Intersubband relaxation of two-dimensional electrons in heterostructures

We calculate the lifetime of a nonequilibrium electron in the first excited subband in the low-density heterostructure where this photocreated carrier occurs at the last stage of its cooling. The electron interaction with acoustic phonons gives the dominant intersubband relaxation mechanism, if the intersubband energy splitting and the Fermi energy splitting are relatively small, 1>εF/Δ₁₀>0.7--0.8. In GaAs-Alₓ{Ga}_{1{{-}}x}$As heterostructures the intersubband relaxation determines the excited-electron lifetime to be of the order of ${{{τ}}}ₚₕₒₙ~nanoseconds, which depends slightly on the value of the two-dimensional electron density. When the ratio{{{ε}}}F$/${{{Δ}}}₁₀$ is smaller, the intersubband relaxation is determined by the Auger-like electron-electron scattering whose rate can increase up to the value ${{{τ}}}Aug^{{{-}}1}~{10}^{{{-}}10}$ ${sec}^{{{-}}1}$.