A1 · Semiconductor basics

Energy Bands: What Lets a Material Conduct

Whether a material conducts is set not by how many electrons it has, but by the energy gap between its full band and its empty band. Widen and shrink that gap yourself.

Change the gap and wake the flow

The lower band is packed with electrons and the upper band is empty. For current to flow, electrons must climb to the upper band and find room to move. Which material sends electrons up?

Tap to change the material.

Band gap Eg

Eg ≈ 5 eV

The gap is too wide. Thermal energy lifts almost no electrons to the upper band.

Blocked

A full band carries no current

Electrons can drift one way only if there is empty room. When every seat is taken, as in a full valence band, an electron that wants to move right has nowhere to go. So no matter how many electrons fill a full band, the net current is zero.

Crossing the gap creates the flow

When a few electrons climb into the empty conduction band, two channels open at once: up top those electrons roam the wide-open room, and down below the vacancies they left (holes) move. The number that makes it up is a contest between thermal energy kT and the gap Eg, so it falls off exponentially as the gap grows.

Observeσ ∝ n

Conductivity tracks the free-carrier count.

Choosen ∝ exp(?)

The number that climbs hangs exponentially on the gap.

Fill inn ∝ exp(-Eg / ?)

The thermal energy in the denominator fights the gap.

On your ownσ ∝ exp(?)

Combine the two: conductivity hangs exponentially on the gap.

Gap size sorts matter into three classes

With no gap (overlapping bands) electrons always sit beside empty room, giving a conductor. With a gap of several eV, too wide for room-temperature heat to cross, you get an insulator. In between, with a narrow gap around 1 eV, sits the semiconductor. Being small, that gap can be switched on and off with heat, doping, or light, and that is what makes semiconductors useful.

Back to the first screen

What sent electrons to the upper band were the conductor and the semiconductor. The conductor has no gap and always flows; the semiconductor barely lifts electrons over its narrow gap with heat to make a trickle. The insulator, blocked by its wide gap, keeps its electrons trapped in a full band, unable to take a single step. In the end, what decided the flow was not the number of electrons but the single gap between the full 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 zero gives a conductor, several eV an insulator, and a narrow ~1 eV a semiconductor. The free-carrier count goes as n ∝ exp(-Eg / 2kT), hanging exponentially on the gap.

What comes next

A narrow gap gives the semiconductor room to play. The next unit mixes in a pinch of impurity atoms (doping) to make either the upper-band electrons or the lower-band holes deliberately the majority. Joining the n-type and p-type you build that way gives the pn junction at the heart of every diode.