Mitigating valley-driven localization in atomically thin dopant chains in Si

Abstract

We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multi-valley effective mass theory (MV-EMT). We extend this model to describe chains of donors as a linear combination of dopant orbitals. Disorder in donor positioning is taken into account, leading to an intricate disorder distribution of hoppings between nearest neighbor donor sites (donor-donor tunnel coupling) -an effect of valley interference. The localization length is obtained for phosphorous (P) donor chains from a transfer matrix approach and is further compared with the chain length. We quantitatively determine the impact of uncertainties δR in the implantation position relative to a target and also compare our results with those obtained without valley interference. We analyse systematically the aimed inter-donor separation dependence (R0) and show that fairly diluted donor chains (R0 = 7.7 nm) may be as long as 100 nm before the effective onset of Anderson localization, as long as the positioning error is under a lattice parameter (δR < 0.543 nm).

Adequacy of Si:P chains as Fermi–Hubbard simulators

“…These atomistic wires may extend throughout several nanometers, and a full description of the Si atoms would not be feasible. Instead, we describe the wire electronic states as a Linear Combination of Donor Orbitals (LCDO) [23]. Each basis orbital is an effective mass Kohn-Luttinger(KL) variational wavefunction for the ground state (A 1 symmetry) [29],…”

“…We study a first nearest neighbors Hamiltonian written in the LCDO basis [23]. Defining the creation and annihilation operators c + i,σ and c i,σ for an electron at the orbital centered in R i with a spin projection σ along a quantization axis, and the corresponding number and charge density operators n i,σ = c + i,σ c i,σ and i = n i,↑ + n i,↓ , the Hamiltonian reads…”

Disordered Si:P nanostructures as switches and wires for nanodevices

“…In this work we extended the LCDO formalism [8,10] to include Gaussian disorder, a multi-orbital description and technical improvements, specified in the Appendix, which results in a more realistic description of P nanochains and to access nanoribbons of arbitrary widths. Our simulations treat the problem considering realistic system sizes and disorder.…”

“…As demonstrated in Refs. [8,10], the Hilbert space can be effectively represented by a reduced basis formed by a Linear Combination of Donor Orbital (LCDO). In this hybrid method each donor orbital is accounted for by a multi-valley central cell effective mass approach, that incorporates the Si host effects in the donor orbital itself.…”

“…As in previous works [8,10] the Hamiltonian terms are calculated by the atomistic HamiltonianĤ =Ĥ i +Ĥ , whereĤ i is the single donor Hamiltonian andĤ is the perturbation due to neighboring donor cores. We project the donor orbital to this atomistic Hamiltonian to extract the onsite and hopping terms.…”