EMR elements and methods of fabricating the EMR elements are disclosed. The EMR structure includes one or more layers that form an active region, such as a two-dimensional electron gas (2DEG). The EMR structure has a first side surface, having a plurality of lead protrusions that extend outwardly from the main body of the EMR structure, and an opposing second side surface. The lead protrusions are used to form the current and voltage leads for the EMR element. The active region extends through each lead protrusion and is accessible along a perimeter of each of the lead protrusions. Conductive material is formed along the perimeter of each lead protrusion and contacts the active region of the EMR structure along the perimeter. The lead protrusion and the corresponding conductive material contacting the active region of each lead protrusion form leads for the EMR element, such as current leads and voltage leads.