Electromagnetic modes in a semiconductor cylinder are described for cases of negative and positive conductivity. These modes, with purely axial electric field orientation, exist only for nonzero conductivity. Formulas for the radiated power, quality factor, and field distributions are presented. The idealized model approximates the LSA mode of a microwave oscillator. For such a cylindrical diode oscillator, a self‐resonance condition determines the frequency×diameter product,f×D=2.4×109cm/sec, and doping concentration/frequency ratio,n/f=6×104sec/cm3. The latter result is coincident with that derived previously from a space‐charge control criterion. The electric field amplitude is uniform to within 16% over the cross section of the self‐resonant diode.