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Author Van de Put, M.L.; Vandenberghe, W.G.; Magnus, W.; Sorée, B.; Fischetti, M.V. url  openurl
  Title Modeling of inter-ribbon tunneling in graphene Type P1 Proceeding
  Year 2015 Publication 18th International Workshop On Computational Electronics (iwce 2015) Abbreviated Journal  
  Volume Issue Pages  
  Keywords P1 Proceeding; Condensed Matter Theory (CMT)  
  Abstract The tunneling current between two crossed graphene ribbons is described invoking the empirical pseudopotential approximation and the Bardeen transfer Hamiltonian method. Results indicate that the density of states is the most important factor determining the tunneling current between small (similar to nm) ribbons. The quasi-one dimensional nature of graphene nanoribbons is shown to result in resonant tunneling.  
  Address  
  Corporate Author Thesis  
  Publisher Ieee Place of Publication New york Editor  
  Language Wos Publication Date  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 978-0-692-51523-5 ISBN Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:134997 Serial 4206  
Permanent link to this record
 

 
Author Moors, K.; Sorée, B.; Magnus, W. url  openurl
  Title Analytic solution of Ando's surface roughness model with finite domain distribution functions Type P1 Proceeding
  Year 2015 Publication 18th International Workshop On Computational Electronics (iwce 2015) Abbreviated Journal  
  Volume Issue Pages  
  Keywords P1 Proceeding; Condensed Matter Theory (CMT)  
  Abstract Ando's surface roughness model is applied to metallic nanowires and extended beyond small roughness size and infinite barrier limit approximations for the wavefunction overlaps, such as the Prange-Nee approximation. Accurate and fast simulations can still be performed without invoking these overlap approximations by averaging over roughness profiles using finite domain distribution functions to obtain an analytic solution for the scattering rates. The simulations indicate that overlap approximations, while predicting a resistivity that agrees more or less with our novel approach, poorly estimate the underlying scattering rates. All methods show that a momentum gap between left- and right-moving electrons at the Fermi level, surpassing a critical momentum gap, gives rise to a substantial decrease in resistivity.  
  Address  
  Corporate Author Thesis  
  Publisher Ieee Place of Publication New york Editor  
  Language Wos Publication Date  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 978-0-692-51523-5 ISBN Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:134996 Serial 4140  
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Author Moors, K.; Sorée, B.; Magnus, W. url  openurl
  Title Modeling and tackling resistivity scaling in metal nanowires Type P1 Proceeding
  Year 2015 Publication International Conference on Simulation of Semiconductor Processes and Devices : [proceedings] T2 – International Conference on Simulation of Semiconductor Processes and, Devices (SISPAD), SEP 09-11, 2015, Washington, DC Abbreviated Journal  
  Volume Issue Pages 222-225  
  Keywords P1 Proceeding; Condensed Matter Theory (CMT)  
  Abstract A self-consistent analytical solution of the multi-subband Boltzmann transport equation with collision term describing grain boundary and surface roughness scattering is presented to study the resistivity scaling in metal nanowires. The different scattering mechanisms and the influence of their statistical parameters are analyzed. Instead of a simple power law relating the height or width of a nanowire to its resistivity, the picture appears to be more complicated due to quantum-mechanical scattering and quantization effects, especially for surface roughness scattering.  
  Address  
  Corporate Author Thesis  
  Publisher Ieee Place of Publication New york Editor  
  Language Wos Publication Date  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 978-1-4673-7860-4 ISBN Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:135046 Serial 4205  
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Author Verreck, D.; Van de Put, M.L.; Verhulst, A.S.; Sorée, B.; Magnus, W.; Dabral, A.; Thean, A.; Groeseneken, G. url  doi
openurl 
  Title 15-band spectral envelope function formalism applied to broken gap tunnel field-effect transistors Type P1 Proceeding
  Year 2015 Publication 18th International Workshop On Computational Electronics (iwce 2015) Abbreviated Journal  
  Volume Issue Pages  
  Keywords P1 Proceeding; Condensed Matter Theory (CMT)  
  Abstract A carefully chosen heterostructure can significantly boost the performance of tunnel field-effect transistors (TFET). Modelling of these hetero-TFETs requires a quantum mechanical (QM) approach with an accurate band structure to allow for a correct description of band-to-band-tunneling. We have therefore developed a fully QM 2D solver, combining for the first time a full zone 15-band envelope function formalism with a spectral approach, including a heterostructure basis set transformation. Simulations of GaSb/InAs broken gap TFETs illustrate the wide body capabilities and transparant transmission analysis of the formalism.  
