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Constantinou P, Stock TJZ, Crane E, Kölker A, van Loon M, Li J, Fearn S, Bornemann H, D'Anna N, Fisher AJ, Strocov VN, Aeppli G, Curson NJ, Schofield SR. Momentum-Space Imaging of Ultra-Thin Electron Liquids in δ-Doped Silicon. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2302101. [PMID: 37469010 PMCID: PMC10520640 DOI: 10.1002/advs.202302101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2023] [Revised: 06/24/2023] [Indexed: 07/21/2023]
Abstract
Two-dimensional dopant layers (δ-layers) in semiconductors provide the high-mobility electron liquids (2DELs) needed for nanoscale quantum-electronic devices. Key parameters such as carrier densities, effective masses, and confinement thicknesses for 2DELs have traditionally been extracted from quantum magnetotransport. In principle, the parameters are immediately readable from the one-electron spectral function that can be measured by angle-resolved photoemission spectroscopy (ARPES). Here, buried 2DEL δ-layers in silicon are measured with soft X-ray (SX) ARPES to obtain detailed information about their filled conduction bands and extract device-relevant properties. This study takes advantage of the larger probing depth and photon energy range of SX-ARPES relative to vacuum ultraviolet (VUV) ARPES to accurately measure the δ-layer electronic confinement. The measurements are made on ambient-exposed samples and yield extremely thin (< 1 nm) and dense (≈1014 cm-2 ) 2DELs. Critically, this method is used to show that δ-layers of arsenic exhibit better electronic confinement than δ-layers of phosphorus fabricated under identical conditions.
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Affiliation(s)
- Procopios Constantinou
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Physics and AstronomyUniversity College LondonLondonWC1E 6BTUK
- Photon Science DivisionPaul Scherrer InstitutVilligen‐PSI5232Switzerland
| | - Taylor J. Z. Stock
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Electronic and Electrical EngineeringUniversity College LondonLondonWC1E 7JEUK
| | - Eleanor Crane
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Electronic and Electrical EngineeringUniversity College LondonLondonWC1E 7JEUK
| | - Alexander Kölker
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Electronic and Electrical EngineeringUniversity College LondonLondonWC1E 7JEUK
| | - Marcel van Loon
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Physics and AstronomyUniversity College LondonLondonWC1E 6BTUK
| | - Juerong Li
- Advanced Technology InstituteUniversity of SurreyGuildfordGU2 7XHUK
| | - Sarah Fearn
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of MaterialsImperial College of LondonLondonSW7 2AZUK
| | - Henric Bornemann
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Physics and AstronomyUniversity College LondonLondonWC1E 6BTUK
| | - Nicolò D'Anna
- Photon Science DivisionPaul Scherrer InstitutVilligen‐PSI5232Switzerland
| | - Andrew J. Fisher
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Physics and AstronomyUniversity College LondonLondonWC1E 6BTUK
| | | | - Gabriel Aeppli
- Photon Science DivisionPaul Scherrer InstitutVilligen‐PSI5232Switzerland
- Institute of PhysicsEcole Polytechnique Fédérale de Lausanne (EPFL)Lausanne1015Switzerland
- Department of PhysicsETH ZürichZurich8093Switzerland
- Quantum CenterEidgenössische Technische Hochschule Zurich (ETHZ)Zurich8093Switzerland
| | - Neil J. Curson
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Electronic and Electrical EngineeringUniversity College LondonLondonWC1E 7JEUK
| | - Steven R. Schofield
- London Centre for NanotechnologyUniversity College LondonLondonWC1H 0AHUK
- Department of Physics and AstronomyUniversity College LondonLondonWC1E 6BTUK
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2
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Røst HI, Tosi E, Strand FS, Åsland AC, Lacovig P, Lizzit S, Wells JW. Probing the Atomic Arrangement of Subsurface Dopants in a Silicon Quantum Device Platform. ACS APPLIED MATERIALS & INTERFACES 2023; 15:22637-22643. [PMID: 37114767 PMCID: PMC10176322 DOI: 10.1021/acsami.2c23011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
High-density structures of subsurface phosphorus dopants in silicon continue to garner interest as a silicon-based quantum computer platform; however, a much-needed confirmation of their dopant arrangement has been lacking. In this work, we take advantage of the chemical specificity of X-ray photoelectron diffraction to obtain the precise structural configuration of P dopants in subsurface Si:P δ-layers. The growth of δ-layer systems with different levels of doping is carefully studied and verified using X-ray photoelectron spectroscopy and low-energy electron diffraction. Subsequent diffraction measurements reveal that in all cases, the subsurface dopants primarily substitute with Si atoms from the host material. Furthermore, no signs of carrier-inhibiting P-P dimerization can be observed. Our observations not only settle a nearly decade-long debate about the dopant arrangement but also demonstrate how X-ray photoelectron diffraction is surprisingly well suited for studying subsurface dopant structure. This work thus provides valuable input for an updated understanding of the behavior of Si:P δ-layers and the modeling of their derived quantum devices.
