Transverse magnetotunneling in AlxGa1−xAs capacitors. II. Electron phase changes in resonant Fowler-Nordheim tunneling

Abstract

The current-voltage (I-V) characteristics of $n^{\mathrm{-}}$-type GaAs–${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As${–\mathit{n}}^{+}$-type -type GaAs (AlGaAs) capacitors that show resonant Fowler-Nordheim tunneling are modulated because of interference between electrons that propagate ballistically in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As and electrons that are reflected at the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/$n^{+}$-type GaAs interface. A transverse magnetic field B, perpendicular to the tunnel current I, changes the phases of electrons; it therefore changes the amplitude and phase of periodicities in I-V characteristics that are observed when B=0 T. I-V curves of two AlGaAs capacitors at B=0 T are analyzed to obtain ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As thicknesses and the dependence on voltage of the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As thickness through which electrons propagate ballistically. The close agreement between experiment and theory shows that the capacitors exhibit ideal resonant Fowler-Nordheim tunneling. The effect of a transverse magnetic field on the I-V curves of AlGaAs capacitors that show resonant Fowler-Nordheim tunneling is reported. I increases when B increases for B≲5 T for particular values of bias $V_G$. The resulting negative magnetoresistance is the simplest case of weak localization since only one scattering event is involved. For large values of B, relative electron phases change so that current maxima due to electron interference become minima.