  Address  
  Corporate Author Thesis  
  Publisher Ieee Place of Publication New york Editor  
  Language Wos 000380398200055 Publication Date 2015-10-26  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 978-0-692-51523-5 ISBN Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:134998 Serial 4131  
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Author Moors, K.; Contino, A.; Van de Put, M.L.; Vandenberghe, W.G.; Fischetti, M., V; Magnus, W.; Sorée, B. url  doi
openurl 
  Title Theoretical study of scattering in graphene ribbons in the presence of structural and atomistic edge roughness Type A1 Journal article
  Year 2019 Publication Physical review materials Abbreviated Journal  
  Volume 3 Issue 2 Pages 024001  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000458161800001 Publication Date 2019-02-06  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2475-9953 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited 4 Open Access  
  Notes ; We acknowledge the Research Foundation – Flanders (FWO) for supporting K.M.'s research visit at the University of Texas at Dallas, as well as the support by the National Research Fund Luxembourg (FNR) with ATTRACT Grant No. 7556175. ; Approved Most recent IF: NA  
  Call Number UA @ admin @ c:irua:157499 Serial 5235  
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Author De Clercq, M.; Moors, K.; Sankaran, K.; Pourtois, G.; Dutta, S.; Adelmann, C.; Magnus, W.; Sorée, B. url  doi
openurl 
  Title Resistivity scaling model for metals with conduction band anisotropy Type A1 Journal article
  Year 2018 Publication Physical review materials Abbreviated Journal  
  Volume 2 Issue 3 Pages 033801  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-) isotropic and anisotropic, respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru.  
  Address  
  Corporate Author Thesis  
  Publisher American Physical Society Place of Publication College Park, Md Editor  
  Language Wos 000426787600001 Publication Date 2018-03-07  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2475-9953 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes ; The authors acknowledge the support by the Fonds National de la Recherche Luxembourg (ATTRACT Grant No. 7556175). ; Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:149866UA @ admin @ c:irua:149866 Serial 4947  
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Author Pourghaderi, M.A.; Magnus, W.; Sorée, B.; Meuris, M.; de Meyer, K.; Heyns, M. url  doi
openurl 
  Title Tunneling-lifetime model for metal-oxide-semiconductor structures Type A1 Journal article
  Year 2009 Publication Physical review : B : solid state Abbreviated Journal Phys Rev B  
  Volume 80 Issue 8 Pages 085315,1-085315,10  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract In this paper we investigate the basic physics of charge carriers (electrons) leaking out of the inversion layer of a metal-oxide-semiconductor capacitor with a biased gate. In particular, we treat the gate leakage current as resulting from two combined processes: (1) the time-dependent decay of electron wave packets representing the inversion-layer charge and (2) the local generation of new electrons replacing those that have leaked away. As a result, the gate current simply emerges as the ratio of the total charge in the inversion layer to the tunneling lifetime. The latter is extracted from the quantum dynamics of the decaying wave packets, while the generation rate is incorporated as a phenomenological source term in the continuity equation. Not only do the gate currents calculated with this model agree very well with experiment, the model also provides an onset to solve the paradox of the current-free bound states representing the resonances of the Schrödinger equation that governs the fully coupled metal-oxide-semiconductor system.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000269639300076 Publication Date 2009-08-21  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 2 Open Access  
  Notes Approved Most recent IF: 3.836; 2009 IF: 3.475  
  Call Number UA @ lucian @ c:irua:78294 Serial 3763  
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Author Li, B.; Partoens, B.; Peeters, F.M.; Magnus, W. url  doi
openurl 
  Title Dielectric mismatch effect on coupled shallow impurity states in a semiconductor nanowire Type A1 Journal article
  Year 2009 Publication Physical review : B : solid state Abbreviated Journal Phys Rev B  
  Volume 79 Issue 8 Pages 085306,1-085306,7  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Coupled shallow impurity states in a freestanding semiconductor nanowire and in a semiconductor nanowire surrounded by a metallic gate are studied within the effective-mass approximation. Bonding and antibonding states are found due to the coupling of the two impurities, and their energy converges with increasing distance di between the two impurities. The dependences of the binding energy on the wire radius R, the distance di between the two impurities, and the impurity radial position in the nanowire are examined.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000263816000051 Publication Date 2009-02-09  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 11 Open Access  
  Notes Approved Most recent IF: 3.836; 2009 IF: 3.475  
  Call Number UA @ lucian @ c:irua:76223 Serial 691  
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Author Li, B.; Slachmuylders, A.F.; Partoens, B.; Magnus, W.; Peeters, F.M. url  doi
openurl 
  Title Dielectric mismatch effect on shallow impurity states in a semiconductor nanowire Type A1 Journal article
  Year 2008 Publication Physical review : B : condensed matter and materials physics Abbreviated Journal Phys Rev B  
  Volume 77 Issue Pages 115335,1-10  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000254542800131 Publication Date 2008-03-19  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 24 Open Access  
  Notes Approved Most recent IF: 3.836; 2008 IF: 3.322  
  Call Number UA @ lucian @ c:irua:69630 Serial 692  
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Author Slachmuylders, A.F.; Partoens, B.; Magnus, W.; Peeters, F.M. url  doi
openurl 
  Title Trions in cylindrical nanowires with a dielectric mismatch Type A1 Journal article
