We report on the selective area molecular beam epitaxy of InAs/AlGaSb heterostructures on a GaSb (001) substrate. This method is used to realize Esaki tunnel diodes with a tunneling area down to 50 nm × 50 nm. The impact of the size reduction on the peak current density of the diode is investigated, and we show how the formation of the InAs facets can deeply affect the band-to-band tunneling properties of the heterostructure. This phenomenon is explained by the surface-dependent incorporation of Si dopant during growth.