Inhomogeneous boundary effects in semiconductor quantum wires

Abslract Boundary effects play an essential role in determining the physical properties of semiconductor quantum wires. Additional features come into play when one considers inhomogeneous boundaries, i.e. wires whose widths are functions of distance along the length of the wire. We show that, in the adiabatic approximation (which assumes that the boundary patential fluctuation effects, or equivalently, the variations in the wire width, occur on a scale much larger than the inverse of Fermi wavelength). the boundary problem far a quantum wire is equivalent to a one-dimensional Schrbdinger equation along the wire with (i) an effective potential provided by the deviation from the homogeneous boundary and, (ii) a wave function coupled to the lateral direclion. In the periodic boundary fluctuation case, the subbands of t h e system split into many mini-subbands, and became a useful system to test ID band theory. When the boundary fluctuates randomly, there exists in each of the subbands a mobility edge, below which lhe e le~t ron slates are localized. The localization of the tail stales of the lop populated subbands makes the conductance drop smoathly whenever the Fermi energy passes thc bottom of a new subband. The theoly explains the recent experiments of Smith and ea-worken.