\ I

In Figure 2 we compare the LO-phonon spontaneous emission rates rph in type-11 InAs/GaSb (left) and type-1 InAs/AISb/InAs (right) DQWs. For type-11 DQW rph is shown as a function of the GaSb QW width d8 , with the lnAs QW width kept constant at dA = 9 nm. This value of dA allows for the cl states to be located near the upper edge of the leaky window 8. The increase of d8 in the range from 4 nm to I 0 nm, while keeping the energy position of the initial electron-like subband cl practically unchanged, makes it possible to scan the final states in the hole-like subbands Er, here - the heavy-hole subband hhi and the light-hole subband lhi, which thus move toward the upper part of the heterostructure leaky window. Type-11 DQW clearly demonstrates three peaks in the LO-phonon emission rate, Rl-R3, which are related to three consecutive resonances indicated in Figure 1. The first, most important resonance, Rl, corresponds to the onset of spatially indirect (interwell) cl ~hh 1 phonon-assisted transition. R I transition is indirect also in the momentum space since the top of the sub band hh I is noticeably displaced from the Brillouin zone center due to the subband spin splitting enhanced by the heavy-hole/light-hole mixing. Final momentum transfer in this resonance is important for the high phonon emission rate, because the interband transition can be engineered so that the peak of the density of states at the top of hh I subband is complemented by the maximum value of the electron-phonon overlap integral l(q); see Figure 3. This design explains the higher value of rph in Rl resonance comparing to the next resonance R2,

Figure 3. Electron-phonon overlap integrals /(q) for c1 ~hh1 (solid lines) and c1 ~lh 1 (dashed line) transitions vs. transferred (phonon) wave vector. Each curve is labeled with GaSb QW width d8 in nm and with a vertical arrow marking the position of the Van Hove singularity.