Photoelectric effect and energy bands

The single atom has discrete energy levels. But when very many atoms combine into a solid, their levels, so close to each other, “smear out” into continuous ranges called bands:

• Valence band: where the electrons “bound” to the atoms of the crystal lattice reside;
• Conduction band: where electrons are free to move through the material, producing electric current.

The energy difference between the two bands is called the gap (energy gap):

$E_\text{gap} = E_\text{cond} - E_\text{val}$

The width of the gap is what fundamentally distinguishes the broad classes of electrical materials.

Principle — Classification of materials

• Insulators: very large gap; even energetic photons struggle to promote an electron into conduction.
• Semiconductors (silicon, germanium): small gap, $\sim 1{,}1$ eV for silicon. At room temperature a few electrons manage to pass into the conduction band. This is the basis of all modern electronics.
• Conductors (metals): the valence band is full and some electrons are already in the conduction band; current flows easily.

The “band-based” photoelectric law

In the band picture, the photoelectric effect is naturally reformulated. If a photon strikes a semiconductor and its energy $hf$ is greater than the gap, the struck electron jumps from the valence band to the conduction band and contributes to the current:

$\ev{E_\text{cin,max} = h\,f - E_\text{gap}}$

If instead $hf < E_\text{gap}$, the photon is not absorbed: no current, regardless of the light intensity. This is what explains the existence of a photoelectric threshold, entirely analogous to the threshold frequency $f_0$ of the original experiment, with the gap $E_\text{gap}$ playing the role of the work function $W$.

Not the intensity, but the energy of the single photon

What counts is not the intensity of the light, but the energy of the single photon. Intense red light excites no electron (if the gap exceeds $\sim 1{,}8$ eV), while weak blue light succeeds. This is a fact incompatible with classical physics, where light is only a wave and only the overall transported energy matters.

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Topics: Fisica quantistica Concepts: Effetto fotoelettrico · Fotone

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