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We theoretically investigate dc electron resonant tunneling through an impurity state in a quantum well assisted by hot acoustical phonons. Numerical results for the tunneling current, obtained by nonequilibrium Green functions, reflect the hot-phonon-induced change in the spectrum and population of the impurity state. The induced change of the I-V characteristics has a typical two-peak form, which for larger populations of the level becomes distorted by increased intralevel phonon emissions. A qualitative agreement with experiments is obtained. ͓S0163-1829͑98͒04224-6͔Here c k,␣ϭL,R ϩ (c k,␣ϭL,R ) and E k,␣ϭL,R are creation ͑annihila-tion͒ operators and energies for electrons in the left (L) and right (R) reservoirs, d † ͑d͒ and E 0 describe the same for the level and ␥ k,␣ϭL,R are the coupling parameters between the level and the reservoirs. The operators b q † (b q ) and energies ប q ͑isotropic͒ describe acoustic phonons coupled by the interaction matrix elements M (q) to the electrons on the level. The structure factor F(q) is a square of the donor wave function transformed in a momentum representation.

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Upper limits have been obtained for the size of any asymmetry in the power dissipation between the current entry and exit points of a Si MOSFET in a quantizing magnetic field. Measurements h a v e been made lor power inputs between 0.3 and 2000 pW and for filling factors between 4 and 32. These show that if t h e total power dissipated /'R, is shared between t h e current entry and exit points in proportions (50 t x ) %. then for example at 8 pW. x 5 1.35 for i = 8. No evidence was obtained for any additional dissipation close to the electron entry point near to quantum Hail breakdown.