Understanding Conductors and Semiconductors: Conductivity, Resistivity, and Carrier Dynamics

What Are Conductors? 

Conductors are those materials where electrons flow like water, facing almost no resistance, because a sea of free electrons is already waiting to move.

In conductors, the valence band and conduction band overlap —
meaning electrons are already free to move without needing extra energy.


Important Notes:

  • The number of free electrons in pure conductors (like copper, silver) is naturally very high and fixed.

  • Heating affects how fast electrons move (mobility), but doping is rarely done in conductors — because they already have an abundance of free electrons.

  • Doping is a concept mainly used in semiconductors, not conductors.

What Are Semiconductors?

Semiconductors are smart materials that can behave like an insulator or a conductor, depending on how we treat them — like a magical gateway between ON and OFF.


  • Semiconductors have a small energy gap (1.1 eV for silicon).
  • At room temperature(300K), a few electrons jump the gap and become free.

But this isn’t enough for proper conduction. To make them conduct effectively, we use doping.

Why Semiconductors Need Doping

Without doping, intrinsic semiconductors can't conduct well because they don't have a majority of charge carriers (electrons or holes) — they are essentially insulators at room temperature. Doping fixes this by adding extra electrons or creating holes, allowing for controlled conduction.

Doping and Dopants

Doping: The process of adding dopants to an intrinsic semiconductor to create extrinsic semiconductors.

  • p-type (positive): Trivalent elements like boron create holes (positive charge carriers, majority carriers).

  • n-type (negative): Pentavalent elements like phosphorus add extra electrons (majority carriers).

Intrinsic vs. Extrinsic Semiconductors

  • Intrinsic Semiconductors: Pure semiconductors like silicon that behave like insulators at room temperature because they don't have enough free electrons to conduct.

  • Extrinsic Semiconductors: Semiconductors that are doped with other elements (dopants) to introduce free charge carriers (either electrons or holes), making them conduct better.

Types of Extrinsic Semiconductors

1. n-type Semiconductors

  • Doped with pentavalent elements (5 valence electrons).

  • Extra electron = extra negative charge carrier (electron = majority).

  • Example: Phosphorus in Silicon.

2. p-type Semiconductors

  • Doped with trivalent elements (3 valence electrons).

  • Creates a hole = missing electron = positive charge carrier (hole = majority).

  • Example: Boron in Silicon.

Conductivity of Conductors

The conductivity (σ) of a conductor:


Where:

  • q = Electron charge

  • n = Number of free electrons per unit volume

  • μ = Mobility of carrier electrons

Conductivity of Semiconductor 

For semiconductors, the conductivity (σ) is expressed as:


Where:

  • n = Electron concentration

  • μₙ = Mobility of electrons

  • p = Hole concentration

  • μₚ = Mobility of holes

Both electrons and holes contribute to conductivity, but their mobilities and concentrations differ.

Key Insight:

  • In an n-type semiconductor, the concentration of electrons (n) increases significantly, while the hole concentration (p) becomes negligible.

  • In a p-type semiconductor, the opposite happens — holes dominate.

Resistivity and Conductivity: 

Resistivity (ρ) is the inverse of conductivity (σ):

The resistance (R) is given by:

Where:

  • L = Length of the material

  • A = Cross-sectional area of the material

In summary, resistivity increases as conductivity decreases and vice versa.

Effect of Temperature on Conductors

  • As temperature increases, atoms vibrate more, causing more collisions with electrons, which decreases mobility (μ).

  • Decreased mobility leads to lower conductivity (σ) and higher resistivity. This is why conductors like copper and silver increase resistance with temperature.

        

  • At low temperatures, conductors become superconductors, showing zero resistance as atomic vibrations slow down — allowing perfect electron flow.

        

Effect of Temperature on Semiconductors

  • For semiconductors, the band gap allows a few electrons to jump into the conduction band as temperature rises.

  • As temperature increases, more electrons gain enough energy to become free, resulting in higher conductivity.

        


  • Negative Temperature Coefficient (NTC): As temperature rises, the resistance decreases, which is the opposite behavior compared to conductors.

            

  • At low temperatures, semiconductors behave like insulators because not enough electrons have enough energy to jump the gap.

Law of Mass Action

In any semiconductor:

 

Where:

  • n = number of free electrons

  • p = number of holes

  • nᵢ = intrinsic carrier concentration (constant for a given temperature)

When you dope a semiconductor:

  • If you add pentavalent atoms, n increases (more electrons).

  • But to keep n × p constant, p must decrease.

    (Minority carriers adjust themselves to maintain balance.)

Similarly:

  • If you add trivalent atoms, p increases (more holes).

  • So n must decrease automatically.

Thus, the Law of Mass Action ensures balance between electrons and holes, no matter what.

Key Insight:

  • Doping increases the majority carriers but suppresses minority carriers.

Why Are these so important?

  • All modern transistors, diodes, LEDs, and solar cells are based on controlling majority and minority carriers.

  • Understanding conductivity, resistivity, and carrier concentration allows us to design faster processors, better sensors, and efficient power devices.

  • Without these basics, electronics engineering itself cannot exist!

If you are curious about Electronic Devices , bookmark us , follow this series and share if you found it helpful

Explore more like this at hobitronics.blog

Stay curious! Stay Charged!

Comments

  1. Ari28 April 2025 at 03:10

    Why does doping with pentavalent atoms (n-type doping) not significantly change the mobility of electrons, but mainly increases the carrier concentration (n)?

    ReplyDelete
  2. Hobitronics28 April 2025 at 03:36

    That is a very good question , doping with pentavalent atoms , injects more free electrons to the conduction band. Therefore the majority carrier concentration (electrons) in this case increases.
    These electron go and occupy holes( holes are absence of electron) , this is in accordance with the Mass Action Law! Still mobility of electron is not changing , cause mobility does not depend on doping or concentration of charge carriers, it depends on external electric field(if provided!).

    ReplyDelete

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