Quantized conductance in silicon quantum wires

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Abstract
The results of studying the quantum-mechanical staircase for the electron and hole conductance of one-dimensional channels obtained by the split-gate method inside self-assembled silicon quantum wells are reported. The characteristics of quantum wells formed spontaneously between the heavily doped δ-shaped barriers at the Si(100) surface as a result of nonequilibrium boron diffusion are analyzed first. To this end, secondary-ion mass spectrometry, and also the detection of angular dependences of the cyclotron resonance and ESR, is used; these methods make it possible to identify both the crystallographic orientation of the self-assembled quantum wells and the ferroelectric properties of heavily doped δ-shaped barriers. Since the obtained silicon quantum wells are ultrathin (∼2 nm) and the confining δ-shaped barriers feature ferroelectric properties, the quantized conductance of one-dimensional channels is first observed at relatively high temperatures (T≥77 K). Further, the current-voltage characteristic of the quantum-mechanical conductance staircase is studied in relation to the kinetic energy of electrons and holes, their concentration in the quantum wells, and the crystallographic orientation and modulation depth of electrostatically induced quantum wires. The results show that the magnitude of quantum steps in electron conductance of crystallographically oriented n-type wires is governed by anisotropy of the Si conduction band and is completely consistent with the valence-valley factor for the [001] (G0=4e2/h and gv=2) and [011] (G0=8e2/h and gv=4) axes in the Si(100) plane. In turn, the quantum staircase of the hole conductance of p-Si quantum wires is caused by independent contributions of the one-dimensional (1D) subbands of the heavy and light holes; these contributions manifest themselves in the study of square-section quantum wires in the doubling of the quantum-step height (G0=4e2/h), except for the first step (G0=2e2/h) due to the absence of degeneracy of the lower 1D subband. An analysis of the heights of the first and second quantum steps indicates that there is a spontaneous spin polarization of the heavy and light holes, which emphasizes the very important role of exchange interaction in the processes of 1D transport of individual charge carriers. In addition, the temperature-and field-related inhibition of the quantum conductance staircase is demonstrated in the situation when kT and the energy of the field-induced heating of the carriers become comparable to the energy gap between the 1D subbands. The use of the split-gate method made it possible to detect the effect of a drastic increase in the height of the quantum conductance steps when the kinetic energy of electrons is increased; this effect is most profound for quantum wires of finite length, which are not described under conditions of a quantum point contact. It is shown in the concluding section of this paper that detection of the quantum-mechanical conductance under the conditions of sweeping the kinetic energy of the charge carriers can act as an experimental test aiding in separating the effects of quantum interference in modulated quantum wires against the background of Coulomb oscillations as a result of the formation of QDs between the delta-shaped barriers.

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