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We report the effect of negative differential resistance (NDR) in the drain circuit of a new type of selectively doped AlGaAs/ GaAs heterojunction transistor. The key new element of our structure is the presence of a subsidiary GaAs conducting layer, separated from the FET channel by an AlGaAs graded barrier. In this work the subsidiary layer is realized by the conducting substrate. The NDR effect arises due to the heating of channel electrons by the source-to-drain field, and the subsequent charge injection over the barrier. This effect is strongly influenced by the gate and substrate voltages. In a floating-substrate arrangement the current-voltage characteristics exhibit memory effects associated with retention of injected charge in the substrate. In this mode, the NDR is seen only at low temperatures with the peak-to-valley ratios in current at 77 K reaching values as high as 30. On the other hand, when the substrate is biased positively, the NDR results from a peculiar effect of dynamical channel depletion by the injected space charge which drifts on the downhill slope of the graded barrier. In this case, the NDR is observed even at room temperature.