  Year 2007 Publication Physical review : B : condensed matter and materials physics Abbreviated Journal Phys Rev B  
  Volume 76 Issue 7 Pages 075405,1-9  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000249155300136 Publication Date 2007-08-07  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 12 Open Access  
  Notes Approved Most recent IF: 3.836; 2007 IF: 3.172  
  Call Number UA @ lucian @ c:irua:66119 Serial 3732  
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Author Slachmuylders, A.F.; Partoens, B.; Magnus, W.; Peeters, F.M. url  doi
openurl 
  Title Dielectric mismatch effect on the exciton states in cylindrical nanowires Type A1 Journal article
  Year 2006 Publication Physical review : B : condensed matter and materials physics Abbreviated Journal Phys Rev B  
  Volume 74 Issue 23 Pages 235321,1-8  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000243195700080 Publication Date 2006-12-20  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 39 Open Access  
  Notes Approved Most recent IF: 3.836; 2006 IF: 3.107  
  Call Number UA @ lucian @ c:irua:62178 Serial 693  
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Author Li, B.; Magnus, W.; Peeters, F.M. url  doi
openurl 
  Title Tunable exciton Aharonov-Bohm effect in a quantum ring Type A1 Journal article
  Year 2010 Publication Journal of physics : conference series T2 – Proceedings of the 11th International Conference on Optics of Excitons in Confined Systems, September 7-11, 2009, Spain / Vina, L. [edit.]; et al. [edit.] Abbreviated Journal  
  Volume 210 Issue 1 Pages 012030,1-01203,4  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We studied the optical Aharonov-Bohm effect for an exciton in a semiconductor quantum ring. A perpendicular electric field applied to a quantum ring with large height, is able to tune the exciton ground state energy such that it exhibits a weak observable Aharonov-Bohm oscillations. This Aharonov-Bohm effect is tunable in strength and period.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Bristol Editor  
  Language Wos 000289715800242 Publication Date 2010-03-03  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1742-6596; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited 3 Open Access  
  Notes ; ; Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:89950 Serial 3741  
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Author Magnus, W.; Brosens, F.; Sorée, B. url  doi
openurl 
  Title Time dependent transport in 1D micro- and nanostructures: solving the Boltzmann and Wigner-Boltzmann equations Type A1 Journal article
  Year 2009 Publication Journal of physics : conference series Abbreviated Journal  
  Volume 193 Issue 1 Pages 012004,1-012004,4  
  Keywords A1 Journal article; Condensed Matter Theory (CMT); Theory of quantum systems and complex systems  
  Abstract For many decades the Boltzmann distribution function has been used to calculate the non-equilibrium properties of mobile particles undergoing the combined action of various scattering mechanisms and externally applied force fields. When the latter give rise to the occurrence of inhomogeneous potential profiles across the region through which the particles are moving, the numerical solution of the Boltzmann equation becomes a highly complicated task. In this work we highlight a particular algorithm that can be used to solve the time dependent Boltzmann equation as well as its quantum mechanical extension, the WignerBoltzmann equation. As an illustration, we show the calculated distribution function describing electrons propagating under the action of both a uniform and a pronouncedly non-uniform electric field.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Bristol Editor  
  Language Wos 000277100400004 Publication Date 2009-11-17  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1742-6596; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited 2 Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:82861 Serial 3667  
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Author Van de Put, M.L.; Vandenberghe, W.G.; Sorée, B.; Magnus, W.; Fischetti, M.V. url  doi
openurl 
  Title Inter-ribbon tunneling in graphene: An atomistic Bardeen approach Type A1 Journal article
  Year 2016 Publication Journal of applied physics Abbreviated Journal J Appl Phys  
  Volume 119 Issue 119 Pages 214306  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract A weakly coupled system of two crossed graphene nanoribbons exhibits direct tunneling due to the overlap of the wavefunctions of both ribbons. We apply the Bardeen transfer Hamiltonian formalism, using atomistic band structure calculations to account for the effect of the atomic structure on the tunneling process. The strong quantum-size confinement of the nanoribbons is mirrored by the one-dimensional character of the electronic structure, resulting in properties that differ significantly from the case of inter-layer tunneling, where tunneling occurs between bulk two-dimensional graphene sheets. The current-voltage characteristics of the inter-ribbon tunneling structures exhibit resonance, as well as stepwise increases in current. Both features are caused by the energetic alignment of one-dimensional peaks in the density-of-states of the ribbons. Resonant tunneling occurs if the sign of the curvature of the coupled energy bands is equal, whereas a step-like increase in the current occurs if the signs are opposite. Changing the doping modulates the onset-voltage of the effects as well as their magnitude. Doping through electrostatic gating makes these structures promising for application towards steep slope switching devices. Using the atomistic empirical pseudopotentials based Bardeen transfer Hamiltonian method, inter-ribbon tunneling can be studied for the whole range of two-dimensional materials, such as transition metal dichalcogenides. The effects of resonance and of step-like increases in the current we observe in graphene ribbons are also expected in ribbons made from these alternative two-dimensional materials, because these effects are manifestations of the one-dimensional character of the density-of-states. Published by AIP Publishing.  
