Quantum Confinement Effects on the Dielectric Constant of Porous Silicon

The reduction of the dielectric constant due to quantum confinement is studied both experimentally and theoretically. Angle resolved ellipsometry measurements with Ar- and He-Ne-lasers give values for the index of refraction far below what can be accounted for from porosity alone. A modified Penn model to include quantum size effects has been used to calculate the reduction in the static dielectric constant (e) with extreme confinement. Since the binding energy of shallow impurities depends inversely on e2, the drastic decrease in the carrier concentration as a result of the decrease in e leads to a self-limiting process for the electrochemical etching of porous silicon.