Theoretical study of phosphorous<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>-doped silicon for quantum computing

Qian, Guojian; Chang, Yia‐Chung; Tucker, J. R.

doi:10.1103/physrevb.71.045309

Cited by 38 publications

(97 citation statements)

References 22 publications

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“…Similar to Ref. 26, we find that electrons are mainly concentrated in the Γ-bands at low densities, while nearly two thirds of the electrons shift to the ∆ band for densities approaching 1/4 ML. We predict that the ∆ filling should approach 70-80% at higher densities, although such densities are not easily achieved in physical systems.…”

Section: Discussionsupporting

confidence: 89%

“…28. Other abbreviations used hence are as follows: our effective mass theory (EMT), the PWO method including short-ranged interactions between the dopants (PWOf), 26 and the fully ordered (SZPo) vs. partially disordered dopant arrays (SZPd) discussed in Ref. 28.…”

Section: Results and Comparisonmentioning

confidence: 99%

“…(1) would imply mixing the effective masses and weaken the theory. Rigorous ab initio band structure calculations with a laterally averaged charge distribution confirm that the 2D effective masses for Si:P with the most prevalent 1/4 monolayer (ML) doping level are almost identical to the bulk masses in Si, 26 and that the bulk bands are simply shifted downward by their respective binding energies. 28 In short, all the evidence suggests that 2D and 3D effective mass theories should both be accurate in this system.…”

Section: Two-dimensional Effective Mass Theorymentioning

confidence: 89%

“…Density functional methods confirm this picture of simple energy shifts in disordered Si:P geometries. 26,28 It is especially important to note that the parabolic shape of the bands and the corresponding curvature (the so-called inverse effective mass) are largely unaffected by the energy shifts. This suggests a straight-forward modification of the bulk effective mass theory to incorporate the confinement effects, which we describe in detail.…”

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confidence: 99%

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Effective mass theory of monolayerδdoping in the high-density limit

et al. 2012

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Monolayer δ-doped structures in silicon have attracted renewed interest with their recent incorporation into atomic-scale device fabrication strategies as source and drain electrodes and in-plane gates. Modeling the physics of δ-doping at this scale proves challenging, however, due to the large computational overhead associated with ab initio and atomistic methods. Here, we develop an analytical theory based on an effective mass approximation. We specifically consider the Si:P materials system, and the limit of high donor density, which has been the subject of recent experiments. In this case, metallic behavior including screening tends to smooth out the local disorder potential associated with random dopant placement. While smooth potentials may be difficult to incorporate into microscopic, single-electron analyses, the problem is easily treated in the effective mass theory by means of a jellium approximation for the ionic charge. We then go beyond the analytic model, incorporating exchange and correlation effects within a simple numerical model. We argue that such an approach is appropriate for describing realistic, high-density, highly disordered devices, providing results comparable to density functional theory, but with greater intuitive appeal, and lower computational effort. We investigate valley coupling in these structures, finding that valley splitting in the low-lying Γ band grows much more quickly than the Γ-∆ band splitting at high densities. We also find that many-body exchange and correlation corrections affect the valley splitting more strongly than they affect the band splitting.

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Section: Discussionsupporting

confidence: 89%

Section: Results and Comparisonmentioning

confidence: 99%

Section: Two-dimensional Effective Mass Theorymentioning

confidence: 89%

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confidence: 99%

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Effective mass theory of monolayerδdoping in the high-density limit

et al. 2012

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“…illustrates our results for the P δ-layer subband structure. [9] Here the zero of energy is placed at the conduction band minimum of undoped Si far from the doping plane. Two sets of lines, dashed and solid, represent the calculation with and without the short-range interaction between electrons and donors.…”

Section: Theoretical Study Of Phosphorous δ δ δ δ-Doped Siliconmentioning

confidence: 99%

Wavefunction Engineering of Individual Donors for Silicon-Based Quantum Computers

Tucker¹

2005

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Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. This project has explored possibilities for realizing a Kane-type quantum computer based on Si:P donor qubits. The overall goal has been to create an integrated process based on STM patterning of individual P-donor qubits, combined with single-electron transistors (SETs) for singlet-triplet spin state detection in the same lithographic step. The main accomplishments during this period have been to: (1) develop processes for positioning P atom donors and self-ordered arrays with near-atomic accuracy inside the silicon crystal lattice, (2) fabricate P donor nanowires as a major step toward an integrated epitaxial single-electron transistor, (3) measure electrical characteristics of the unpatterned P δ-layer and P donor nanowires, (4) compare the electrical data with our band structure calculations on the P δ-layer and previous theories of weak localization, (5) propose a new Kane-type architecture employing the idea of 'universal exchange' based on composite 3-electron spin qubits, and (6) perform extensive simulations to confirm the fundamental aspects of this approach, and quantify major difficulties to be overcome. Sustained effort in these directions will be required to realize a working qubit.

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Multi‐Scale Modeling of Tunneling in Nanoscale Atomically Precise Si:P Tunnel Junctions

Donnelly

Keizer

et al. 2023

Adv Funct Materials

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Controlling electron tunneling is of fundamental importance in the design and operation of semiconductor nanostructures such as field effect transistors (FETs) and quantum computing device architectures. The exponential sensitivity of tunneling with distance requires precise fabrication techniques to engineer the desired device dimensions to achieve the appropriate tunneling resistances/tunnel rates. This is particularly important for high fidelity spin readout and qubit exchange in quantum computing architectures. Here, it is shown by combining precision fabrication techniques with accurate atomistic modeling, predictive device design criteria are achieved at atomic length scales. Such a tool is useful when devices become more complex or have arbitrary shapes/geometries. In particular, in this study, atomic precision patterning of monolayer degenerately phosphorus-doped silicon tunnel junctions patterned by scanning tunnelling microscopy lithography and tight-binding nonequilibrium Green's function (TB-NEGF) modeling is combined to describe the dependence of tunnel junction resistance R T on junction length. An agreement with experiment to within a factor of 2 over 4 orders of magnitude in R T is found, and this model allows to accurately determine the barrier height V 0 = 57.5 ± 1 meV and lateral seam s xy = 0.39 ± 0.01 nm in these nanoscale junctions. This study confirms the use of the TB-NEGF formalism to accurately model highly doped atomically precise tunnel junctions in silicon. Further applications of this model will enable improved device performance at the nanoscale.

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Theoretical study of phosphorousδ-doped silicon for quantum computing

Cited by 38 publications

References 22 publications

Effective mass theory of monolayerδdoping in the high-density limit

Effective mass theory of monolayerδdoping in the high-density limit

Wavefunction Engineering of Individual Donors for Silicon-Based Quantum Computers

Multi‐Scale Modeling of Tunneling in Nanoscale Atomically Precise Si:P Tunnel Junctions

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