  Address  
  Corporate Author Thesis  
  Publisher American Institute of Physics Place of Publication New York, N.Y. Editor  
  Language Wos 000378923100022 Publication Date 2016-06-07  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0021-8979; 1089-7550 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.068 Times cited 6 Open Access  
  Notes ; ; Approved Most recent IF: 2.068  
  Call Number UA @ lucian @ c:irua:134652 Serial 4198  
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Author Moors, K.; Sorée, B.; Magnus, W. url  doi
openurl 
  Title Modeling surface roughness scattering in metallic nanowires Type A1 Journal article
  Year 2015 Publication Journal of applied physics Abbreviated Journal J Appl Phys  
  Volume 118 Issue 118 Pages 124307  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction. (C) 2015 AIP Publishing LLC.  
  Address  
  Corporate Author Thesis  
  Publisher American Institute of Physics Place of Publication New York, N.Y. Editor  
  Language Wos 000362565800032 Publication Date 2015-09-24  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0021-8979; 1089-7550 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.068 Times cited 11 Open Access  
  Notes ; ; Approved Most recent IF: 2.068; 2015 IF: 2.183  
  Call Number UA @ lucian @ c:irua:129425 Serial 4207  
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Author Moors, K.; Sorée, B.; Tokei, Z.; Magnus, W. url  doi
openurl 
  Title Resistivity scaling and electron relaxation times in metallic nanowires Type A1 Journal article
  Year 2014 Publication Journal of applied physics Abbreviated Journal J Appl Phys  
  Volume 116 Issue 6 Pages 063714  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxation time strongly depends on the sub-band state, something that remained unclear with the methods of previous work. The resistivity scaling is obtained for different roughness and grain-boundary properties, showing large differences in scaling behavior and relaxation times. Our model clearly indicates that the resistivity is dominated by grain-boundary scattering, easily surpassing the surface roughness contribution by a factor of 10. (C) 2014 AIP Publishing LLC.  
  Address  
  Corporate Author Thesis  
  Publisher American Institute of Physics Place of Publication New York, N.Y. Editor  
  Language Wos 000341179400036 Publication Date 2014-08-15  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0021-8979;1089-7550; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.068 Times cited 17 Open Access  
  Notes ; ; Approved Most recent IF: 2.068; 2014 IF: 2.183  
  Call Number UA @ lucian @ c:irua:119260 Serial 2882  
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Author Sorée, B.; Magnus, W.; Vandenberghe, W. url  doi
openurl 
  Title Low-field mobility in ultrathin silicon nanowire junctionless transistors Type A1 Journal article
  Year 2011 Publication Applied physics letters Abbreviated Journal Appl Phys Lett  
  Volume 99 Issue 23 Pages 233509-233509,3  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We theoretically investigate the phonon, surface roughness and ionized impurity limited low-field mobility of ultrathin silicon n-type nanowire junctionless transistors in the long channel approximation with wire radii ranging from 2 to 5 nm, as function of gate voltage. We show that surface roughness scattering is negligible as long as the wire radius is not too small and ionized impurity scattering is the dominant scattering mechanism. We also show that there exists an optimal radius where the ionized impurity limited mobility exhibits a maximum.  
