Charge Carrier
A charge carrier is any particle or quasi-particle that is free to move through a material and so carry electric current. In metals the carriers are conduction electrons; in semiconductors they are electrons and holes; in electrolytes, batteries, seawater and nerve cells they are ions such as sodium, potassium and lithium; and in a plasma both electrons and ions contribute. Whatever the medium, a material conducts only to the extent that it contains carriers that are both numerous and able to move, and nearly all the differences between a copper wire, a silicon chip, a salt solution and a glass rod can be traced to those two quantities.
Conductivity is, in words, the charge on each carrier multiplied by the number of carriers per unit volume and by how easily they move. Written compactly it is σ = q × n × μ for a single kind of carrier, and for a semiconductor with both electrons and holes the two contributions are added, with n and p the electron and hole concentrations and μ the mobility of each. Mobility is the drift velocity a carrier acquires per unit electric field; it is limited by scattering from lattice vibrations, from impurity atoms and from surfaces. Resistivity is simply the inverse of conductivity, so the same three ingredients explain the resistance of any wire or resistor. Charge is fixed by nature, so engineers adjust conductivity by changing concentration, through doping or temperature, or by changing mobility, through crystal quality and strain.
Pure silicon has remarkably few carriers, which is why it is a semiconductor and not a metal. The intrinsic carrier concentration, the number of electrons, equal to the number of holes, present in an undoped crystal in thermal equilibrium, is about 10^10 per cubic centimetre at room temperature for silicon, widely quoted values ranging from about 1.0 to 1.5 × 10^10 depending on convention and temperature. The crystal contains about 5 × 10^22 atoms per cubic centimetre, so only about one atom in five trillion has given up a carrier. For germanium, with its smaller gap, the figure is of order 10^13, and for wide-gap materials such as silicon carbide it is minute. The intrinsic concentration depends exponentially on temperature, which is why leakage rises steeply in a hot chip and why the pure-silicon resistivity of about 2 × 10^5 ohm-centimetres is of no practical use in a transistor.
Doping decouples carrier concentration from temperature and makes conduction controllable. Adding phosphorus at 10^16 atoms per cubic centimetre supplies about 10^16 electrons, a million times more than the intrinsic crystal has, dropping the resistivity to roughly half an ohm-centimetre. Because the majority carrier count is pinned to the dopant level, conductivity is stable across the normal operating range, while the minority carriers, the holes in n-type material, remain tiny and temperature dependent. The product of the two concentrations in equilibrium stays equal to the square of the intrinsic concentration, which is the mass-action law behind every pn junction. This control, with the ability to inject extra carriers across a junction, is what the transistor exploits.
The sign and number of carriers can be measured, and doing so is how many material properties are known. In the Hall effect, discovered by Edwin Hall in 1879, a magnetic field deflects moving carriers sideways and generates a voltage across the sample whose sign shows whether electrons or holes dominate and whose size gives their concentration. Combined with a resistivity measurement, it yields mobility. Hall measurements on germanium and silicon in the late 1940s and 1950s, along with the Haynes-Shockley drift experiment, helped establish the existence of holes as real carriers. Today Hall-effect sensors in cars and phones, and routine Hall characterization in wafer laboratories, rely on the same physics.
Carriers are not always electrons, and fast does not mean far. In a lithium-ion battery, lithium ions shuttle between electrodes while electrons travel through the external circuit, and ions in water move with mobilities thousands of times smaller than electrons in silicon, which is why electrolytes conduct so much worse than metals even when ions are plentiful. In superconductors the carriers are paired electrons. Even in silicon, carriers cannot speed up forever: above a field of several kilovolts per centimetre scattering limits their velocity to a saturation value near 10^7 centimetres per second, a limit that shapes the switching speed of every modern transistor, including those in AI accelerators. A common misconception is that carriers are used up like fuel; they merely move through, are replaced, and recombine, so a circuit does not drain charge.
Read a charge carrier as the mobile unit of electric current in any medium: its charge, its numbers and its mobility, set by chemistry, doping, temperature and crystal quality, together determine whether a material is a conductor, a semiconductor or an insulator.