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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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Donnelly MB, Keizer JG, Chung Y, Simmons MY. Monolithic Three-Dimensional Tuning of an Atomically Defined Silicon Tunnel Junction. NANO LETTERS 2021; 21:10092-10098. [PMID: 34797661 DOI: 10.1021/acs.nanolett.1c03879] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
A requirement for quantum information processors is the in situ tunability of the tunnel rates and the exchange interaction energy within the device. The large energy level separation for atom qubits in silicon is well suited for qubit operation but limits device tunability using in-plane gate architectures, requiring vertically separated top-gates to control tunnelling within the device. In this paper, we address control of the simplest tunnelling device in Si:P, the tunnel junction. Here we demonstrate that we can tune its conductance by using a vertically separated top-gate aligned with ±5 nm precision to the junction. We show that a monolithic 3D epitaxial top-gate increases the capacitive coupling by a factor of 3 compared to in-plane gates, resulting in a tunnel barrier height tunability of 0-186 meV. By combining multiple gated junctions in series we extend our monolithic 3D gating technology to implement nanoscale logic circuits including AND and OR gates.
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Affiliation(s)
- Matthew B Donnelly
- Centre for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney 2052, New South Wales, Australia
| | - Joris G Keizer
- Centre for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney 2052, New South Wales, Australia
| | - Yousun Chung
- Centre for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney 2052, New South Wales, Australia
| | - Michelle Y Simmons
- Centre for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney 2052, New South Wales, Australia
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Ryu H. A multi-subband Monte Carlo study on dominance of scattering mechanisms over carrier transport in sub-10-nm Si nanowire FETs. NANOSCALE RESEARCH LETTERS 2016; 11:36. [PMID: 26815605 PMCID: PMC4729720 DOI: 10.1186/s11671-016-1249-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Accepted: 01/12/2016] [Indexed: 06/05/2023]
Abstract
Dominance of various scattering mechanisms in determination of the carrier mobility is examined for silicon (Si) nanowires of sub-10-nm cross-sections. With a focus on p-type channels, the steady-state hole mobility is studied with multi-subband Monte Carlo simulations to consider quantum effects in nanoscale channels. Electronic structures of gate-all-around nanowires are described with a 6-band k · p model. Channel bandstructures and electrostatics under gate biases are determined self-consistently with Schrödinger-Poisson simulations. Modeling results not only indicate that the hole mobility is severely degraded as channels have smaller cross-sections and are inverted more strongly but also confirm that the surface roughness scattering degrades the mobility more severely than the phonon scattering does. The surface roughness scattering affects carrier transport more strongly in narrower channels, showing ∼90 % dominance in determination of the mobility. At the same channel population, [110] channels suffer from the surface roughness scattering more severely than [100] channels do, due to the stronger corner effect and larger population of carriers residing near channel surfaces. With a sound theoretical framework coupled to the spatial distribution of channel carriers, this work may present a useful guideline for understanding hole transport in ultra-narrow Si nanowires.
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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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Ryu H, Lee S, Fuechsle M, Miwa JA, Mahapatra S, Hollenberg LCL, Simmons MY, Klimeck G. A tight-binding study of single-atom transistors. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2015; 11:374-381. [PMID: 25293353 DOI: 10.1002/smll.201400724] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Revised: 07/29/2014] [Indexed: 06/03/2023]
Abstract
A detailed theoretical study of the electronic and transport properties of a single atom transistor, where a single phosphorus atom is embedded within a single crystal transistor architecture, is presented. Using a recently reported deterministic single-atom transistor as a reference, the electronic structure of the device is represented atomistically with a tight-binding model, and the channel modulation is simulated self-consistently with a Thomas-Fermi method. The multi-scale modeling approach used allows confirmation of the charging energy of the one-electron donor charge state and explains how the electrostatic environments of the device electrodes affects the donor confinement potential and hence extent in gate voltage of the two-electron charge state. Importantly, whilst devices are relatively insensitive to dopant ordering in the highly doped leads, a ∼1% variation of the charging energy is observed when a dopant is moved just one lattice spacing within the device. The multi-scale modeling method presented here lays a strong foundation for the understanding of single-atom device structures: essential for both classical and quantum information processing.
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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; Network for Computational Nanotechnology, Purdue University, Indiana, 47907, USA
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Ryu H, Kim J, Hong KH. Atomistic study on dopant-distributions in realistically sized, highly P-doped Si nanowires. NANO LETTERS 2015; 15:450-456. [PMID: 25555203 DOI: 10.1021/nl503770z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The dependency of dopant-distributions on channel diameters in realistically sized, highly phosphorus-doped silicon nanowires is investigated with an atomistic tight-binding approach coupled to self-consistent Schrödinger-Poisson simulations. By overcoming the limit in channel sizes and doping densities of previous studies, this work examines electronic structures and electrostatics of free-standing circular silicon nanowires that are phosphorus-doped with a high density of ∼ 2 × 10(19) cm(-3) and have 12 nm-28 nm cross-sections. Results of analysis on the channel energy indicate that the uniformly distributed dopant profile would be hardly obtained when the nanowire cross-section is smaller than 20 nm. Insufficient room to screen donor ions and shallower impurity bands are the primary reasons of the nonuniform dopant-distributions in smaller nanowires. Being firmly connected to the recent experimental study (Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 15254-15258), this work establishes the first theoretical framework for understanding dopant-distributions in over-10 nm highly doped silicon nanowires.
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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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Neupane MR, Rahman R, Lake RK. Effect of strain on the electronic and optical properties of Ge–Si dome shaped nanocrystals. Phys Chem Chem Phys 2015; 17:2484-93. [DOI: 10.1039/c4cp03711a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An atomistic study of Ge-core–Si-shell nanocrystals gives a detailed picture of how strain and confinement effect the electronic and optical properties.
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Affiliation(s)
- Mahesh R. Neupane
- Department of Electrical and Computer Engineering
- University of California
- Riverside
- USA
| | - Rajib Rahman
- Network for Computational Nanotechnology (NCN)
- Purdue University
- West Lafayette
- USA
| | - Roger K. Lake
- Department of Electrical and Computer Engineering
- University of California
- Riverside
- USA
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Weber B, Ryu H, Tan YHM, Klimeck G, Simmons MY. Limits to metallic conduction in atomic-scale quasi-one-dimensional silicon wires. PHYSICAL REVIEW LETTERS 2014; 113:246802. [PMID: 25541793 DOI: 10.1103/physrevlett.113.246802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2014] [Indexed: 06/04/2023]
Abstract
The recent observation of ultralow resistivity in highly doped, atomic-scale silicon wires has sparked interest in what limits conduction in these quasi-1D systems. Here we present electron transport measurements of gated Si:P wires of widths 4.6 and 1.5 nm. At 4.6 nm we find an electron mobility, μ(el)≃60 cm²/V s, in excellent agreement with that of macroscopic Hall bars. Metallic conduction persists to millikelvin temperatures where we observe Gaussian conductance fluctuations of order δG∼e²/h. In thinner wires (1.5 nm), metallic conduction breaks down at G≲e²/h, where localization of carriers leads to Coulomb blockade. Metallic behavior is explained by the large carrier densities in Si:P δ-doped systems, allowing the occupation of all six valleys of the silicon conduction band, enhancing the number of 1D channels and hence the localization length.
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Affiliation(s)
- Bent Weber
- Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Hoon Ryu
- National Institute of Supercomputing and Networking, KISTI, Daejeon 305-806, South Korea
| | - Y-H Matthias Tan
- Network for Computational Nanotechnology, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Gerhard Klimeck
- Network for Computational Nanotechnology, Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - 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
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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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