Transverse magnetotunneling inAlxGa1−xAs capacitors. III. Tunneling into interface Landau states inn+-type GaAs

Current-voltage (I-V) characteristics of two ${\mathit{n}}^{\mathrm{-}}$-type GaAs–undoped ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As–${\mathit{n}}^{+}$-type GaAs (${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As) capacitors have been measured in transverse magnetic fields B, in which B is parallel to the capacitor interfaces and perpendicular to the tunnel current J. Structure is observed in I-V curves due to tunneling into interface Landau states at the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/(${\mathit{n}}^{+}$-type GaAs) interface. Capacitance-voltage curves of the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As capacitors are used to correct the measured voltage spacing of extrema in derivatives of I-V curves for band bending in the ${\mathit{n}}^{+}$-type GaAs gate electrode and to derive the spacing of Landau states at the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/(${\mathit{n}}^{+}$-type GaAs) interface. From the spacing of Landau states, cyclotron effective masses for electrons at the ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/(${\mathit{n}}^{+}$-type GaAs) interface are obtained that vary between ∼0.042 for electrons with energies less than the band discontinuity and 0.10 for electrons that have energies that are much larger than the band discontinuity. The results agree qualitatively with the calculations of Johnson and MacKinnon [J. Phys. C 21, 3091 (1988)] of the nature of magnetic interface states between materials of different effective mass.