Energy Eigenvalues and Quantized Conductance Values of Electrons in Si Quantum Wires on {100} Plane

A method to obtain the eigenstates of electrons in Si wires with arbitrary cross-sectional shapes and wire directions on the {100} plane is presented within the effective mass approximation, taking into account the six anisotropic valleys near the X points in bulk Si. In general, six equivalent valleys in bulk Si change to three pairs of doubly degenerate valleys in wires, and each pair has a quantized conductance value of 4e2/h(eis elementary charge andhis the Planck constant). In <110>-oriented wires, two of the three pairs become fourfold degenerate and the quantized conductance value of these states becomes 8e2/h. Calculated energy levels for quantized motion perpendicular to the wire direction in wires with rectangular, triangular and trapezoidal cross sections show that the order of the energy levels in different degenerated pairs of valleys depends strongly on both the cross-sectional shape and the wire direction. It is also shown that calculated conductance as a function of gate voltage agrees with an experimental result semiquantitatively.