  Address  
  Corporate Author Thesis  
  Publisher American Institute of Physics Place of Publication New York, N.Y. Editor  
  Language Wos 000298006100095 Publication Date 2011-12-09  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0003-6951; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.411 Times cited 20 Open Access  
  Notes ; This work is supported by the EU project SQWIRE (FP7-ICT-STREP nr. 257111). William Vandenberghe gratefully acknowledges the Ph.D. stipend from the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). ; Approved Most recent IF: 3.411; 2011 IF: 3.844  
  Call Number UA @ lucian @ c:irua:92865 Serial 1850  
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Author Slachmuylders, A.F.; Partoens, B.; Peeters, F.M.; Magnus, W. url  doi
openurl 
  Title Effect of a metallic gate on the energy levels of a shallow donor Type A1 Journal article
  Year 2008 Publication Applied physics letters Abbreviated Journal Appl Phys Lett  
  Volume 92 Issue 8 Pages 083104,1-3  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher American Institute of Physics Place of Publication New York, N.Y. Editor  
  Language Wos 000254297300074 Publication Date 2008-02-27  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0003-6951; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.411 Times cited 14 Open Access  
  Notes Approved Most recent IF: 3.411; 2008 IF: 3.726  
  Call Number UA @ lucian @ c:irua:69618 Serial 792  
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Author Magnus, W.; Brosens, F. pdf  url
doi  openurl
  Title Occupation numbers in a quantum canonical ensemble : a projection operator approach Type A1 Journal article
  Year 2019 Publication Physica: A : theoretical and statistical physics Abbreviated Journal Physica A  
  Volume 518 Issue 518 Pages 253-264  
  Keywords A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT)  
  Abstract Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is (1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and (2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons. (C) 2018 Elsevier B.V. All rights reserved.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000456359200021 Publication Date 2018-11-28  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0378-4371 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.243 Times cited 1 Open Access  
  Notes ; ; Approved Most recent IF: 2.243  
  Call Number UA @ admin @ c:irua:157468 Serial 5223  
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Author Dabral, A.; Pourtois, G.; Sankaran, K.; Magnus, W.; Yu, H.; de de Meux, A.J.; Lu, A.K.A.; Clima, S.; Stokbro, K.; Schaekers, M.; Collaert, N.; Horiguchi, N.; Houssa, M. doi  openurl
  Title Study of the intrinsic limitations of the contact resistance of metal/semiconductor interfaces through atomistic simulations Type A1 Journal article
  Year 2018 Publication ECS journal of solid state science and technology Abbreviated Journal Ecs J Solid State Sc  
  Volume 7 Issue 6 Pages N73-N80  
  Keywords A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)  
  Abstract In this contribution, we report a fundamental study of the factors that set the contact resistivity between metals and highly doped n-type 2D and 3D semiconductors. We investigate the case of n-type doped Si contacted with amorphous TiSi combining first principles calculations with Non-Equilibrium Green functions transport simulations. The evolution of the intrinsic contact resistivity with the doping concentration is found to saturate at similar to 2 x 10(-10) Omega.cm(2) for the case of TiSi and imposes an intrinsic limit to the ultimate contact resistance achievable for n-doped Silamorphous-TiSi (aTiSi). The limit arises from the intrinsic properties of the semiconductors and of the metals such as their electron effective masses and Fermi energies. We illustrate that, in this regime, contacting heavy electron effective mass metals with semiconductor helps reducing the interface intrinsic contact resistivity. This observation seems to hold true regardless of the 3D character of the semiconductor, as illustrated for the case of three 2D semiconducting materials, namely MoS2, ZrS2 and HfS2. (C) The Author(s) 2018. Published by ECS.  
