Double injection in cylindrical germanium structures

Abstract

Current-voltage characteristics and electric field distributions have been measured on large hollow-core coaxial germanium devices operating in the double-injection semiconductor regime. The I-V characteristics obey an I α V2 relationship and the magnitude of the current is predicted to within a factor of 2 by I = δqμpμnτ (p0−n0)V2, where the term δ is a constant scaling factor dependent upon the concentric cylindrical geometry. The shape of the electric field is obtained from potential probe measurements taken along the radius r of a p+ − π − n+ structure with the current density directed radially outward. In this case the field follows an E α [(r2/r)2 − 1]1/2 dependence over the central portion of the device and diffusion effects are present at the inner (r1) and outer (r2) injecting boundaries. A first-order correction for diffusion at the contacts is made by the application of an effective radii difference r2eff − r1eff = r2 − r1 − 2QLa, where La is the ambipolar diffusion length and Q is a constant with values ≈ 0.5. A small-signal equivalent circuit representation for double injection in the concentric cylindrical geometry is established from impedance measurements over the frequency range 103≲ω≲106. Field and charge carrier distributions for cylindrical double injection in the diffusion-dominated regime are also discussed.