Heavy-hole doublet detuning in triple V-shaped type-II quantum wells for long-wavelength interband cascade lasers

In a triple V-shaped InAs/Ga1 − xInxSb type-II quantum well, the two hole layers form a heavy-hole doublet with a tunnel splitting of a few meV, which an electric field detunes. Eight-band k ⋅ p calculations with Bir–Pikus strain at 300 K show that the transition energy is, therefore, quadratic in field only below a crossover field F* = Δh/(edh), 8.3 kV cm−1 for an 8 μm design, and essentially linear at the 50–100 kV cm−1 fields at which interband cascade lasers operate. A two-level model reproduces the k ⋅ p field dependence to 0.006 meV rms, and its fitted hole-well separation matches the geometric spacing to 0.6%. Across 6.5–12 μm, the triple-V is 5.7–7.5 times more field-sensitive than a matched W-shaped well; this ratio changes by less than 9% under parameter perturbations that shift the absolute wavelength by about ±20%, although one InSb-like monolayer per interface reduces it to about 3. The same mechanism removes the zero-field overlap advantage of the triple-V under bias: at 75 kV cm−1, a symmetric triple-V has 24% less electron–hole overlap than the W reference. A hole-well asymmetry, realizable with integer-monolayer layers and a small composition difference, moves the overlap maximum to the operating field, giving 57% more overlap than the W there, but only within about ±25 kV cm−1 of the design field; a large tuning range and a high overlap cannot be obtained in the same design. The results concern zone-center transition energies and overlaps, not gain or laser tuning.