  Address  
  Corporate Author Thesis  
  Publisher Electrochemical society Place of Publication Pennington (N.J.) Editor  
  Language Wos 000440836000004 Publication Date 2018-05-25  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2162-8769; 2162-8777 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 1.787 Times cited 2 Open Access Not_Open_Access  
  Notes ; The authors thank the imec core CMOS program members, the European Commission, its TAKEMI5 ECSEL research project and the local authorities for their support. ; Approved Most recent IF: 1.787  
  Call Number UA @ lucian @ c:irua:153205UA @ admin @ c:irua:153205 Serial 5130  
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Author Pourtois, G.; Dabral, A.; Sankaran, K.; Magnus, W.; Yu, H.; de de Meux, A.J.; Lu, A.K.A.; Clima, S.; Stokbro, K.; Schaekers, M.; Houssa, M.; Collaert, N.; Horiguchi, N. pdf  doi
openurl 
  Title Probing the intrinsic limitations of the contact resistance of metal/semiconductor interfaces through atomistic simulations Type P1 Proceeding
  Year 2017 Publication Semiconductors, Dielectrics, And Metals For Nanoelectronics 15: In Memory Of Samares Kar Abbreviated Journal  
  Volume Issue Pages 303-311  
  Keywords P1 Proceeding; Engineering sciences. Technology; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)  
  Abstract In this contribution, we report a fundamental study of the factors that set the contact resistivity between metals and highly doped semiconductors. We investigate the case of n-type doped Si contacted with amorphous TiSi combining first-principles calculations with Non-Equilibrium Green functions transport simulations. The intrinsic contact resistivity is found to saturate at similar to 2x10(-10) Omega.cm(2) with the doping concentration and sets an intrinsic limit to the ultimate contact resistance achievable for n-doped Si vertical bar amorphous-TiSi. This limit arises from the intrinsic properties of the semiconductor and of the metal such as their electron effective masses and Fermi energies. We illustrate that, in this regime, contacting metals with a heavy electron effective mass helps reducing the interface intrinsic contact resistivity.  
  Address  
  Corporate Author Thesis  
  Publisher Electrochemical soc inc Place of Publication Pennington Editor  
  Language Wos 000426271800028 Publication Date 2017-10-17  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume 80 Series Issue 1 Edition  
  ISSN 978-1-62332-470-4; 978-1-60768-818-1 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited 1 Open Access Not_Open_Access  
  Notes ; ; Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:149966 Serial 4976  
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Author Kao, K.-H.; Verhulst, A.S.; Vandenberghe, W.G.; Sorée, B.; Magnus, W.; Leonelli, D.; Groeseneken, G.; De Meyer, K. doi  openurl
  Title Optimization of gate-on-source-only tunnel FETs with counter-doped pockets Type A1 Journal article
  Year 2012 Publication IEEE transactions on electron devices Abbreviated Journal Ieee T Electron Dev  
  Volume 59 Issue 8 Pages 2070-2077  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We investigate a promising tunnel FET configuration having a gate on the source only, which is simultaneously exhibiting a steeper subthreshold slope and a higher ON-current than the lateral tunneling configuration with a gate on the channel. Our analysis is performed based on a recently developed 2-D quantum-mechanical simulator calculating band-to-band tunneling and including quantum confinement (QC). It is shown that the two disadvantages of the structure, namely, the sensitivity to gate alignment and the physical oxide thickness, are mitigated by placing a counter-doped parallel pocket underneath the gate-source overlap. The pocket also significantly reduces the field-induced QC. The findings are illustrated with all-Si and all-Ge gate-on-source-only tunnel field-effect transistor simulations.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication New York, N.Y. Editor  
  Language Wos 000306920200011 Publication Date 2012-06-27  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0018-9383;1557-9646; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.605 Times cited 72 Open Access  
  Notes ; Manuscript received February 17, 2012; revised May 7, 2012; accepted May 11, 2012. Date of publication June 26, 2012; date of current version July 19, 2012. This work was supported by the Interuniversity Microelectronics Center's Industrial Affiliation Program. The work of W. G. Vandenberghe was supported by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) through a Ph.D. stipend. The review of this paper was arranged by Editor H. S. Momose. ; Approved Most recent IF: 2.605; 2012 IF: 2.062  
  Call Number UA @ lucian @ c:irua:100820 Serial 2487  
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Author Lujan, G.S.; Magnus, W.; Soree, B.; Pourghaderi, M.A.; Veloso, A.; van Dal, M.J.H.; Lauwers, A.; Kubicek, S.; De Gendt, S.; Heyns, M.; De Meyer, K.; doi  isbn
openurl 
  Title A new method to calculate leakage current and its applications for sub-45nm MOSFETs Type H1 Book chapter
  Year 2005 Publication Solid-State Device Research (ESSDERC), European Conference T2 – ESSDERC 2005 : proceedings of 35th European Solid-State Device Research Conference, September 12-16, 2005, Grenoble, France Abbreviated Journal  
  Volume Issue Pages 489-492  
  Keywords H1 Book chapter; Condensed Matter Theory (CMT)  
  Abstract This paper proposes a new quantum mechanical model for the calculation of leakage currents. The model incorporates both variational calculus and the transfer matrix method to compute the subband energies and the life times of the inversion layer states. The use of variational calculus simplifies the subband energy calculation due to the analytical firm of the wave functions, which offers an attractive perspective towards the calculation of the electron mobility in the channel. The model can be extended to high-k dielectrics with several layers. Good agreement between experimental data and simulation results is obtained for metal gate capacitors.  
