Use of Ansoft Maxwell software platform for investigation of electrostatic properties of a hemisphere on a post geometry aimed to model field emission devices Authors: D.S.Roveri 1, H.H.Bertan 1, M.A.R.Alves 1, J.F.Mologni 2, E.S.Braga 1 1. DEMIC - Unicamp Dep. of electronics and microelectronics - State University of Campinas Campinas, SP, Brazil 2. ESSS Engineering Simulation & Scientific Software São Paulo, SP, Brazil
Company Overview DEMIC, Plasma Laboratory 2000-2005: Research on device fabrication for field emission [1, 2] Need for simulations: ANSYS Classic [3] 2011: ESSS provides licenses for MAXWELL Today: 4 PhD Thesis currently in progress
Research Applications Field-Emission Displays (FEDs) [4]
Research Applications Field-Emission Displays (FEDs) [5,6]
Research Applications Field-Emission Array (FEA) in a travelling wave tube [7]
Problem Description Various fabrication processes and the use of distinct materials produce emitting electrodes with different geometrical structures Results presented by literature are too empirical showing lack of geometry optimization
Problem Description Metallic Nanocones [8]
Problem Description Silicon Emitter [7]
Problem Description Metallic Nanoneedles [9] : In x Ga (1-x) As
Problem Description Carbon Nanotubes CNTs [4] (a) (b) (c)
Problem Description Geometry for best Enhancement Factor [10] EmitterApex Macroscopi c Utsumi s Figure of Merit [11]
Goals Establish a workflow to analyze different emitter geometries Create a know-how of electrostatic simulations using FEM (finite element method) Evaluate electrostatic characteristics of the simplest geometric model: hemisphere on a post
Methodology Set of electrostatic simulations using Maxwell 2D simulations: E-Field evaluation Single emitter Array 3D simulations: Screening effect evaluation Single emitter Matrix 9x9
Methodology 2D Simulations Anode Electrodes: PEC Neumann Boundary Emitter Vacuum Cathode Single emitter Axis symmetric about Z 2D Array Cartesian XY
Methodology 2D Simulations Mesh Operations Inside the green area
Methodology 2D Simulations Extra Convergence Criteria Integrate electric field inside the green area
Methodology 2D Simulations Geometry parameterization Aspect Ratio Gap Anode-EmitterApex
Methodology 3D Simulations Automatic Adaptative Meshing Sheet as a Virtual Probe Measure E-field over the surface Emitted Current [12] (Fowler-Nordheim equation) J ( E) A 2 t ( y) E 2 exp 3 2 B E v( y)
Methodology For All Simulations Geometry setup: Radius = 10nm Aspect Ratio = 100 Height = 1μm Gap = 10μm (anode-cathode) Anode voltage = 0V to 1.8kV Spacing = 0.1μm to 2μm (between emitters)
Results Single Emitter E-Field around emitter apex E-Field at apex = 7.63E+9 V/m γ = 76 (anode voltage set to 1000V)
Results Single Emitter Considering: 10<A.R.<300 Excellent fit to the most cited references Deviation < 7% (from Edgcombe [10] )
Results Single Emitter I-V relationship
Results 2D Array Equipotential lines due to screening effect
Results 3D Matrix 9x9 E-Field due to screening effect Max E-Field ~1.3E+8 V/m Min E-Field ~1E+8 V/m Spacing = 0.1 μm
Results 3D Matrix 9x9 E-Field due to screening effect Max E-Field ~2.8E+8 V/m Min E-Field ~9.3E+7 V/m Spacing = 0.4 μm
Results 3D Matrix 9x9 E-Field due to screening effect Max E-Field ~5.5E+8 V/m Min E-Field ~9.1E+7 V/m Spacing = 1 μm
Results 3D Matrix 9x9 E-Field due to screening effect Max E-Field ~6.8E+8 V/m Min E-Field ~7E+7 V/m Spacing = 2 μm
Results 3D Matrix 9x9 Enhancement Factor due to screening effect (anode voltage: 1kV)
Results 3D Matrix 9x9 Total emitted current by the matrix due to screening effect (anode voltage: 1kV)
Conclusion Excellent agreement with results found in specialized literature Successful establishment of a workflow
Next Steps Replicate modeling strategy and simulation methodology for other geometries, like conical and hemi-ellipsoid Simulate gated emitters
References [1] D.F. Takeuti, et al Fabrication of silicon field-emission arrays using masks of amorphous hydrogenated carbon films Microelectronics Journal, n38, p31-34, 2007 doi:10.1016/j.mejo.2006.10.003 [2] E.J. Carvalho, et al SiO 2 single layer for reduction of the standing wave effects in the interference lithography of deep photoresist structures on Si Microelectronics Journal, n37, p1265-1270, 2006 doi:10.1016/j.mejo.2006.07.027 [3] J.F. Mologni, et al Numerical study on performance of pyramidal and conical isotropic etched single emitters Microelectronics Journal, n37, p152-157, 2006 doi:10.1016/j.mejo.2005.03.002 [4] W.I. Milne, et al Carbon nanotubes as field emission sources Journal of Materials Chemistry, n14, p1-12, 2004 doi:10.1039/b314155c [5] D.S. Chung, et al Carbon nanotube electron emitters with a gated structure using backside exposure processes Applied Physics Letters, n80, p4045, 2002 doi:10.1063/1.1480104 [6] W.B. Choi, et al Fully sealed, high-brightness carbon-nanotube field-emission display Applied Physics Letters, n75, p3129, 1999 doi:10.1063/1.125253 [7] D. Temple Recent progress in field emitter array development for high performance applications Materials Science and Engineering, R24, p185-239, 1999 [8] J.M. Kontio, et al Arrays of metallic nanocones fabricated by UV-nanoimprint lithography Microelectronic Engineering, n87, p1711 1715, 2010 [9] M. Moewe, et al Core-shell InGaAs/GaAs quantum well nanoneedles grown on silicon with silicon-transparent emission Optics Express, v17, n10, p7831, 2009 [10] C.J. Edgcombe, et al Microscopy and computational modelling to elucidate the enhancement factor for field electron emitters Journal of Microscopy, v203, p188-194, 2001 [11] T. Utsumi Vacuum Microelectronics: What s New and Exciting IEEE Transactions on Electron Devices, v38, n10, p2276-2283, 1991
References [12] J.M. Bonard, et al Field Emission of Individual Carbon Nanotubes in the Scanning Electron Microscope Physical Review Letters, v89, n19, p1-4, 2002 doi:10.1103/physrevlett.89.197602 [13] F.H. Read, et al Field enhancement factors of random arrays of carbon nanotubes Nuclear Instruments and Methods in Physics Research A, n519, p305-314, 2004 doi:10.1016/j.nima.2003.11.167 [14] G.C. Kokkorakis, et al Local electric field at the emitting surface of a carbon nanotube Journal of Applied Physics, v91, n7, p4580-4584, 2002 doi:10.1063/1.1448403 [15] X.Q. Wang, et al Model calculation for the field enhancement factor of carbon nanotube Journal of Applied Physics, v96, n11, p6752-6755, 2004 doi:10.1063/1.1814439
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