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Affiliation(s)
- Håkon I Røst
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
- Department of Physics and Technology, University of Bergen (UiB), Allégaten 55, 5007 Bergen, Norway
| | - Ezequiel Tosi
- Elettra-Sincrotrone Trieste, s.s. 14-km.163,5 in Area Science Park, Basovizza, Trieste 34149, Italy
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC) C/Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Frode S Strand
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
| | - Anna Cecilie Åsland
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
| | - Paolo Lacovig
- Elettra-Sincrotrone Trieste, s.s. 14-km.163,5 in Area Science Park, Basovizza, Trieste 34149, Italy
| | - Silvano Lizzit
- Elettra-Sincrotrone Trieste, s.s. 14-km.163,5 in Area Science Park, Basovizza, Trieste 34149, Italy
| | - Justin W Wells
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
- Department of Physics and Centre for Materials Science and Nanotechnology, University of Oslo (UiO), Oslo 0318, Norway
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3
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Mendez JP, Mamaluy D. Conductivity and size quantization effects in semiconductor [Formula: see text]-layer systems. Sci Rep 2022; 12:16397. [PMID: 36180529 PMCID: PMC9525305 DOI: 10.1038/s41598-022-20105-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 09/08/2022] [Indexed: 11/17/2022] Open
Abstract
We present an open-system quantum-mechanical 3D real-space study of the conduction band structure and conductive properties of two semiconductor systems, interesting for their beyond-Moore and quantum computing applications: phosphorus [Formula: see text]-layers and P [Formula: see text]-layer tunnel junctions in silicon. In order to evaluate size quantization effects on the conductivity, we consider two principal cases: nanoscale finite-width structures, used in transistors, and infinitely-wide structures, electrical properties of which are typically known experimentally. For devices widths [Formula: see text] nm, quantization effects are strong and it is shown that the number of propagating modes determines not only the conductivity, but the distinctive spatial distribution of the current-carrying electron states. For [Formula: see text] nm, the quantization effects practically vanish and the conductivity tends to the infinitely-wide device values. For tunnel junctions, two distinct conductivity regimes are predicted due to the strong conduction band quantization.
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Affiliation(s)
| | - Denis Mamaluy
- Sandia National Laboratories, Albuquerque, NM 87123 USA
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4
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Radue MS, Mo Y, Butera R. Dopant precursor adsorption into single-dimer windows: Towards guided self-assembly of dopant arrays on Si(100). Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2021.139258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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5
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Pakpour-Tabrizi AC, Schenk AK, Holt AJU, Mahatha SK, Arnold F, Bianchi M, Jackman RB, Butler JE, Vikharev A, Miwa JA, Hofmann P, Cooil SP, Wells JW, Mazzola F. The occupied electronic structure of ultrathin boron doped diamond. NANOSCALE ADVANCES 2020; 2:1358-1364. [PMID: 36133056 PMCID: PMC9417656 DOI: 10.1039/c9na00593e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 01/27/2020] [Indexed: 06/13/2023]
Abstract
Using angle-resolved photoelectron spectroscopy, we compare the electronic band structure of an ultrathin (1.8 nm) δ-layer of boron-doped diamond with a bulk-like boron doped diamond film (3 μm). Surprisingly, the measurements indicate that except for a small change in the effective mass, there is no significant difference between the electronic structure of these samples, irrespective of their physical dimensionality, except for a small modification of the effective mass. While this suggests that, at the current time, it is not possible to fabricate boron-doped diamond structures with quantum properties, it also means that nanoscale boron doped diamond structures can be fabricated which retain the classical electronic properties of bulk-doped diamond, without a need to consider the influence of quantum confinement.
