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Ultrafast and nanoscale diodes

Published online by Cambridge University Press:  19 October 2016

Peng Zhang
Affiliation:
Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104, USA
Y. Y. Lau
Affiliation:
Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109-2104, USA

Abstract

Charge carrier transport across interfaces of dissimilar materials (including vacuum) is the essence of all electronic devices. Ultrafast charge transport across a nanometre length scale is of fundamental importance in the miniaturization of vacuum and plasma electronics. With the combination of recent advances in electronics, photonics and nanotechnology, these miniature devices may integrate with solid-state platforms, achieving superior performance. This paper reviews recent modelling efforts on quantum tunnelling, ultrafast electron emission and transport, and electrical contact resistance. Unsolved problems and challenges in these areas are addressed.

Type
Research Article
Copyright
© Cambridge University Press 2016 

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References

Ang, L. K., Kwan, T. J. T. & Lau, Y. Y. 2003 New scaling of Child–Langmuir law in the quantum regime. Phys. Rev. Lett. 91 (20), 208303.Google Scholar
Ang, L. K. & Zhang, P. 2007 Ultrashort-pulse Child–Langmuir law in the quantum and relativistic regimes. Phys. Rev. Lett. 98 (16), 164802.Google Scholar
Armstrong, C. M. 2015 The quest for the ultimate vacuum tube. In IEEE Spectrum: Technology, Engineering, and Science News 24 November 2015, http://spectrum.ieee.org/semiconductors/ devices/the-quest-for-the-ultimate-vacuum-tube.Google Scholar
Bâldea, I. 2012 Transition voltage spectroscopy in vacuum break junction: possible role of surface states. Europhys. Lett. 98 (1), 17010.Google Scholar
Bâldea, I. 2014 Concurrent conductance and transition voltage spectroscopy study of scanning tunneling microscopy vacuum junctions. Does it unravel new physics? RSC Advances 4 (63), 3325733261.Google Scholar
Bâldea, I. & Köppel, H. 2012 Evidence on single-molecule transport in electrostatically-gated molecular transistors. Phys. Lett. A 376 (17), 14721476.Google Scholar
Barletta, W. A., Bisognano, J., Corlett, J. N., Emma, P., Huang, Z., Kim, K.-J., Lindberg, R., Murphy, J. B., Neil, G. R., Nguyen, D. C. et al. 2010 Free electron lasers: present status and future challenges. Nucl. Instrum. Meth. A 618 (1–3), 6996.Google Scholar
Benford, J., Swegle, J. A. & Schamiloglu, E. 2015 High Power Microwaves, 3rd edn. CRC Press.Google Scholar
Berger, H. H. 1972 Models for contacts to planar devices. Solid-State Electron. 15 (2), 145158.Google Scholar
Bhattacharjee, S. & Chowdhury, T. 2009 Experimental investigation of transition from Fowler–Nordheim field emission to space-charge-limited flows in a nanogap. Appl. Phys. Lett. 95 (6), 61501.Google Scholar
Bhattacharjee, S., Vartak, A. & Mukherjee, V. 2008 Experimental study of space-charge-limited flows in a nanogap. Appl. Phys. Lett. 92 (19), 191503.Google Scholar
Booske, J. H. 2008 Plasma physics and related challenges of millimeter-wave-to-terahertz and high power microwave generationa. Phys. Plasmas 15 (5), 55502.Google Scholar
Booske, J. H., Dobbs, R. J., Joye, C. D., Kory, C. L., Neil, G. R., Park, G.-S., Park, J. & Temkin, R. J. 2011 Vacuum electronic high power terahertz sources. IEEE Trans. Terahertz Sci. Technol. 1 (1), 5475.Google Scholar
Bormann, R., Gulde, M., Weismann, A., Yalunin, S. V. & Ropers, C. 2010 Tip-enhanced strong-field photoemission. Phys. Rev. Lett. 105 (14), 147601.Google Scholar
Büttiker, M. 1988 Symmetry of electrical conduction. IBM J. Res. Dev. 32 (3), 317334.CrossRefGoogle Scholar
Caflisch, R. E. & Rosin, M. S. 2012 Beyond the Child–Langmuir limit. Phys. Rev. E 85 (5), 56408.Google Scholar
Cahay, M., McLennan, M., Datta, S. & Lundstrom, M. S. 1987 Importance of space-charge effects in resonant tunneling devices. Appl. Phys. Lett. 50 (10), 612614.Google Scholar
Carbonero, J. L., Morin, G. & Cabon, B. 1995 Comparison between beryllium-copper and tungsten high frequency air coplanar probes. IEEE Trans. Microw. Theory Technol. 43 (12), 27862793.Google Scholar
Chen, C., Tao, Z., Hernández-García, C., Matyba, P., Carr, A., Knut, R., Kfir, O., Zusin, D., Gentry, C., Grychtol, P. et al. 2016 Tomographic reconstruction of circularly polarized high-harmonic fields: 3D attosecond metrology. Sci. Adv. 2 (2), e1501333.Google Scholar
