The con6ned acoustic phonons in free-standing quantum wells are considered in detail. She Hamiltonian describing interactions of the confined acoustic phonons with electrons in the approximation of the deformation potential and the corresponding electron transition probability density are derived. They are used to analyze the electron scattering times (inverse scattering rate, momentum relaxation time, and the energy relaxation time) in the test-particle approximation as well as in the kinetic approximation. It is shown that the first dilatational mode makes the main contribution to electron scattering in the lowest electron subband. The contribution of the zeroth mode and the second mode are also essential while the modes of higher order are insignificant. Our analysis is performed for both nondegenerate and degenerate electron gases. It is shown that electron scattering by con6ned acoustic phonons interacting through the deformation potential is substantially suppressed up to the electron energies corresponding to the energy of the first dilatational mode.

a), V. MITIN (a), and M. STROSCIO (b)The Lagrangian of an isotropic continuous medium and Lagrangian formalism are used to consistently derive acoustic eigenmodes, to normalize them, and to determine the acoustic phonons (confined acoustic phonons) in a free-standing quantum well. These phonons may be classified as shear, dilatational, and flexural phonons in accordance with the acoustic terminology for eigenmodes. The Hamiltonians describing interactions of the confined acoustic phonons with electrons in the approximations of the deformation potential and the piezoelectric scattering potential are obtained and analyzed.

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The self-consistent Monte Carlo technique has been used to solve coupled nonlinear kinetic equations for electrons and optical phonons confined in a GaAs quantum well. We have studied the influence of nonequilibrium phonons on quasi-two-dimensional electron transport for a lattice temperature of 30 K and for a wide range of applied electric fields. A substantial difference in generation and decay times as well as the confinement inside the GaAs/AlAs heterostructure-bounded active region lead to a significant growth of nonequilibrium optical-phonon population generated by a heated electron gas. We have found that when the phonon generation ͑as well as phonon reabsorption by the quasi-two-dimensional carriers͒ becomes significant, there are substantial effects on transport in the quantum well. We show that for low electron concentrations, the hot optical-phonon distribution reflects the main features of the carrier distribution; indeed, it preserves an average quasi-momentum in the forward ͑opposite to electric field͒ direction. However, hot-phonon feedback to the electron system is found to be not essential in this case. For high electron concentrations, enhanced nonequilibrium optical-phonon reabsorption results in phonon distribution which spreads significantly in the quasi-momentum space and essentially loses the characteristic of the forward-peaked anisotropy. The interactions with the confined electron subsystem typically result in an isotropic phonon distribution. In this case, nonequilibrium optical phonons lead to an increase in the mean electron energy and a reduction in the carrier drift velocity.

Monte Carlo simulations have been used to study the spatial scales of electron ballistic transport in GaN. The large optical phonon energy (92 meV) and the large intervalley energy separation between the Γ and satellite conduction band valleys (⩾1.5 eV) suggest an increasing role for ballistic electron effects in GaN, especially when compared with most III–V semiconductors such as GaAs. However, the concomitant high polar optical phonon scattering rate in GaN tends to diminish the desirable electron transport properties. The relationships between these two factors have been studied for the range of electric fields up to 140 kV/cm and lattice temperatures between 300 and 600 K. We demonstrate that in most cases electrons in GaN lose their directed average velocity over distances of only 100−200 Å, and ballistic transport occurs only over such short distances. The main cause for the small spatial scales of ballistic transport in GaN is the strong electron–optical phonon coupling which results in rapid relaxation of the directed electron velocity.