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Affiliation(s)
- A C Pakpour-Tabrizi
- London Centre for Nanotechnology, Department of Electronic and Electrical Engineering, University College London 17-19 Gordon Street London WC1H 0AH UK
| | - A K Schenk
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology NO-7491 Trondheim Norway
| | - A J U Holt
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - S K Mahatha
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - F Arnold
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - M Bianchi
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - R B Jackman
- London Centre for Nanotechnology, Department of Electronic and Electrical Engineering, University College London 17-19 Gordon Street London WC1H 0AH UK
| | - J E Butler
- Cubic Carbon Ceramics 855 Carson Road Huntingtown MD 20639 USA
| | - A Vikharev
- Institute of Applied Physics, Russian Academy of Sciences 46 Ul'yanov Street Nizhny Novgorod 603950 Russia
| | - J A Miwa
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - P Hofmann
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center, Aarhus University 8000 Aarhus C Denmark
| | - S P Cooil
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology NO-7491 Trondheim Norway
- Department of Physics, Aberystwyth University Aberystwyth SY23 3BZ UK
| | - J W Wells
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology NO-7491 Trondheim Norway
| | - F Mazzola
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology NO-7491 Trondheim Norway
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6
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Mazzola F, Wells JW, Pakpour-Tabrizi AC, Jackman RB, Thiagarajan B, Hofmann P, Miwa JA. Simultaneous Conduction and Valence Band Quantization in Ultrashallow High-Density Doping Profiles in Semiconductors. PHYSICAL REVIEW LETTERS 2018; 120:046403. [PMID: 29437461 DOI: 10.1103/physrevlett.120.046403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Revised: 12/08/2017] [Indexed: 06/08/2023]
Abstract
We demonstrate simultaneous quantization of conduction band (CB) and valence band (VB) states in silicon using ultrashallow, high-density, phosphorus doping profiles (so-called Si:P δ layers). We show that, in addition to the well-known quantization of CB states within the dopant plane, the confinement of VB-derived states between the subsurface P dopant layer and the Si surface gives rise to a simultaneous quantization of VB states in this narrow region. We also show that the VB quantization can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantized VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantized CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantized CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.
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Affiliation(s)
- F Mazzola
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - J W Wells
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - A C Pakpour-Tabrizi
- London Centre for Nanotechnology and Department of Electronic and Electrical Engineering, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - R B Jackman
- London Centre for Nanotechnology and Department of Electronic and Electrical Engineering, University College London, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | | | - Ph Hofmann
- Department of Physics and Astronomy and Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Ny Munkegade 120, DK-8000 Aarhus, Denmark
| | - J A Miwa
- Department of Physics and Astronomy and Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Ny Munkegade 120, DK-8000 Aarhus, Denmark
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7
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Smith JS, Budi A, Per MC, Vogt N, Drumm DW, Hollenberg LCL, Cole JH, Russo SP. Ab initio calculation of energy levels for phosphorus donors in silicon. Sci Rep 2017; 7:6010. [PMID: 28729674 PMCID: PMC5519722 DOI: 10.1038/s41598-017-06296-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2017] [Accepted: 06/09/2017] [Indexed: 11/09/2022] Open
Abstract
The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modeling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T 2) and 1s(E) states, finding them to be 32 and 31 meV respectively.
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Affiliation(s)
- J S Smith
- Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, VIC, 3001, Australia.
