Question

What factors decrease the conductivity of a conductor as temperature increases? Are these factors also present in a semiconductor, and if so, how can its conductivity vary with temperature in the opposite sense?

Short answer

In conductors, temperature increase leads to decreased conductivity due to increased lattice vibrations that increase the degree of scattering and decrease the mean free path and relaxation time of the electrons. In a semiconductor, however, as temperature increases, more free charges are created due to electrons jumping the energy gap. This increase in the number of free charges surpasses the increased scattering due to lattice vibrations, leading to increased conductivity with temperature.

Step-by-step solution

Analysis of temperature effect on conduction in conductors

Upon heating a conductor, the kinetic energy of the valence electrons increases, causing them to vibrate more vigorously. This, in turn, increases the degree of scattering and the opposition to the current, hence conductivity. Additionally, due to the increased lattice vibrations, the mean free path and relaxation time of the electrons decrease, causing the resistivity to increase and conductivity to decrease.

Understanding the difference between conductors and semiconductors

In terms of conductivity, semiconductors behave differently from conductors. Two types of charge carriers contribute to the conductivity in semiconductors: electrons and holes. At absolute zero, semiconductors behave like insulators. As the temperature increases, the number of charge carriers and, therefore, the conductivity increases.

Analysis of temperature effect on conduction in semiconductors

In semiconductors, with the increase in temperature, a larger number of electrons are excited across the energy gap (from the valence band to the conduction band), creating more free charges (both electrons and holes) for conduction. This increase of free charges with temperature surpasses the effect of increased scattering, hence the overall conductivity of a semiconductor increases with temperature.

Key concepts

Temperature Effects on Conductivity

As temperature rises, the conductivity of materials can change significantly. In conductors like metals, increasing temperature often leads to decreased conductivity. This happens because the atoms in the material start vibrating more.
These vibrations obstruct the flow of electrons, increasing resistance.
In contrast, the scenario is different for semiconductors. When temperature goes up, more electrons get enough energy to move into the conduction band. The increase in mobile charge carriers enhances the conductivity, making temperature a key factor in improving the performance of semiconductor devices.

• More heat = fewer obstacles in semiconductors but more in conductors.
• Conductivity in conductors decreases with heat, while it increases in semiconductors.

Conductors vs Semiconductors

Conductors and semiconductors show distinct behaviors when it comes to conductivity. Conductors, generally metals, have plenty of free electrons that can move around easily. This quality makes them very conductive at room temperature but less effective at higher temperatures due to increased scattering events.
Meanwhile, semiconductors like silicon have limited charge carriers at low temperatures. However, their number increases significantly with temperature, boosting their conductivity. This fundamental difference in behavior highlights why semiconductors are preferred in electronic devices, as their conductivity can be readily controlled.

• Conductors: High conductivity initially; decreases with heat.
• Semiconductors: Low conductivity initially; increases with heat.

Charge Carriers in Semiconductors

Charge carriers are crucial for electrical conduction. In semiconductors, these carriers consist of electrons and holes. Electrons are negatively charged while holes effectively carry a positive charge. At low temperatures, these carriers are sparse, making semiconductors poor conductors.
As temperature rises, more electrons gain enough energy to cross the energy gap from the valence band to the conduction band. This movement creates holes in the valence band, and each electron-hole pair acts as charge carriers. Thus, the increase in charge carriers with temperature makes semiconductors better conductors.

• Electrons move to the conduction band at higher temperatures.
• Greater number of carriers = better conductivity.

Electron Scattering

In conductive materials, electron scattering plays a crucial role in determining conductivity. Scattering occurs when electrons collide with atoms, imperfections, or other electrons. In conductors, increased temperature causes increased scattering events due to more intense atomic vibrations.
This results in more collisions, hindering the smooth flow of electrons and therefore reducing conductivity. In semiconductors, however, even though scattering also increases with temperature, the effect is countered by the greater number of charge carriers generated at elevated temperatures. This highlights a key difference in how temperature affects conductivity in different materials.

• More temperature = more scattering in conductors.
• In semiconductors, charge carriers compensate for increased scattering.

Energy Bands

Energy bands are a pivotal concept in understanding conductivity. In solids, electrons occupy energy bands rather than discrete energy levels. The valence band is filled with electrons that are bound to atoms, whereas the conduction band contains electrons free to conduct electricity.
In semiconductors, there's a gap between these two bands—known as the energy gap. At absolute zero, this gap makes semiconductors insulative. As temperature increases, electrons can jump this gap, moving from the valence to the conduction band.
This transition enables conduction. The size of the energy gap determines how easily electrons can be excited to the conduction band; materials with a smaller energy gap are better conductors of electricity.

• Valence band: Electrons are bound.
• Conduction band: Electrons can move freely.
• Energy gap: Determines ease of conduction.