We report on the phonon cooled NbN hot electron bolometer as mixer in the terahertz frequency range. Its hybrid antenna consists of a hyperhemispheric silicon lens and a logarithmic-spiral feed antenna. Noise temperatures have been measured between 0.7 THz and 5.2 THz. A quarter wavelength layer of Parylene works as antireflection coating for the silicon lens and reduces the noise temperature by about 30%. It was found that the antenna ...