ELECTRON-WAVE QUARTER-WAVELENGTH QUANTUM-WELL IMPEDANCE TRANSFORMERS BETWEEN DIFFERING ENERGY-GAP SEMICONDUCTORS

Impedance transformers for ballistic (collisionless) electron waves traveling between dissimilar energy-gap semiconductors are designed as a series of quarter (electron) wavelength layers in the form of a compositional superlattice. The quantitative analogies that have been previously established [J. Appl. Phys. 65, 814 (1989)] between electron-wave propagation in semiconductors and electromagnetic-wave propagation in dielectrics are used. For the design energy, the electron wave would be totally transmitted and the structure is analogous to an antireflection coating in electromagnetic optics. Practical constraints on the impedance transformer layers are (1) their compositions must be within the usable compositional range and (2) their thicknesses must be integer multiples of a monolayer thickness. These constraints are included in the design process. Procedures for designing narrow-band, maximally flat (Butterworth), and equal-ripple (Chebyshev) impedance transformers of arbitrary spectral bandwidth are presented. Example practical single-layer and three-layer transformers for connecting GaAs and Ga0.8Al0.2As are presented.