Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells

A new calculation is made of the quantum-well intersubband absorption by electrons that occupy valleys with ellipsoidal constant-energy surfaces. Application of the results to the special case of spherical-valley materials yields excellent agreement with recent experimental results for GaAs quantum wells. According to the calculation, strong intersubband absorption is exhibited by ellipsoidal-valley quantum wells in indirect-band-gap ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As and ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$Sb alloys, and both materials have the advantage over GaAs of being able to absorb light incident normal to the quantum-well plane. For a wavelength of 10 μm, sheet concentration of 7.6×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$, and a linewidth of 11 meV, the calculated fractional absorptions for normally incident light on a (111) ${\mathrm{Al}}_{0.5}$ ${\mathrm{Ga}}_{0.5}$As and (100) ${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$Sb quantum well are 0.000 73 and 0.0022, respectively, independent of the azimuthal angle of polarization. The absorption is stronger for ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$Sb than for ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As because the ellipsoid eccentricity is greater for L valleys than for X valleys in these materials.