  Address  
  Corporate Author Thesis  
  Publisher Ieee Place of Publication S.l. Editor  
  Language Wos 000236176200114 Publication Date 2005-12-13  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN ISBN 0-7803-9203-5 Additional Links UA library record; WoS full record  
  Impact Factor Times cited Open Access  
  Notes Approved Most recent IF: NA  
  Call Number UA @ lucian @ c:irua:103691 Serial 2323  
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Author Compemolle, S.; Pourtois, G.; Sorée, B.; Magnus, W.; Chibotaru, L.F.; Ceulemans, A. doi  openurl
  Title Conductance of a copper-nanotube bundle interface: impact of interface geometry and wave-function interference Type A1 Journal article
  Year 2008 Publication Physical review : B : condensed matter and materials physics Abbreviated Journal Phys Rev B  
  Volume 77 Issue 19 Pages 193406,1-4  
  Keywords A1 Journal article; Condensed Matter Theory (CMT); Plasma Lab for Applications in Sustainability and Medicine – Antwerp (PLASMANT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Lancaster, Pa Editor  
  Language Wos 000256971600032 Publication Date 2008-05-20  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1098-0121;1550-235X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.836 Times cited 8 Open Access  
  Notes Approved Most recent IF: 3.836; 2008 IF: 3.322  
  Call Number UA @ lucian @ c:irua:70215 Serial 479  
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Author Kenawy, A.; Magnus, W.; Milošević, M.V.; Sorée, B. pdf  doi
openurl 
  Title Electronically tunable quantum phase slips in voltage-biased superconducting rings as a base for phase-slip flux qubits Type A1 Journal article
  Year 2020 Publication Superconductor Science & Technology Abbreviated Journal Supercond Sci Tech  
  Volume 33 Issue 12 Pages 125002  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Quantum phase slips represent a coherent mechanism to couple flux states of a superconducting loop. Since their first direct observation, there have been substantial developments in building charge-insensitive quantum phase-slip circuits. At the heart of these devices is a weak link, often a nanowire, interrupting a superconducting loop. Owing to the very small cross-sectional area of such a nanowire, quantum phase slip rates in the gigahertz range can be achieved. Instead, here we present the use of a bias voltage across a superconducting loop to electrostatically induce a weak link, thereby amplifying the rate of quantum phase slips without physically interrupting the loop. Our simulations reveal that the bias voltage modulates the free energy barrier between subsequent flux states in a very controllable fashion, providing a route towards a phase-slip flux qubit with a broadly tunable transition frequency.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000577207000001 Publication Date 2020-09-16  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0953-2048 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 3.6 Times cited 4 Open Access  
  Notes ; ; Approved Most recent IF: 3.6; 2020 IF: 2.878  
  Call Number UA @ admin @ c:irua:172643 Serial 6503  
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Author Vanherck, J.; Sorée, B.; Magnus, W. pdf  doi
openurl 
  Title Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields Type A1 Journal article
  Year 2018 Publication Journal of physics : condensed matter Abbreviated Journal J Phys-Condens Mat  
  Volume 30 Issue 27 Pages 275801  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-2D magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane and easy-axis anisotropic ferromagnet-both in two and three dimensions-subjected to a uniform magnetic field, applied along an arbitrary direction. In this paper, a spin-1/2 Heisenberg Hamiltonian with anisotropic exchange interactions is solved using double-time temperature-dependent Green's functions and the Tyablikov decoupling approximation. We determine various magnetic properties such as the Curie temperature and the magnetization as a function of temperature and the applied magnetic field, discussing the impact of the system's dimensionality and the type of anisotropy. The magnetic reorientation transition taking place in anisotropic Heisenberg ferromagnets is studied in detail. Importantly, spontaneous magnetization is found to be absent for easy-plane 2D spin systems with short range interactions.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication London Editor  
  Language Wos 000434980600001 Publication Date 2018-05-21  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0953-8984 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.649 Times cited Open Access  
  Notes ; ; Approved Most recent IF: 2.649  
  Call Number UA @ lucian @ c:irua:151945UA @ admin @ c:irua:151945 Serial 5012  
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Author Moors, K.; Sorée, B.; Magnus, W. pdf  doi
openurl 
  Title Validity criteria for Fermi's golden rule scattering rates applied to metallic nanowires Type A1 Journal article
  Year 2016 Publication Journal of physics : condensed matter Abbreviated Journal J Phys-Condens Mat  
