Optical absorption and emission describe how light interacts with the electronic structure of a semiconductor. Absorption occurs when photons excite electrons from the valence band to the conduction band, creating excess carriers. Emission happens when those electrons relax back down, releasing photons. Together, these processes underpin devices like solar cells, LEDs, photodetectors, and lasers.

Absorption of photons

When a semiconductor absorbs a photon with energy at least equal to the bandgap ( $h\nu \geq E_g$ ), an electron gets promoted from the valence band to the conduction band, leaving behind a hole. The absorption process can be direct or indirect, depending on the semiconductor's band structure, and the absorption coefficient tells you how quickly light intensity drops as it travels into the material.

Direct vs indirect absorption

Direct absorption happens when the conduction band minimum and valence band maximum sit at the same crystal momentum ( $k$ -value). The electron transitions straight up in an $E$ - $k$ diagram, conserving momentum without any help.

Occurs in direct bandgap semiconductors like GaAs and InP
Produces strong absorption and efficient light emission because no extra particle is needed

Indirect absorption requires a change in both energy and momentum. Since a photon carries very little momentum, a phonon (a quantum of lattice vibration) must participate to supply the momentum difference.

Occurs in indirect bandgap semiconductors like Si and Ge
The need for a phonon makes the process less probable, so absorption is weaker and radiative emission is far less efficient

This distinction matters a lot in practice: it's why GaAs is used for LEDs and laser diodes, while Si dominates solar cells and detectors (where weaker absorption can be compensated with thicker material).

Absorption coefficient

The absorption coefficient $\alpha$ quantifies how rapidly light intensity decays inside the semiconductor. Light intensity at depth $x$ follows Beer-Lambert's law:

$I(x) = I_0 \, e^{-\alpha x}$

where $I_0$ is the incident intensity. A large $\alpha$ means the light is absorbed within a short distance (small penetration depth, roughly $1/\alpha$ ).

The absorption coefficient relates to the imaginary part $k$ of the complex refractive index:

$\alpha = \frac{4\pi k}{\lambda}$

For direct bandgap materials near the band edge, $\alpha$ rises steeply once $h\nu > E_g$ , roughly following $\alpha \propto (h\nu - E_g)^{1/2}$ . For indirect bandgap materials, the onset is more gradual because phonon assistance is required, and $\alpha$ follows a weaker dependence on $(h\nu - E_g)$ .

Factors affecting absorption

Bandgap energy: Photons with $h\nu < E_g$ pass through largely unabsorbed. Once $h\nu$ exceeds $E_g$ , absorption rises sharply.
Temperature: Higher temperatures narrow the bandgap slightly (described by the Varshni relation), shifting the absorption edge to lower photon energies.
Doping concentration: Heavy doping introduces free carriers that can absorb sub-bandgap photons (free carrier absorption) and can also cause band-tail states that blur the absorption edge.
Material composition: Alloying (e.g., $Al_xGa_{1-x}As$ ) lets you tune the bandgap and therefore the absorption spectrum continuously.

Emission of photons

Emission is the reverse of absorption: an electron in the conduction band recombines with a hole in the valence band, releasing a photon with energy close to $E_g$ . This is called radiative recombination, and it's the mechanism behind all semiconductor light sources.

Spontaneous vs stimulated emission

Spontaneous emission occurs when an electron drops to the valence band on its own, without any external photon triggering it.

The emitted photons have random phase, polarization, and direction
This is the dominant emission mechanism in LEDs, producing incoherent light

Stimulated emission occurs when an incoming photon of the right energy triggers an electron to recombine, producing a second photon that is identical to the first in phase, frequency, polarization, and direction.

This is the mechanism behind laser operation
It requires population inversion: more electrons must occupy the conduction band states than the valence band states at the transition energy, which is a non-equilibrium condition achieved by strong electrical or optical pumping

Radiative recombination

In radiative recombination, the photon energy approximately equals the bandgap: $h\nu \approx E_g$ . The recombination rate $R_r$ depends on the electron and hole concentrations:

$R_r = B \, n \, p$

where $B$ is the radiative recombination coefficient (material-dependent, typically on the order of $10^{-10}$ cm $^3$ /s for direct bandgap materials). Direct bandgap semiconductors have much larger $B$ values than indirect ones, which is why they dominate light-emission applications.

Luminescence in semiconductors

Luminescence is a general term for light emission from a semiconductor due to electron relaxation from excited states. The name changes depending on how you create the excitation:

Photoluminescence (PL): Excitation by absorbed light (a laser or lamp). Widely used as a characterization tool to probe bandgap, defects, and carrier lifetimes.
Electroluminescence (EL): Excitation by injected current, as in LEDs and laser diodes.
Cathodoluminescence (CL): Excitation by an electron beam, often used in electron microscopy for spatially resolved optical characterization.

Optical transitions

Optical transitions are the specific electronic transitions that occur when photons are absorbed or emitted. The type of transition depends on the band structure and whether impurities or defects are present.

Band-to-band transitions

These are transitions directly between the valence band and the conduction band. The photon energy satisfies $h\nu \approx E_g$ . Band-to-band transitions are the dominant absorption and emission mechanism in intrinsic (undoped) semiconductors and set the fundamental absorption edge.

Direct vs indirect absorption, Indirect to direct bandgap transition in methylammonium lead halide perovskite - Energy ...