| | - A Budi
- Materials Chemistry, Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100, København Ø, Denmark
| | - M C Per
- Data 61 CSIRO, Door 34 Goods Shed, Village Street, Docklands, VIC, 3008, Australia
| | - N Vogt
- Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, VIC, 3001, Australia
| | - D W Drumm
- Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, VIC, 3001, Australia.,Australian Research Council Centre of Excellence for Nanoscale BioPhotonics, School of Science, RMIT University, Melbourne, VIC, 3001, Australia
| | - L C L Hollenberg
- Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, 3010, Victoria, Australia
| | - J H Cole
- Chemical and Quantum Physics Group, ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne, 3000, Australia
| | - S P Russo
- Chemical and Quantum Physics Group, ARC Centre of Excellence in Exciton Science, School of Science, RMIT University, Melbourne, 3000, Australia
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8
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Cooil SP, Mazzola F, Klemm HW, Peschel G, Niu YR, Zakharov AA, Simmons MY, Schmidt T, Evans DA, Miwa JA, Wells JW. In Situ Patterning of Ultrasharp Dopant Profiles in Silicon. ACS NANO 2017; 11:1683-1688. [PMID: 28182399 DOI: 10.1021/acsnano.6b07359] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We develop a method for patterning a buried two-dimensional electron gas (2DEG) in silicon using low kinetic energy electron stimulated desorption (LEESD) of a monohydride resist mask. A buried 2DEG forms as a result of placing a dense and narrow profile of phosphorus dopants beneath the silicon surface; a so-called δ-layer. Such 2D dopant profiles have previously been studied theoretically, and by angle-resolved photoemission spectroscopy, and have been shown to host a 2DEG with properties desirable for atomic-scale devices and quantum computation applications. Here we outline a patterning method based on low kinetic energy electron beam lithography, combined with in situ characterization, and demonstrate the formation of patterned features with dopant concentrations sufficient to create localized 2DEG states.
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Affiliation(s)
- Simon P Cooil
- Department of Physics, Norwegian University of Science and Technology (NTNU) , N-7491 Trondheim, Norway
- Department of Physics, Aberystwyth University , SY23 3BZ Aberystwyth, United Kingdom
| | - Federico Mazzola
- Department of Physics, Norwegian University of Science and Technology (NTNU) , N-7491 Trondheim, Norway
- School of Physics and Astronomy (SUPA), University of St. Andrews , St. Andrews, Fife KY16 9SS, United Kingdom
| | - Hagen W Klemm
- Fritz-Harber-Insitute Max-Planck Society , Faradayweg 4-6 14195 Berlin, Germany
| | - Gina Peschel
- Fritz-Harber-Insitute Max-Planck Society , Faradayweg 4-6 14195 Berlin, Germany
| | - Yuran R Niu
- MAX IV Laboratory, Lund University , 221 00 Lund, Sweden
| | | | - Michelle Y Simmons
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales , Sydney, New South Wales 2052, Australia
| | - Thomas Schmidt
- Fritz-Harber-Insitute Max-Planck Society , Faradayweg 4-6 14195 Berlin, Germany
| | - D Andrew Evans
- Department of Physics, Aberystwyth University , SY23 3BZ Aberystwyth, United Kingdom
| | - Jill A Miwa
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), University of Aarhus , 8000 Aarhus C, Denmark
| | - Justin W Wells
- Department of Physics, Norwegian University of Science and Technology (NTNU) , N-7491 Trondheim, Norway
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9
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Mazzola F, Edmonds MT, Høydalsvik K, Carter DJ, Marks NA, Cowie BCC, Thomsen L, Miwa J, Simmons MY, Wells JW. Determining the electronic confinement of a subsurface metallic state. ACS NANO 2014; 8:10223-10228. [PMID: 25243326 DOI: 10.1021/nn5045239] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Dopant profiles in semiconductors are important for understanding nanoscale electronics. Highly conductive and extremely confined phosphorus doping profiles in silicon, known as Si:P δ-layers, are of particular interest for quantum computer applications, yet a quantitative measure of their electronic profile has been lacking. Using resonantly enhanced photoemission spectroscopy, we reveal the real-space breadth of the Si:P δ-layer occupied states and gain a rare view into the nature of the confined orbitals. We find that the occupied valley-split states of the δ-layer, the so-called 1Γ and 2Γ, are exceptionally confined with an electronic profile of a mere 0.40 to 0.52 nm at full width at half-maximum, a result that is in excellent agreement with density functional theory calculations. Furthermore, the bulk-like Si 3pz orbital from which the occupied states are derived is sufficiently confined to lose most of its pz-like character, explaining the strikingly large valley splitting observed for the 1Γ and 2Γ states.
