Recent suggestions have been made for the design of bulk semiconductor millimeter wave devices, and in particular, a new type of phase shifter. In order for these designs to perform in a satisfactory manner it was found necessary to demonstrate that that electromagnetic propagation would occur largely in the interior of a semiconductor dielectric waveguide with relatively low loss. In this report an analysis is made of electromagnetic waves guided in an infinite slab of material with the properties of high resistivity silicon. Calculations and preliminary experiments are demonstrated at frequencies near 16.0 GHz. It is concluded that propagation in the semiconductor medium offers the possibility of low loss circuitry and satisfies the requisites for device design.