Electrons & Atomic Structure

Intuition

Where the moving charge comes from

Every material is made of atoms, and every atom has the same basic plan: a tiny, dense nucleus at the centre, with electrons around it. The nucleus contains protons, which carry positive charge, and neutrons, which carry none. The electrons carry negative charge.

In an undisturbed atom the numbers match exactly — as many electrons as protons — so the positive and negative cancel and the atom is neutral. That is why a copper wire, made of enormous numbers of copper atoms, does not shock you when it is sitting in a drawer.

How tightly an electron is held depends on where it sits. The ones close to the nucleus are gripped firmly, while those out at the edge — the outer or valence electrons — are held only loosely, and in some materials barely at all.

In a metal, those outermost electrons are so weakly attached that they leave their own atoms altogether and wander through the material as a shared pool. Nudge them with a voltage and they drift, which is exactly what current is. In rubber, glass or plastic, every electron stays firmly with its own atom, so no matter how hard you push, almost nothing moves.

Whether the outer electrons can wander is what separates a wire from the insulation wrapped around it, and it is a property of the material itself rather than of the voltage applied to it. The rest of this lesson works out where that property comes from.

Practitioner

Valence electrons and what they predict

Electrons around an atom occupy shells, and each shell holds a fixed maximum number. What matters electrically is only the outermost occupied shell, the valence shell, because a full inner shell is chemically and electrically inert. Atoms are most stable with a full valence shell, and how far an atom sits from that condition predicts most of a material's electrical behaviour:

• One valence electron — copper, silver, gold, aluminium. The lone electron is barely held, escapes easily, and joins a shared "sea" of free electrons permeating the metal. Wires are made from these, the best conductors there are.
• Four valence electrons — silicon, germanium, carbon. The shell is half filled, so the atom shares its electrons with neighbours in a rigid covalent lattice instead of releasing them. Almost none are free at room temperature, though a small amount of energy sets some loose. These are the semiconductors.
• Seven or eight valence electrons, or shared covalent bonds in a polymer — the halogens, the noble gases, and the long-chain molecules that make up plastics and rubber. Either the electrons are held tightly or the shell is already full, and in both cases nothing is available to move. That is what an insulator is.

This is the practitioner's rule of thumb behind conductors and insulators, and it is why the periodic table's left-hand side is where wires come from and its right-hand side is where insulation comes from.

An atom that has gained or lost electrons is an ion, and it is no longer neutral: losing electrons leaves it positive, gaining them makes it negative. Ions are the carriers in a battery's electrolyte, in seawater and in the human body, so electrons are not the only thing that can carry a current, only the most common thing in the materials circuits are built from.

Loosely held outer electrons can also be scraped off a surface by nothing more than contact and separation, which is why insulating materials pick up and hold static charge so readily. That is the mechanism behind electrostatic discharge, and it is why plastics are the problem material on a bench rather than the safe one.

Engineer

From shells to bands

The shell picture is exact for an isolated atom and misleading for a solid. Bring 10²³ atoms together and their outer orbitals overlap; the sharp energy levels of the individual atoms spread into near-continuous bands of allowed energy, separated by gaps where no electron state exists at all. Only the highest filled band and the first empty one above it decide whether the material conducts:

• The valence band, the highest band that is full of electrons at absolute zero. Electrons in it are bound to particular bonds and cannot carry current, because a full band has no empty states to move into.
• The conduction band, the next band up. An electron here is free to move through the crystal, and the empty state it left behind in the valence band — a hole — behaves as a mobile positive carrier.

The band gap is the energy separating those two bands, and its size alone sorts materials into conductors, semiconductors and insulators:

An electron can cross the gap only if something gives it at least that much energy — heat, light, or a strong field. At room temperature the available thermal energy is small, so a gap is best judged as a ratio against that thermal energy rather than read in electronvolts on its own.

Charge itself is granular at this level, and that granularity is measurable. The classic demonstration is the oil-drop experiment: measure the charge on many small droplets and every result turns out to be a whole-number multiple of one indivisible amount.

The Fermi level is the energy at which a state has an even chance of being occupied. Where it sits relative to the bands is what doping changes, and the alignment of Fermi levels across a junction is what creates a built-in potential — the foundation of the PN junction.

Effective mass is the other correction, and it explains why mobility differs so sharply between materials, and between electrons and holes in the same material. A carrier moving through a crystal does not respond to a field the way a free electron would, because the lattice's periodic potential modifies its inertia.

Band structure also explains a difference that puzzles beginners: metals get more resistive as they warm, because more lattice vibration means more scattering of carriers whose number is fixed. Semiconductors get less resistive, because heating creates carriers far faster than it increases scattering. Both effects are quantified in temperature effects on resistance.

Professional

What the band gap decides in practice

The gap sets the voltage and temperature envelope a device can work inside. A wider gap means a higher critical electric field before avalanche breakdown, and far fewer thermally generated carriers at elevated temperature. Silicon carbide and gallium nitride are sold on exactly that: for a given blocking voltage the drift region can be far thinner and more heavily doped, so conduction loss falls, and junction temperatures that would put silicon into thermal runaway are routine. The cost is substrate price, gate-drive fussiness and, for GaN, no avalanche rating to fall back on.

Forward drop and leakage move together, and the gap is what ties them. Germanium's narrow gap gives both the low forward voltage that made it attractive in detector and low-signal work and the large reverse leakage that made it unusable at temperature; silicon trades the other way. Schottky diodes reach a low forward drop through a metal–semiconductor barrier instead of a PN junction, and pay for it in leakage that climbs steeply with temperature (see Schottky diodes). Junction leakage roughly doubles for every ten-degree rise, so a leakage figure quoted at room temperature is almost never the figure that matters.

An LED's photon energy is essentially its band gap, so choosing the material and choosing the colour are one decision: the blue and white LED industry exists because gallium nitride's gap happens to land in the right place. Running the relation backwards makes photodiodes and solar cells material-specific. Silicon is blind beyond the near infrared, because a photon below its gap cannot excite a carrier at all. See LEDs and photodiodes.

What fixes the carrier count in a working device is doping rather than purity. Parts-per-million of a group-five or group-three impurity swamps the intrinsic carrier population and holds the conductivity steady across the whole useful temperature range, which is what makes semiconductor devices predictable. The temperature at which intrinsic carriers catch up with the dopants is the real ceiling on junction temperature, and it belongs to the material rather than to the package. Semiconductor materials develops this.

Precision analogue work runs into a different consequence of the same electronic structure. Every junction between dissimilar metals develops a small contact potential from the difference in work function, and any temperature difference across such a junction generates a thermal EMF of tens of microvolts per degree. In a microvolt-level measurement chain, unmatched solder joints and connector plating become the dominant error source long before amplifier offset does. Exploit that effect deliberately and you have a thermocouple.

Conductors also wear out at the atomic scale. At high current density the momentum handed over by drifting electrons physically moves metal atoms, thinning a conductor until it opens and piling material up until it shorts. Electromigration is why on-chip and thin-film conductors carry an explicit current-density limit, and why copper displaced aluminium as IC metallisation.