Recombination

Recombination is the process in which a free electron falls into an empty state in the valence band, a hole, so that both mobile carriers disappear and their energy is released. It is the reverse of generation, in which energy lifts an electron across the band gap and creates a pair. In equilibrium the two processes balance exactly; whenever a device pushes carriers out of balance, by injecting current or absorbing light, recombination is the mechanism that works to restore the balance, and the time it takes defines the carrier lifetime that appears throughout semiconductor physics.

Recombination comes in three main varieties, which differ in where the released energy goes. In radiative recombination the energy leaves as a photon, with wavelength in micrometers about 1.24 divided by the gap in electron-volts. In Shockley-Read-Hall recombination, described in 1952 by William Shockley and William Read and independently by Robert Hall, an electron and a hole meet at a defect level near the middle of the gap and the energy is turned into lattice vibrations, which is heat. In Auger recombination, named for Pierre Auger, the energy is handed to a third carrier that is kicked high into a band and then relaxes thermally; it grows rapidly with carrier density, roughly as the cube of concentration, so it dominates in heavily doped or strongly injected material. Radiative recombination is the one engineers want in light sources; the other two are non-radiative losses.

Whether a material is a good light emitter depends on the shape of its band structure. In a direct-gap semiconductor such as gallium arsenide or gallium nitride, the lowest conduction-band state and the highest valence-band state occur at the same crystal momentum, so an electron can drop straight into a hole and emit a photon with no extra help. In an indirect-gap semiconductor such as silicon, with a gap of about 1.12 electron-volts, the band extremes sit at different momenta, so recombination also needs a lattice vibration, a phonon, to conserve momentum. That makes the radiative process a three-body event that is far less probable than non-radiative routes, and in silicon the radiative rate is lower than in gallium arsenide by several orders of magnitude.

The same physics splits devices into those that want recombination and those that fear it. In an LED the injected electrons and holes are squeezed into a thin active layer so they recombine radiatively before they wander off; Nick Holonyak demonstrated a visible red LED in 1962, and the efficient blue gallium nitride LED, for which Isamu Akasaki, Hiroshi Amano and Shuji Nakamura received the 2014 Nobel Prize in Physics, made white solid-state lighting possible. A laser diode adds a resonant cavity so that radiative recombination becomes stimulated emission. A solar cell and a bipolar transistor are the opposite: every recombination event before collection is a lost carrier, so efficiency and gain depend on long lifetimes, clean crystals and passivated surfaces, the same surface states that once blocked the field effect.

Silicon's poor light emission is a deep reason why optical links and silicon chips are built from different materials. Because silicon recombines almost entirely non-radiatively, a pure-silicon laser has remained out of reach, and silicon photonics instead couples silicon waveguides and modulators to indium phosphide or gallium arsenide lasers that are bonded or attached to the chip. A common misconception is that low recombination is always good; in a transistor it is, but a switch-off that relies on recombination, or a power device that wants fast turn-off, may deliberately shorten the lifetime by adding gold or by irradiation. Recombination is therefore not a defect to be abolished but a rate to be tuned, up for lamps and down for cells.

Read recombination as the universal undo button of semiconductors: every injected or photo-generated pair is eventually erased, and whether that erasure produces a useful photon in an LED, a wasted bit of heat in a solar cell, or a lifetime that sets transistor gain depends on whether the gap is direct or indirect and on how clean the crystal is.