A1 · Semiconductor basics

Energy Bands: What Lets a Material Conduct

Whether a material conducts electricity is set not by how densely packed its electrons are but by the energy gap between its full band and its empty band. In this unit you switch between an insulator, a semiconductor and a conductor and see how that gap decides the flow.

One band gap decides the flow

The blue band at the bottom is the valence band, full of electrons, and the orange-outlined band above is the empty conduction band. For current to flow, electrons must climb into the upper band and find empty room, and the gap marked in red between the two bands is the obstacle. Of the three materials, find which ones send electrons upward by watching for gold electrons drifting in the upper band.

Switch among the three materials with the buttons.

Band gap Eg

Eg ≈ 5 eV

The gap is too wide. Room-temperature thermal energy lifts almost no electrons to the upper band, so there are no gold electrons at all.

Blocked

A full band carries no current

An electron can only drift in one direction if there is an empty place to move into. In a band where every place is filled, like the valence band, an electron trying to go right has nowhere to go, and whenever one moves, another is pushed back by the same amount, so the motions cancel. That is why the net current is 0 however many electrons a full band holds.

Crossing the gap creates the flow

When a few electrons climb into the empty conduction band, two channels open at once: in the upper band the electrons that climbed roam wide-open room, and in the lower band the empty places they left behind, the holes, move. The number that climbs is set by a contest between the thermal energy kT and the gap Eg, and it drops off exponentially as the gap grows.

Observeσ ∝ n

Conductivity follows the number of free carriers.

Choosen ∝ exp(?)

The number that climbs depends exponentially on the gap.

Fill inn ∝ exp(-Eg / ?)

The thermal energy in the denominator opposes the gap.

On your ownσ ∝ exp(?)

Combined, conductivity depends exponentially on the gap.

Gap size sorts matter into three classes

With no gap, where the bands overlap, electrons always have empty room beside them, giving a conductor. With a gap of several eV, too wide for room-temperature heat to cross, the material is an insulator. In between, with a narrow gap of around 1 eV, sits the semiconductor. Because its gap is small, its flow can be switched on and off with heat, doping or light, and that is exactly why semiconductors are useful.

Back to the first screen

What sent electrons to the upper band were the conductor and the semiconductor. The conductor has no gap, so gold electrons always flow in the upper band; the semiconductor barely lifts electrons over its narrow gap with heat, making a thin flow from a few electrons and as many holes. The insulator, blocked by its wide gap, kept its electrons trapped in the full band, unable to move a single step. In the end, what decided the flow was not the number of electrons but the single gap between the filled band and the empty one.

The band gap Eg is the energy distance between the top of the full valence band and the bottom of the empty conduction band. A gap of 0 gives a conductor, a gap of several eV an insulator, and a narrow gap of about 1 eV a semiconductor. The number of free carriers goes as n ∝ exp(-Eg / 2kT), depending exponentially on the gap.

What comes next

A narrow gap leaves room to tinker with a semiconductor. The next unit mixes in a tiny amount of impurity atoms (doping) to deliberately make either the upper-band electrons or the lower-band holes the majority. Join the n-type and p-type made this way and you get the pn junction at the core of the diode.