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Affiliation(s)
- Federico Mazzola
- Department of Physics, Norwegian University of Science and Technology (NTNU) , N-7491 Trondheim, Norway
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10
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Drumm DW, Per MC, Budi A, Hollenberg LCL, Russo SP. Ab initio electronic properties of dual phosphorus monolayers in silicon. NANOSCALE RESEARCH LETTERS 2014; 9:443. [PMID: 25246862 PMCID: PMC4158386 DOI: 10.1186/1556-276x-9-443] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2014] [Accepted: 08/15/2014] [Indexed: 05/29/2023]
Abstract
IN THE MIDST OF THE EPITAXIAL CIRCUITRY REVOLUTION IN SILICON TECHNOLOGY, WE LOOK AHEAD TO THE NEXT PARADIGM SHIFT: effective use of the third dimension - in particular, its combination with epitaxial technology. We perform ab initio calculations of atomically thin epitaxial bilayers in silicon, investigating the fundamental electronic properties of monolayer pairs. Quantitative band splittings and the electronic density are presented, along with effects of the layers' relative alignment and comments on disordered systems, and for the first time, the effective electronic widths of such device components are calculated.
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Affiliation(s)
- Daniel W Drumm
- Theoretical Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne, VIC 3001, Australia
- School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Manolo C Per
- Theoretical Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne, VIC 3001, Australia
- CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville, VIC 3052, Australia
| | - Akin Budi
- School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
- Now at NanoGeoScience, Nano-Science Centre, University of Copenhagen, Universitetsparken 5, København Ø 2100, Denmark
| | - Lloyd CL Hollenberg
- School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Salvy P Russo
- Theoretical Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne, VIC 3001, Australia
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11
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Miwa JA, Warschkow O, Carter DJ, Marks NA, Mazzola F, Simmons MY, Wells JW. Valley splitting in a silicon quantum device platform. NANO LETTERS 2014; 14:1515-1519. [PMID: 24571617 DOI: 10.1021/nl404738j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
By suppressing an undesirable surface Umklapp process, it is possible to resolve the two most occupied states (1Γ and 2Γ) in a buried two-dimensional electron gas (2DEG) in silicon. The 2DEG exists because of an atomically sharp profile of phosphorus dopants which have been formed beneath the Si(001) surface (a δ-layer). The energy separation, or valley splitting, of the two most occupied bands has critical implications for the properties of δ-layer derived devices, yet until now, has not been directly measurable. Density functional theory (DFT) allows the 2DEG band structure to be calculated, but without experimental verification the size of the valley splitting has been unclear. Using a combination of direct spectroscopic measurements and DFT we show that the measured band structure is in good qualitative agreement with calculations and reveal a valley splitting of 132 ± 5 meV. We also report the effective mass and occupation of the 2DEG states and compare the dispersions and Fermi surface with DFT.
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Affiliation(s)
- Jill A Miwa
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), University of Aarhus , 8000 Aarhus C, Denmark
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12
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Ryu H, Lee S, Weber B, Mahapatra S, Hollenberg LCL, Simmons MY, Klimeck G. Atomistic modeling of metallic nanowires in silicon. NANOSCALE 2013; 5:8666-8674. [PMID: 23897026 DOI: 10.1039/c3nr01796f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Scanning tunneling microscope (STM) lithography has recently demonstrated the ultimate in device scaling with buried, conducting nanowires just a few atoms wide and the realization of single atom transistors, where a single P atom has been placed inside a transistor architecture with atomic precision accuracy. Despite the dimensions of the critical parts of these devices being defined by a small number of P atoms, the device electronic properties are influenced by the surrounding 10(4) to 10(6) Si atoms. Such effects are hard to capture with most modeling approaches, and prior to this work no theory existed that could explore the realistic size of the complete device in which both dopant disorder and placement are important. This work presents a comprehensive study of the electronic and transport properties of ultra-thin (<10 nm wide) monolayer highly P δ-doped Si (Si:P) nanowires in a fully atomistic self-consistent tight-binding approach. This atomistic approach covering large device volumes allows for a systematic study of disorder on the physical properties of the nanowires. Excellent quantitative agreement is observed with recent resistance measurements of STM-patterned nanowires [Weber et al., Science, 2012, 335, 64], confirming the presence of metallic behavior at the scaling limit. At high doping densities the channel resistance is shown to be insensitive to the exact channel dopant placement highlighting their future use as metallic interconnects. This work presents the first theoretical study of Si:P nanowires that are realistically extended and disordered, providing a strong theoretical foundation for the design and understanding of atomic-scale electronics.
