A high electron mobility transistor (HEMT) includes a channel semiconductor structure including a stack of layers arranged on top of each other in an order of magnitudes of the polarization of materials of the layers to form multiple carrier channels at heterojunctions formed by each pair of layers in the stack. The stack of layers includes a first layer and a second layer. The magnitude of polarization of the first layer is greater than the magnitude of polarization of the second layer arranged in the stack below the first layer, and the width of the first layer is less than the width of the second layer to form a staircase profile of the semiconductor structure. The HEMT includes a source semiconductor structure including a heavily doped semiconductor material, a drain semiconductor structure including the heavily doped semiconductor material. The HEMT includes a source, a drain, and a gate electrodes to modulate the conductivity of the carrier channels. The gate electrode has a staircase shape having trends and risers tracking the staircase profile of the semiconductor structure.