  Volume 28 Issue 28 Pages 365302  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Fermi's golden rule underpins the investigation of mobile carriers propagating through various solids, being a standard tool to calculate their scattering rates. As such, it provides a perturbative estimate under the implicit assumption that the effect of the interaction Hamiltonian which causes the scattering events is sufficiently small. To check the validity of this assumption, we present a general framework to derive simple validity criteria in order to assess whether the scattering rates can be trusted for the system under consideration, given its statistical properties such as average size, electron density, impurity density et cetera. We derive concrete validity criteria for metallic nanowires with conduction electrons populating a single parabolic band subjected to different elastic scattering mechanisms: impurities, grain boundaries and surface roughness.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication London Editor  
  Language Wos 000380754400013 Publication Date 2016-07-12  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0953-8984 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.649 Times cited 2 Open Access  
  Notes ; ; Approved Most recent IF: 2.649  
  Call Number UA @ lucian @ c:irua:135011 Serial 4274  
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Author Slachmuylders, A.F.; Partoens, B.; Magnus, W.; Peeters, F.M. doi  openurl
  Title Exciton states in cylindrical nanowires Type A1 Journal article
  Year 2006 Publication Journal of physics : condensed matter Abbreviated Journal J Phys-Condens Mat  
  Volume 18 Issue 16 Pages 3951-3966  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication London Editor  
  Language Wos 000237749000013 Publication Date 2006-04-04  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0953-8984;1361-648X; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.649 Times cited 27 Open Access  
  Notes Approved Most recent IF: 2.649; 2006 IF: 2.038  
  Call Number UA @ lucian @ c:irua:59473 Serial 1118  
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Author Kerner, C.; Hackens, B.; Golubović, D.S.; Poli, S.; Faniel, S.; Magnus, W.; Schoenmaker, W.; Bayot, V.; Maes, H. doi  openurl
  Title Control and readout of current-induced magnetic flux quantization in a superconducting transformer Type A1 Journal article
  Year 2009 Publication Superconductor science and technology Abbreviated Journal Supercond Sci Tech  
  Volume 22 Issue 2 Pages 025001,1-025001,4  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract We demonstrate a simple and robust method for inducing and detecting changes of magnetic flux quantization in the absence of an externally applied magnetic field. In our device, an isolated ring is interconnected with two access loops via permalloy cores, forming a superconducting transformer. By applying and tuning a direct current at the first access loop, the number of flux quanta trapped in the isolated ring is modified without the aid of an external field. The flux state of the isolated ring is simply detected by recording the evolution of the critical current of the second access loop.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Bristol Editor  
  Language Wos 000262786000003 Publication Date 2008-12-24  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0953-2048;1361-6668; ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.878 Times cited 2 Open Access  
  Notes Approved Most recent IF: 2.878; 2009 IF: 2.694  
  Call Number UA @ lucian @ c:irua:76001 Serial 497  
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Author Vanherck, J.; Bacaksiz, C.; Sorée, B.; Milošević, M.V.; Magnus, W. pdf  doi
openurl 
  Title 2D ferromagnetism at finite temperatures under quantum scrutiny Type A1 Journal article
  Year 2020 Publication Applied Physics Letters Abbreviated Journal Appl Phys Lett  
  Volume 117 Issue 5 Pages 052401  
  Keywords A1 Journal article; Condensed Matter Theory (CMT)  
  Abstract Recent years have seen a tremendous rise of two-dimensional (2D) magnetic materials, several of which were verified experimentally. However, most of the theoretical predictions to date rely on ab initio methods, at zero temperature and fluctuation-free, while one certainly expects detrimental quantum fluctuations at finite temperatures. Here, we present the solution of the quantum Heisenberg model for honeycomb/hexagonal lattices with anisotropic exchange interaction up to third nearest neighbors and in an applied field in arbitrary direction, which answers the question whether long-range magnetization can indeed survive in the ultrathin limit of materials, up to which temperature, and what the characteristic excitation (magnon) frequencies are, all essential to envisaged applications of magnetic 2D materials. We find that long-range magnetic order persists at finite temperature for materials with overall easy-axis anisotropy. We validate the calculations on the examples of monolayers CrI3, CrBr3, and MnSe2. Moreover, we provide an easy-to-use tool to calculate Curie temperatures of new 2D computational materials.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000559330100001 Publication Date 2020-08-03  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0003-6951; 1077-3118 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 4 Times cited 8 Open Access  
  Notes ; This work was supported by the Research Foundation-Flanders (FWO) and the special research funds of the University of Antwerp (BOF-UA). ; Approved Most recent IF: 4; 2020 IF: 3.411  
  Call Number UA @ admin @ c:irua:171176 Serial 6445  
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