Why resistance is inversely proportional to relaxation time and relationship between conductivity mobility and carrier concentration of a semiconductor?
Understanding the Relationship between Resistance, Relaxation Time, and Conductivity:
Resistance (R) is a material's opposition to the flow of electric current. In conductors like metals, this opposition arises due to collisions between free electrons (electrons not bound to specific atoms) and the metal's positive ions (atomic cores). These collisions impede the smooth flow of electrons, causing resistance.
Relaxation time (τ) represents the average time between these collisions. Imagine electrons traveling through a corridor with obstacles. The time it takes for an electron to hit one obstacle and then another defines its relaxation time.
The relationship between resistance and relaxation time is:
R ∝ 1/τ (where ∝ represents "proportional to")
This means as the relaxation time increases (fewer collisions), the resistance decreases (easier flow of electrons) and vice versa.
Conductivity (σ) is the inverse of resistance, signifying a material's ability to conduct electricity. It relates to how easily current flows:
σ = 1/R
Therefore, from the first equation, we can also say:
σ ∝ τ
Relating Conductivity, Mobility, and Carrier Concentration in Semiconductors:
Semiconductors are materials with conductivity between conductors and insulators. Their conductivity depends on the number and mobility of charge carriers, typically electrons or holes (vacancies where electrons would be).
Carrier concentration (n) refers to the number of charge carriers per unit volume in the material. More carriers generally lead to more current flow, potentially increasing conductivity.
Mobility (μ) signifies the ease with which these carriers move under an electric field. Carriers with higher mobility experience fewer collisions and move faster, enhancing conductivity.
The relationship between conductivity, mobility, and carrier concentration in a semiconductor is:
σ = n * e * μ
where:
- e is the charge of an electron (constant)
Therefore, for semiconductors, increasing either carrier concentration or mobility can lead to higher conductivity.
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