A semiconductor structure having mesa structure comprising: a lower semiconductor layer; an upper semiconductor layer having a higher band gap than, and in direct contact with, the lower semiconductor layer to form a two-dimension electron gas (2DEG) region between the upper semiconductor layer. The 2DEG region has outer edges terminating at sidewalls of the mesa. An additional electron donor layer has a band gap higher than the band gap of the lower layer disposed on sidewall portions of the mesa structure and on the region of the 2DEG region terminating at sidewalls of the mesa. An ohmic contact material is disposed on the electron donor layer. In effect, a sideway HEMT is formed with the electron donor layer, the 2DEG region and the ohmic contact material increasing the concentration of electrons (i.e., lowering ohmic contact resistance) all along the contact between the lower semiconductor layer and the electron donor layer.