Intervalence-band absorption (IVBA)

Intervalence-band absorption (IVBA) is the absorption of light by holes that are excited from one valence band to another. A hole near the top of the heavy-hole band absorbs a photon and ends in the split-off band, or less often the light-hole band, at the same crystal momentum. Because the transition is vertical in momentum, it needs no phonon, and in InGaAsP at these wavelengths it exceeds the intraband free-carrier absorption of the same holes. In InGaAsP and InGaAlAs at 1.3–1.55 µm, reported hole absorption cross-sections are of order 10⁻¹⁷ cm², roughly ten times the electron value, so a hole density of 10¹⁸ cm⁻³ absorbs about 10 cm⁻¹. IVBA is a leading contribution to the internal loss of InP-based lasers and one of the reasons their threshold and efficiency depend more strongly on temperature than those of GaAs-based lasers.

Band structure and wavelength dependence

Spin-orbit coupling splits the split-off band below the heavy- and light-hole bands at the zone center by the spin-orbit energy $\Delta_\text{so}$: 0.34 eV in GaAs, 0.11 eV in InP and about 0.39 eV in InAs, with quaternary alloys in between. A heavy-hole to split-off transition at photon energy $h\nu$ takes place at the wavevector where the two bands are separated by $h\nu$. The photon energy is 0.80 eV at 1550 nm and 0.95 eV at 1310 nm, larger than $\Delta_\text{so}$ in these alloys, so the transition happens away from the zone center at a wavevector that holes in a warm, heavily injected or doped layer still occupy. In GaAs lasers at 850 nm the photon energy is 1.46 eV, and the matching wavevector lies so deep in the band that few holes are there; IVBA is correspondingly weak at short wavelengths and grows toward the infrared.

The absorption is proportional to the hole density and to the occupation of the states at the transition wavevector:

$$\alpha_\text{IVBA} = \sigma_\text{IVBA}(\lambda, T)\,p.$$

Both factors rise with temperature. The Fermi distribution spreads holes to larger wavevectors, raising the occupation of the absorbing states, and the hole density needed to reach threshold grows as the gain spectrum broadens.

Effect on threshold, T₀ and rollover

The threshold condition requires the modal gain to cover the internal and mirror losses, $\Gamma g_\text{th} = \alpha_i + \alpha_m$. IVBA from holes in the active region and in the p-doped cladding enters $\alpha_i$. With an order-of-magnitude cross-section of $10^{-17}$ cm², a cladding doped p-type to $10^{18}$ cm⁻³ absorbs 10 cm⁻¹, and if 20 % of the mode overlaps it the modal loss is 2 cm⁻¹. The injected holes in the wells add to this in proportion to the confinement factor.

The temperature dependence makes the effect self-reinforcing. A rise in temperature raises the threshold carrier density, which raises IVBA, which raises the gain required at threshold, which raises the carrier density again. Henry, Logan, Merritt and Luongo analyzed this feedback for InGaAsP lasers in 1983 and showed that it lowers the characteristic temperature $T_0$, together with Auger recombination and carrier leakage. This is part of why InGaAsP lasers have $T_0$ of 50–70 K against 120–160 K for AlGaAs lasers.

Above threshold the carrier density is nominally clamped, but the junction heats with drive current, and IVBA raises $\alpha_i$. The differential efficiency falls as

$$\eta_d = \eta_i\,\frac{\alpha_m}{\alpha_i + \alpha_m}.$$

For a 500 µm cleaved InP laser with $\alpha_m = 22.8$ cm⁻¹ and $\eta_i = 0.8$, raising $\alpha_i$ from 10 to 15 cm⁻¹ lowers $\eta_d$ from 0.56 to 0.48, and 20 cm⁻¹ gives 0.43. Combined with the rising threshold, this bends the LI curve over at high current, the thermal rollover that limits the maximum power of long-wavelength lasers and the slope efficiency at high temperature.

Measurement and design

In a laser, IVBA is seen through the internal loss, extracted from the length dependence of the differential efficiency or the long-wavelength floor of a Hakki-Paoli gain spectrum, and through how it changes with temperature. Cross-sections come from absorption spectra of p-doped layers.

Designs reduce IVBA in four ways: keeping the p-doping low near the active layer and grading it toward the contact; asymmetric waveguides that shift the mode toward the n-side cladding, where electrons absorb far less; reducing the number of holes needed for gain, which is one benefit of compressive strain in a strained quantum well, since the lighter in-plane hole mass lowers the transparency density; and good heat sinking, which slows the temperature feedback.

Common questions

How does IVBA differ from free-carrier absorption?

Free-carrier absorption moves a carrier to a higher state within the same band and needs a phonon or impurity to supply momentum. IVBA moves a hole between two different valence bands at the same momentum, so no third particle is needed. Both scale with the hole density, and in III-V lasers at 1.3–1.55 µm the intervalence process is the larger.

Why does IVBA matter at 1550 nm but much less at 850 nm?

At 1550 nm the photon energy is not far above the spin-orbit splitting, so the absorbing transitions involve holes near the band edge, which are plentiful. At 850 nm the matching transitions lie deep in the valence band, where the hole occupation is small.

References: C. H. Henry, R. A. Logan, F. R. Merritt and J. P. Luongo, "The effect of intervalence band absorption on the thermal behavior of InGaAsP lasers," IEEE Journal of Quantum Electronics 19, 947 (1983); G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012).