Theory of the spectral acoustic phonon emission intensity of hot 2D electrons in quantized n-inversion layers

The spectral acoustic phonon emission intensity of the hot quasi two-dimensional electron gas (2DEG) in quantized n-Si (GaAs) inversion layers is calculated as a function of the phonon angular frequency w at different values of the carrier temperature T_e and density N_s. In the long wave length limit (ℏw ⪡ k_BT_e) the emission intensity increases ∝ w^s(w^s+1) for bulk- (surface-) modes where s = 3 for the unscreened acoustic deformation potential coupling. At w ≈ v_j2k_F (v_j: sound velocity of the phonon mode j, k_F: radius of the Fermi-circle) the emission intensity reaches a maximum whose position is shifted to higher w-values if N_s increases. For given values of N_s, T_e, T (lattice temperature) and ϑ (emission angle) the emission intensity maximum of the n-GaAs inversion layer is found to be about one order of magnitude smaller than the intensity maximum of the n-Si inversion layer.