The temperature and magnetic field dependences of the conductivity of the heterostructures with asymmetric In$_x$Ga$_{1-x}$As quantum well are studied. It is shown that the metallic-like temperature dependence of the conductivity observed in the structures investigated is quantitatively understandable within the whole temperature range, $T=0.4-20$ K. It is caused by the interference quantum correction at fast spin relaxation for 0.4 K$ < T < 1.5$ K. At higher temperatures, 1.5 K$<T<4$ K, it is due to the interaction quantum correction. Finally, at $T>4-6$ K, the metallic-like behavior is determined by the phonon scattering.
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