Excitonic transitions

When an electron is excited to the conduction band, it can remain Coulomb-bound to the hole it left behind, forming an exciton. This bound pair has a binding energy $E_x$ (typically a few meV in bulk semiconductors like GaAs, but can be tens of meV in wide-bandgap materials like GaN or ZnO).

Because of this binding energy, excitonic absorption and emission occur at a photon energy slightly below the bandgap:

$h\nu = E_g - E_x$

Excitonic features appear as sharp peaks in absorption and emission spectra, especially at low temperatures where thermal energy doesn't break apart the excitons.

Free carrier absorption

Free carrier absorption (FCA) involves electrons or holes that are already in a band absorbing photons and moving to higher-energy states within the same band. No band-to-band transition occurs.

FCA increases with carrier concentration, so it's most significant in heavily doped material
It scales roughly as $\alpha_{FCA} \propto \lambda^2$ (stronger at longer wavelengths), making it a concern in the infrared
In devices like lasers, FCA represents a parasitic optical loss that reduces efficiency

Optical properties of semiconductors

The optical properties of a semiconductor describe how it bends, slows, disperses, and absorbs light. These properties are captured by the complex refractive index $\tilde{n} = n + ik$ , where $n$ governs refraction and phase velocity, and $k$ governs absorption.

Refractive index

The real part of the refractive index $n$ tells you how much light slows down inside the semiconductor relative to vacuum. It connects to the relative dielectric constant:

$n = \sqrt{\varepsilon_r}$

(valid when absorption is negligible). Typical values: Si has $n \approx 3.5$ and GaAs has $n \approx 3.3$ at wavelengths near their bandgaps. A high refractive index means strong reflection at air-semiconductor interfaces, which is why anti-reflection coatings matter for solar cells.

Optical dispersion

Dispersion means the refractive index changes with wavelength (or photon energy). This happens because the semiconductor's polarization response depends on the frequency of the incoming light.

Normal dispersion: $n$ increases with increasing photon energy (away from resonances). This is the typical behavior for photon energies well below the bandgap.
Anomalous dispersion: $n$ decreases with increasing photon energy, occurring near absorption resonances (close to $E_g$ ).

Dispersion is important for designing waveguides, optical fibers, and any device where different wavelengths of light need to travel together.

Kramers-Kronig relations

The Kramers-Kronig relations are integral equations that link the real part $n(\omega)$ and imaginary part $k(\omega)$ of the complex refractive index. They arise from a fundamental physical requirement: causality (the material can't respond before the light arrives).

In practice, these relations are useful because:

If you measure the absorption spectrum (giving you $k$ vs. $\omega$ ), you can calculate $n$ vs. $\omega$ without a separate measurement, and vice versa
They serve as a consistency check on experimental optical data

Applications of optical absorption and emission

The absorption and emission properties covered above are directly exploited in a range of optoelectronic devices.

Photodetectors

Photodetectors convert light into an electrical signal by absorbing photons and generating electron-hole pairs.

Photodiodes: Reverse-biased p-n junctions where photogenerated carriers are swept by the built-in and applied fields, producing a photocurrent proportional to light intensity.
Phototransistors: Transistors where photogenerated carriers in the base region get amplified by transistor action, giving higher sensitivity but slower response.
Avalanche photodiodes (APDs): Operate at high reverse bias so that photogenerated carriers undergo impact ionization, multiplying the signal. Useful for detecting very weak optical signals.

Solar cells

Solar cells absorb sunlight and convert it to electricity via the photovoltaic effect. Photons with $h\nu \geq E_g$ generate electron-hole pairs, which are separated by the built-in electric field of a p-n junction and collected at external contacts.

Key performance parameters:

Power conversion efficiency (PCE): Electrical power out divided by optical power in. Single-junction Si cells reach about 26% in the lab.
Open-circuit voltage ( $V_{OC}$ ): Maximum voltage under illumination with no current flowing. Related to the bandgap and recombination losses.
Short-circuit current ( $I_{SC}$ ): Maximum current under illumination with zero voltage. Depends on how many photons are absorbed and how efficiently carriers are collected.

Light-emitting diodes (LEDs)

LEDs produce light through electroluminescence. A forward-biased p-n junction injects electrons and holes into an active region where they recombine radiatively.

Emission wavelength: Set by the bandgap of the active material. GaN-based LEDs emit blue/UV light; AlGaInP-based LEDs emit red/orange.
Internal quantum efficiency (IQE): Fraction of injected electron-hole pairs that recombine radiatively (as opposed to non-radiatively).
External quantum efficiency (EQE): Fraction of injected electrons that produce photons that actually escape the device. Always lower than IQE due to internal reflection and absorption losses.

Semiconductor lasers

Semiconductor lasers generate coherent, monochromatic light via stimulated emission. They consist of a p-n junction with a thin active region inside an optical cavity (typically formed by cleaved crystal facets acting as mirrors).

Threshold current: The minimum injection current needed to reach population inversion and begin lasing. Below threshold, the device behaves like an LED.
Spectral linewidth: Much narrower than LED emission because stimulated emission produces photons of nearly identical wavelength.
Wall-plug efficiency: Ratio of optical output power to total electrical input power. Modern telecom lasers can exceed 50%.

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