Effects of spacer layer in modulation-doped GaAs/AlGaAs heterostructures on a localization in quantized Hall resistance

The quantum Hall effect measurements have been applied on modulation-doped GaAs/AlGaAs heterostructures with various spacer-layer thicknesses (0-100 Å) for investigating the effects of an undoped layer on localization. The fraction of localized states (α) of Landau levels has been evaluated from the plateau widths in the quantized Hall resistance, and its functional dependences are proposed in terms of electron mobility and magnetic field. The mobility dependence gives an exponential profile, α∼exp(-μ/ μ₀), which results from a change in the long-range interaction by the variation of spacer-layer thickness. The characteristic mobility, μ₀, is within (2.55±0.20)×10⁵ cm ²/V s for all step indices from i=4 to i=10, but the localized fraction has an additional dependence on step index. The fraction of localized states as a function of magnetic field shows B^3/4 dependence which may be attributed to short-range contribution by interface states or interface roughness between the AlGaAs undoped layer and the GaAs buffer layer.