviors, we get valuable insights into developing and using materials in different temperature conditions for applications in electronics and other fields.

Semiconductors occupy a middle ground between conductors and insulators, with their ability to conduct electricity being highly tunable. They are made of materials like silicon and germanium, which under normal conditions don't have many free charge carriers. However, as temperature increases, the thermal energy encourages electrons to jump from the valence band (where they are bound to the atom) to the conduction band (where they can move freely).

This band-gap energy is smaller in semiconductors than in insulators, making electron promotion possible at relatively modest temperature increases. Hence, semiconductors become better conductors as temperature rises. This unique behavior has critical implications in the field of electronics, particularly in the fabrication of devices like diodes, transistors, and thermistors.

Metals are characterized by their sea of electrons, which gives them their excellent conductive properties. These metals have a lattice-like structure composed of positively charged ion cores surrounded by a cloud of free electrons. This structure allows electrons to move relatively unhindered through the metal, carrying electric current.

However, with increasing temperature, these same metallic cores vibrate more intensively. They can scatter the flow of electrons, akin to throwing obstacles in a stream, which slows down the passage of water. This phenomenon leads to an increase in the metal's resistance with temperature—a foundational concept in the field of electrical engineering and materials science, particularly when dealing with metallic conductors in circuits that experience changing temperatures.

Electron mobility refers to how quickly electrons can move through a material when subjected to an electric field. High mobility means that electrons can travel through the material quickly, which is indicative of high electrical conductivity. Factors affecting mobility include the material's crystal structure, impurities, and thermal vibrations of the atoms.

In metals, electron mobility is high because the delocalized electrons aren't hindered by tight binding to any particular atom. However, as temperature increases, the increased lattice vibrations (phonons) can scatter electrons, reducing mobility and thus conductivity. In semiconductors, mobility can be a more complex consideration because it not only depends on the lattice quality but also varies with the amount of energy available to promote electrons into a higher energy band where they can contribute to conduction.