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The low-temperature mobility in a two-dimensional electron gas with specified electron density Ns in a single, ungated GaAs-Ga1−xAlxAs heterojunction is calculated using several simplifying approximations. The highest mobility for given Ns is attained by using the highest practical donor doping level in the Ga1−xAlxAs and the corresponding undoped spacer layer thickness for charge neutrality. The calculated mobility for given Ns is insensitive to this doping level if values near or above 1018 cm−3 are used, but is sensitive to the doping level in the GaAs and to the difference between the barrier height Vb and the donor binding energy EDb in the Ga1−xAlxAs . For Vb−EDb=0.2 eV, peak mobilities near 2×106 cm2/Vs are reached, at electron densities near 1.3×1011 cm−2, if background doping levels can be held to 1014 cm−3.
Frank Stern (Tue,) studied this question.