Conduction Band

The conduction band is the lowest band of allowed electron energies that is empty, or only partly filled, at absolute zero, and the electrons that occupy it are free to move through the crystal and carry current. In a metal the conduction band is partly full from the start. In a semiconductor or insulator it is empty at absolute zero and sits above the valence band across a band gap, so electrons appear in it only after being excited across the gap by heat, light or a dopant atom. The bottom edge of the band, the conduction-band minimum, sets the energy scale for nearly everything that electrons do in a semiconductor device.

Electrons reach the conduction band by thermal excitation, photoexcitation or donation from dopants, and the lowest-energy route usually dominates. At room temperature the typical thermal energy is only about 0.026 electron-volts, so lifting an electron across silicon's 1.12 electron-volt gap is a rare event: the equilibrium number of such electrons falls off exponentially with the size of the gap, giving about 10^10 per cubic centimetre in pure silicon. A photon with energy at or above the gap can do the same job, which is why silicon absorbs light with wavelengths shorter than about 1.1 micrometres, the property that image sensors and solar cells exploit. Dopants such as phosphorus provide electrons by an easier route: their extra electron sits only about 0.045 electron-volts below the band edge and is released at room temperature almost completely.

Where the minimum sits in momentum space decides whether a material can emit light. In gallium arsenide, with a gap of 1.42 electron-volts, the conduction-band minimum lies directly above the valence-band maximum, so an electron can fall straight across and release a photon. This direct gap is why gallium arsenide, and gallium nitride with a gap near 3.4 electron-volts, make efficient lasers and light-emitting diodes, including the blue LEDs recognized by the 2014 Nobel Prize in Physics to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura. Silicon and germanium have indirect gaps: the minimum sits at a different crystal momentum, in silicon about 85 percent of the way along the cubic axis toward the edge of the Brillouin zone, so the transition must also exchange momentum with a lattice vibration, a phonon. That extra step makes light emission by silicon highly inefficient and is the reason on-chip lasers have required other materials bonded or grown onto silicon.

Electrons in the conduction band do not behave as free-space electrons, and their pockets of occupation have a shape. Silicon has six equivalent conduction-band minima, called valleys, along the principal crystal axes, each elongated like a rugby ball: the effective mass is about 0.98 of the free-electron mass along the long axis and 0.19 across it. Strain, confinement in thin films and nanowires, and choice of crystal orientation shift which valleys are lower and so how fast carriers move, a lever that chip makers use deliberately. The conduction-band minimum also governs energy barriers at interfaces: the step between the conduction bands of silicon and silicon dioxide is about 3.1 electron-volts, which is the barrier that holds electrons in a flash-memory floating gate and which hot carriers must surmount to damage a gate oxide over time.

The Fermi level tells how far the conduction band is populated. In pure silicon the Fermi level lies near the middle of the gap and the conduction band is nearly empty; n-type doping moves it toward the conduction-band minimum, increasing the number of electrons exponentially with the shift, and in very heavily doped contacts it can enter the band, so the material behaves as a metal. Applying a gate voltage bends the bands near the oxide in a transistor, pulling the conduction-band edge toward the Fermi level until an electron channel forms, and in a bipolar device a forward-biased junction lowers the barrier for electrons to cross. A frequent misunderstanding is to treat the band as a place: the diagram's vertical axis is energy, and electrons in the conduction band occupy the whole crystal rather than a layer above the atoms. A second is to imagine conduction-band electrons as moving at constant speed; they scatter every fraction of a picosecond.

Read the conduction band as the empty upper level of the crystal where electrons become mobile: how high its bottom lies, where in momentum it sits and how many electrons are lifted into it explain how semiconductors conduct, emit light, absorb sunlight and switch.