Absorption edge

The absorption edge of a semiconductor is the photon energy at which its absorption rises from nearly zero to strong, close to the bandgap $E_g$. Photons with less energy cannot lift an electron from the valence band to the conduction band and pass through; photons with more are absorbed. The edge sets the long-wavelength limit of a photodetector and the transparency window of a waveguide material, and its wavelength follows from the photon energy relation

$$\lambda_c\,[\text{nm}] = \frac{1239.84}{E_g\,[\text{eV}]}$$

So silicon is transparent at 1310 and 1550 nm, which is why it serves as a waveguide core there and why silicon photodiodes stop responding near 1.1 µm, while InGaAs covers every telecom band.

Shape of the edge: direct and indirect gaps

How sharply absorption turns on depends on the band structure. In a direct-gap material such as GaAs or InGaAs, an electron can make the transition without changing momentum, and the absorption coefficient rises roughly as $\sqrt{h\nu - E_g}$, reaching about $10^4$ cm⁻¹ (an absorption length of 1 µm) within a small fraction of an electron-volt above the gap. In an indirect-gap material such as silicon, the transition needs a phonon, absorption grows roughly as $(h\nu - E_g \pm E_\text{ph})^2$, and it stays weak for a wide range above the edge: a silicon detector at 1000 nm needs a thick absorber, while at 850 nm a few tens of micrometers suffice.

Germanium shows both behaviors. Its indirect gap of 0.66 eV places the nominal edge at 1879 nm, but strong absorption begins at the direct gap near 0.80 eV, which corresponds to 1550 nm. That is why germanium-on-silicon photodetectors respond well through the C band and weaken in the L band unless tensile strain moves the direct edge to longer wavelengths.

Measuring the edge

The edge is measured from transmission spectra of a thin sample, converted to $\alpha(h\nu)$ with the Beer-Lambert law after correcting for reflection at both faces. A Tauc plot then extracts the gap: $(\alpha h\nu)^2$ against $h\nu$ is linear near the edge for an allowed direct transition, and $(\alpha h\nu)^{1/2}$ for an indirect one, with the intercept on the energy axis giving $E_g$. Photoluminescence gives a complementary measure for direct-gap materials, peaking slightly above $E_g$. Photodetector datasheets show the edge as the long-wavelength fall of the responsivity curve.

The Urbach tail

Real edges are not abrupt. Below the gap, absorption falls exponentially,

$$\alpha = \alpha_0 \exp\!\left[(h\nu - E_0)/E_U\right]$$

where the Urbach energy $E_U$ describes thermal and structural disorder. It is about 6 to 8 meV in good crystalline GaAs at room temperature and of order 50 meV in amorphous silicon. With $E_U = 10$ meV, $\alpha$ falls by a factor of ten for every 23 meV below the edge. The tail matters for waveguides and modulators operated just below the gap, where it sets a residual loss.

Temperature and doping shifts

The gap narrows as temperature rises, so the edge moves to longer wavelength. For GaAs, the Varshni parameters of Vurgaftman et al. give $dE_g/dT \approx -0.45$ meV/K at 300 K, a shift of about 0.28 nm/K near 870 nm, or 17 nm over a 60 K rise. The same effect moves the cutoff of an InGaAs detector to shorter wavelengths when it is cooled. Heavy n-type doping shifts the measured edge to higher energy through band filling (the Burstein-Moss shift), while bandgap renormalization at high carrier density works in the opposite direction.

Electroabsorption

An electric field moves and broadens the edge. In bulk material the Franz-Keldysh effect adds a field-dependent tail below the gap; in quantum wells the quantum-confined Stark effect shifts the sharp excitonic edge to lower energy while it stays well defined. An electro-absorption modulator operates a little below the zero-field edge and uses reverse bias to pull the edge onto the signal wavelength.

Common questions

How do I find the cutoff wavelength from a bandgap?

Divide 1239.84 by the gap in electron-volts to get the wavelength in nanometers: 1.12 eV gives 1107 nm for silicon. The usable detector cutoff lies slightly shorter, because absorption near the edge is weak.

Why does silicon absorb weakly near 1 µm?

Silicon's gap is indirect, so absorption near the edge requires a phonon and rises slowly with photon energy. Photons just above the gap travel far before being absorbed.

Is the absorption edge the same as the bandgap?

They are close but not identical. The edge observed in a spectrum includes the Urbach tail, excitonic features and doping shifts; the gap is the band-structure quantity extracted from it.

References: S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed. (Wiley, 2007); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001); F. Urbach, Phys. Rev. 92, 1324 (1953).