The saturation of the free-electron concentration at high doping densities in delta -doped GaAs is studied by Shubnikov-de Haas measurements under hydrostatic pressure. Saturation occurs as soon as the depth of the Hartree potential is large enough to make the energy of the DX centre line up with the Fermi energy. The ultimate limit of the low-temperature equilibrium free-electron concentration in truly delta -doped GaAs is estimated to be 5.5*1012cm-2for Si donors. For realistic samples grown at Ts=500 degrees C the electron concentration is saturated at 7*1012cm-2due to the occupation of DX centres in a doping sheet, of finite thickness ( approximately=30 AA). For samples grown at higher temperatures (Ts=600 degrees C) autocompensation can occur prior to the population of the DX centre. Increases in mobility with increasing pressure observed in the Shubnikov-de Haas measurements for the i=0 sub-band provide additional evidence for a movement of the donors away from the original doping plane.
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