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Affiliation(s)
- Hoon Ryu
- National Institute of Supercomputing and Networking, Korea Institute of Science and Technology Information, Daejeon 305-806, Republic of Korea
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13
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Miwa JA, Hofmann P, Simmons MY, Wells JW. Direct measurement of the band structure of a buried two-dimensional electron gas. PHYSICAL REVIEW LETTERS 2013; 110:136801. [PMID: 23581353 DOI: 10.1103/physrevlett.110.136801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2012] [Indexed: 06/02/2023]
Abstract
We directly measure the band structure of a buried two dimensional electron gas (2DEG) using angle resolved photoemission spectroscopy. The buried 2DEG forms 2 nm beneath the surface of p-type silicon, because of a dense delta-type layer of phosphorus n-type dopants which have been placed there. The position of the phosphorous layer is beyond the probing depth of the photoemission experiment but the observation of the 2DEG is nevertheless possible at certain photon energies where emission from the states is resonantly enhanced. This permits direct access to the band structure of the 2DEG and its temperature dependence.
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Affiliation(s)
- Jill A Miwa
- Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
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14
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Drumm DW, Smith JS, Per MC, Budi A, Hollenberg LCL, Russo SP. Ab Initio electronic properties of monolayer phosphorus nanowires in silicon. PHYSICAL REVIEW LETTERS 2013; 110:126802. [PMID: 25166832 DOI: 10.1103/physrevlett.110.126802] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2012] [Indexed: 06/03/2023]
Abstract
Epitaxial circuitry offers a revolution in silicon technology, with components that can be fabricated on atomic scales. We perform the first ab initio calculation of atomically thin epitaxial nanowires in silicon, investigating the fundamental electronic properties of wires two P atoms thick, similar to those produced this year by Weber et al. For the first time, we catch a glimpse of disorder-related effects in the wires--a prerequisite for understanding real fabricated systems. Interwire interactions are made negligible by including 40 ML of silicon in the vertical direction (and the equivalent horizontally). Accurate pictures of band splittings and the electronic density are presented, and for the first time the effective masses of electrons in such device components are calculated.
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Affiliation(s)
- D W Drumm
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia and Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
| | - J S Smith
- Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
| | - M C Per
- Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia and Virtual Nanoscience Laboratory, CSIRO Materials Science and Engineering, Parkville, Victoria 3052, Australia
| | - A Budi
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - L C L Hollenberg
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - S P Russo
- Applied Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
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Drumm DW, Budi A, Per MC, Russo SP, L Hollenberg LC. Ab initio calculation of valley splitting in monolayer δ-doped phosphorus in silicon. NANOSCALE RESEARCH LETTERS 2013; 8:111. [PMID: 23445785 PMCID: PMC3606473 DOI: 10.1186/1556-276x-8-111] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2012] [Accepted: 01/26/2013] [Indexed: 05/29/2023]
Abstract
: The differences in energy between electronic bands due to valley splitting are of paramount importance in interpreting transport spectroscopy experiments on state-of-the-art quantum devices defined by scanning tunnelling microscope lithography. Using vasp, we develop a plane-wave density functional theory description of systems which is size limited due to computational tractability. Nonetheless, we provide valuable data for the benchmarking of empirical modelling techniques more capable of extending this discussion to confined disordered systems or actual devices. We then develop a less resource-intensive alternative via localised basis functions in siesta, retaining the physics of the plane-wave description, and extend this model beyond the capability of plane-wave methods to determine the ab initio valley splitting of well-isolated δ-layers. In obtaining an agreement between plane-wave and localised methods, we show that valley splitting has been overestimated in previous ab initio calculations by more than 50%.
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Affiliation(s)
- Daniel W Drumm
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia
- School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
| | - Akin Budi
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia
- School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
| | - Manolo C Per
- School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
- Virtual Nanoscience Laboratory, CSIRO Materials Science and Engineering, Parkville, Victoria 3052, Australia
| | - Salvy P Russo
- School of Applied Sciences, RMIT University, Melbourne, Victoria 3001, Australia
| | - Lloyd C L Hollenberg
- School of Physics, The University of Melbourne, Parkville, Victoria 3010, Australia
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