Question

Predict the effect (if any) of a decrease in temperature on the electrical conductivity of (a) silicon; (b) lead; (c) germanium.

Short answer

For silicon and germanium, a decrease in temperature reduces conductivity. For lead, a decrease in temperature increases conductivity.

Step-by-step solution

Understanding Electrical Conductivity

Electrical conductivity is the measure of a material's ability to conduct an electric current. It depends on the type of material and the availability of charge carriers (electrons or holes).

Silicon - Semiconductor Properties

Silicon is a semiconductor. In semiconductors, the number of charge carriers decreases as temperature decreases. Hence, for silicon, a decrease in temperature will reduce the electrical conductivity because fewer electrons have the energy to jump into the conduction band.

Lead - Metal Properties

Lead is a metal, and its conductivity is primarily due to free-moving electrons. In metals, as the temperature decreases, the vibrations of the atomic lattice reduce, which in turn decreases the scattering of electrons. Hence, for lead, a decrease in temperature will increase the electrical conductivity.

Germanium - Semiconductor Properties

Germanium, like silicon, is a semiconductor. The decrease in temperature will reduce the number of charge carriers (electrons and holes). Therefore, for germanium, a decrease in temperature will also reduce the electrical conductivity.

Key concepts

Electrical Conductivity

Electrical conductivity refers to a material's ability to allow the flow of electric current. The units of conductivity are Siemens per meter (S/m). This property depends on the number of charge carriers (electrons or holes) available, and their mobility through the material. Materials can be broadly categorized into conductors, like metals, which have high conductivity, semiconductors with moderate conductivity, and insulators with low conductivity. In metals, free electrons are the primary carriers, while in semiconductors, electron movement depends highly on the material's temperature and impurity levels.

Semiconductor Properties

Semiconductors like silicon and germanium have unique properties that place them between conductors and insulators. Their conductivity isn't as high as metals but can increase significantly with temperature or doping (adding impurities). At absolute zero, semiconductors act like insulators as the valence band's electrons lack the energy to jump into the conduction band. However, as temperature increases, more electrons can gain enough energy to jump into the conduction band, increasing conductivity. Semiconductors are vital in modern electronics because their conductivity can be controlled, making them ideal for creating diodes, transistors, and solar cells.

Temperature Dependence of Conductivity

The relationship between temperature and conductivity varies across different materials. For conductors like metals, decreasing the temperature reduces the lattice vibrations, which lessens electron scattering and increases conductivity. In contrast, the conductivity of semiconductors decreases with a drop in temperature. As temperature decreases, fewer electrons gain enough energy to break free from their atoms, reducing the number of charge carriers and thus the material's ability to conduct electricity. This temperature dependence is critical in designing electronic devices, which need to maintain proper function across various operating temperatures.

Silicon Conductivity

Silicon is one of the most widely used semiconductors in the electronics industry due to its stable properties and abundance. Its electrical conductivity is highly dependent on temperature. At lower temperatures, silicon's conductivity drops because fewer electrons have sufficient energy to move from the valence band to the conduction band. This behavior makes silicon suitable for temperature-sensitive applications. Silicon's conductivity can be increased significantly by doping it with elements like phosphorus or boron, introducing extra free charge carriers that enhance its performance in electronic devices.

Lead Conductivity

Lead is a metal with substantial electrical conductivity due to its many free-moving electrons. Unlike semiconductors, lead's conductivity increases as temperature decreases. This is because lower temperatures decrease atomic vibrations, resulting in fewer electron scattering events. The reduced scattering allows electrons to move more freely through the metal, enhancing conductivity. Lead's stable conductivity at varying temperatures makes it useful in specific applications, even though it is not as widely used in modern electronics due to its toxicity and availability of better alternatives.

Germanium Conductivity

Germanium, another semiconductor, shares similar properties with silicon but is less common in commercial electronics. Like silicon, germanium's electrical conductivity decreases with a reduction in temperature. The reason is the same - fewer electrons have the thermal energy to jump from the valence band to the conduction band at lower temperatures. Germanium was one of the first materials used to make transistors, but it has largely been supplanted by silicon. However, germanium is still used in some high-speed electronic devices and infrared optics due to its unique properties.