Band transport across a chain of dopant sites in silicon over micron distances and high temperatures.

Enrico Prati,Kuninori Kumagai,Masahiro Hori,Takahiro Shinada

doi:10.1038/srep19704

Enrico Prati, Kuninori Kumagai + Show 2 more

Open Access

https://doi.org/10.1038/srep19704

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Abstract

Macroscopic manifestations of quantum mechanics are among the most spectacular effects of physics. In most of them, novel collective properties emerge from the quantum mechanical behaviour of their microscopic constituents. Others, like superconductivity, extend a property typical of the atomic scale to macroscopic length scale. Similarly, features of quantum transport in Hubbard systems which are only observed at nanometric distances in natural and artificial atoms embedded in quantum devices, could be in principle extended to macroscopic distances in microelectronic devices. By employing an atomic chain consists of an array of 20 atoms implanted along the channel of a silicon transistor with length of 1 μm, we extend to such unprecedented distance both the single electron quantum transport via sequential tunneling, and to room temperature the features of the Hubbard bands. Their observation provides a new example of scaling of quantum mechanical properties, previously observed only at the nanoscale, up to lengths typical of microelectronics, by opening new perspectives towards passage of quantum states and band engineering in silicon devices.

Highlights

Artificial atoms[9], as well as donor atoms in silicon[17,22,23,24,25,26,27], are conveniently treated as Hubbard systems[21] in which onsite Coulomb repulsion is able to create a gap[28]
Single-band Hubbard Hamiltonian expresses the competition between two energy scales, consisting of the kinetic energy, which depends on the overlap between electronic wave functions on neighboring lattice sites, and the Coulomb energy U, which returns the strength of the onsite Coulomb repulsion between two electrons
In the case of fermions in a linear array of N elements, generated for instance by a series of quantum dots or donor atoms (Fig. 1), in which only first neighboring sites interact, the whole system is treated as a single quantum system (Fig. 2a) and many-body eigenstates have been calculated by exact diagonalization leading to single electron tunneling effect[9,31]

Summary

Introduction

Artificial atoms[9], as well as donor atoms in silicon[17,22,23,24,25,26,27], are conveniently treated as Hubbard systems[21] in which onsite Coulomb repulsion is able to create a gap[28]. The second band, because of the larger extension of electron wavefunction of D− states (forming the upper Hubbard band already above a density equivalent to 3 × 1015 cm−3 in bulk36) is a full thermally activated band, based on variable range hopping between localized sites, as already reported in ref.

Results

Conclusion