The Effect of Frequency, Doping and Temperature on the Complex Permittivity of N-Type Germanium

Abstract

<p> A number of microwave measuring techniques for the measurement of the complex permittivity (^ɛ = ɛo ɛr - j σ/ω) have been investigated and a new method based on the replacement of the narrow wall of a rectangular wave-guide by a block of semi-conductor has been developed. This technique is shown to be suitable for the measurement of σ when σ >> ωɛo ɛr and for the measurement of σ and ɛr for σ ≃ ωɛo ɛr. </p> <p> An investigation has been made of the propagation characteristics of a rectangular wave-guide containing a centrally placed slab of semi-conductor parallel to the narrow walls of the guide. A comparison of exact solutions for the propagation constant in such a structure with the approximate solutions normally used has shown that the conditions for the validity of the approximate solutions are much more stringent than has been reported previously. It is further shown that under certain conditions the structure offers a convenient method of measuring the conductivity of a semi-conductor. In addition, a theoretical and experimental investigation of the effects of the higher order modes excited at the interface of such a structure with an empty wave-guide has been made. The study has shown that under certain conditions, the effects of these modes can be significant.</p> <p> A theoretical and experimental study has also been made of the effects of temperature, frequency and doping on the complex permittivity of lightly doped n-type germanium. Measurements of these effects which have not been reported previously have been made over a temperature range 100°K - 500°K at frequencies 9.25 and 34.5 GHz and confirm the theoretical model used.</p>