Pure silicon at room temperature contains approximately 1.0 ×10^16 free electrons per cubic mete

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Pure silicon at room temperature contains approximately 1.0...

Pure silicon at room temperature contains approximately 1.0 $\times$ 10$^{16}$ free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time $\tau$ for silicon at room temperature. (b) Your answer in part (a) is much greater than the mean free time for copper given in Example 25.11. Why, then, does pure silicon have such a high resistivity compared to copper?

Key Concepts

Charge Carrier Density

Charge carrier density is the number of free charge carriers (electrons or holes) available per unit volume in a material. This density is fundamental in determining conductivity or resistivity, as a low carrier density can result in high resistivity even if each carrier can move freely.

Resistivity

Resistivity is a material property that quantifies how strongly a material opposes the flow of electric current. It is influenced by both the mobility of the charge carriers (which depends on mean free time and scattering) and the carrier density, with lower densities typically leading to higher resistivity.

Mean Free Time

Mean free time is the average time interval between successive collisions (scattering events) of charge carriers like electrons. It is a critical parameter in understanding how quickly carriers can move through a material before being deflected, affecting the overall conductivity and mobility.

Electron Scattering

Electron scattering refers to the interactions between electrons and imperfections, phonons, or other electrons in a material that disrupt the motion of the electrons. A longer mean free time indicates fewer collisions, which typically leads to higher mobility; however, mobility alone does not determine a material's conductivity.

Semiconductor Conduction

Semiconductor conduction involves the movement of charge carriers that are generated by thermal excitation across a band gap. In intrinsic semiconductors like pure silicon at room temperature, the number of free carriers is much lower compared to metals, leading to inherently higher resistivity despite potentially longer mean free times.

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