Child, C. D. 1911 Discharge from hot CaO. Phys. Rev. Ser. I 32 (5), 492511.Google Scholar
Chin, M., Barber, J. R. & Hu, S. J. 2006 Effect of elastic recovery on the electrical contact resistance in anisotropic conductive adhesive assemblies. IEEE Trans. Compon. Packag. Technol. 29 (1), 137144.Google Scholar
Cocker, T. L., Jelic, V., Gupta, M., Molesky, S. J., Burgess, J. A. J., Reyes, G. D. L., Titova, L. V., Tsui, Y. Y., Freeman, M. R. & Hegmann, F. A. 2013 An ultrafast terahertz scanning tunnelling microscope. Nat. Photon. 7 (8), 620625.Google Scholar
Corkum, P. B. 1993 Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71 (13), 19941997.Google Scholar
Corkum, P. B., Brunel, F., Sherman, N. K. & Srinivasan-Rao, T. 1988 Thermal response of metals to ultrashort-pulse laser excitation. Phys. Rev. Lett. 61 (25), 28862889.Google Scholar
Corkum, P. B., Burnett, N. H. & Ivanov, M. Y. 1994 Subfemtosecond pulses. Opt. Lett. 19 (22), 18701872.Google Scholar
Corkum, P. B. & Krausz, F. 2007 Attosecond science. Nat. Phys. 3 (6), 381387.Google Scholar
Das, V. D. & Jagadeesh, M. S. 1981 Tunneling in $\text{Al}{-}\text{Al}_{2}\text{O}_{3}$ –Al MIM structures. Phys. Stat. Solid. A 66 (1), 327333.Google Scholar
Datta, S. 2005 Quantum Transport: Atom to Transistor, 2nd edn. Cambridge University Press.Google Scholar
Datta, S. & Anantram, M. P. 1992 Steady-state transport in mesoscopic systems illuminated by alternating fields. Phys. Rev. B 45 (23), 1376113764.Google Scholar
England, R. J., Noble, R. J., Bane, K., Dowell, D. H., Ng, C.-K., Spencer, J. E., Tantawi, S., Wu, Z., Byer, R. L., Peralta, E. et al. 2014 Dielectric laser accelerators. Rev. Mod. Phys. 86 (4), 13371389.Google Scholar
Esteban, R., Borisov, A. G., Nordlander, P. & Aizpurua, J. 2012 Bridging quantum and classical plasmonics with a quantum-corrected model. Nat. Commun. 3, 825.Google Scholar
Fairchild, S. B., Boeckl, J., Back, T. C., Ferguson, J. B., Koerner, H., Murray, P. T., Maruyama, B., Lange, M. A., Cahay, M. M., Behabtu, N. et al. 2015 Morphology dependent field emission of acid-spun carbon nanotube fibers. Nanotechnology 26 (10), 105706.Google Scholar
Fan, T., Grychtol, P., Knut, R., Hernández-García, C., Hickstein, D. D., Zusin, D., Gentry, C., Dollar, F. J., Mancuso, C. A., Hogle, C. W. et al. 2015 Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism. Proc. Natl Acad. Sci. 112 (46), 1420614211.Google Scholar
Feng, Y. & Verboncoeur, J. P. 2005 A model for effective field enhancement for Fowler–Nordheim field emission. Phys. Plasmas 12 (10), 103301.Google Scholar
Feng, Y. & Verboncoeur, J. P. 2006 Transition from Fowler–Nordheim field emission to space charge limited current density. Phys. Plasmas 13 (7), 73105.Google Scholar
Feng, Y. & Verboncoeur, J. P. 2008 Consistent solution for space-charge-limited current in the relativistic regime for monoenergetic initial velocities. Phys. Plasmas 15 (11), 112101.Google Scholar
Feng, Y., Verboncoeur, J. P. & Lin, M. C. 2008 Solution for space charge limited field emission current densities with injection velocity and geometric effects corrections. Phys. Plasmas 15 (4), 43301.Google Scholar
Fowler, R. H. & Nordheim, L. 1928 Electron emission in intense electric fields. Proc. R. Soc. Lond. A 119 (781), 173181.Google Scholar
Gomez, M. R., French, D. M., Tang, W., Zhang, P., Lau, Y. Y. & Gilgenbach, R. M. 2009 Experimental validation of a higher dimensional theory of electrical contact resistance. Appl. Phys. Lett. 95 (7), 72103.Google Scholar
Gomez, M. R., Zier, J. C., Gilgenbach, R. M., French, D. M., Tang, W. & Lau, Y. Y. 2008 Effect of soft metal gasket contacts on contact resistance, energy deposition, and plasma expansion profile in a wire array Z pinch. Rev. Sci. Instrum. 79 (9), 93512.Google Scholar
Griswold, M. E. & Fisch, N. J. 2016 Maximum time-dependent space-charge limited diode currents. Phys. Plasmas 23 (1), 14502.Google Scholar
Griswold, M. E., Fisch, N. J. & Wurtele, J. S. 2010 An upper bound to time-averaged space-charge limited diode currents. Phys. Plasmas 17 (11), 114503.Google Scholar
Griswold, M. E., Fisch, N. J. & Wurtele, J. S. 2012 Amended conjecture on an upper bound to time-dependent space-charge limited current. Phys. Plasmas 19 (2), 24502.CrossRefGoogle Scholar
Grosse, K. L., Bae, M.-H., Lian, F., Pop, E. & King, W. P. 2011 Nanoscale Joule heating, Peltier cooling and current crowding at graphene-metal contacts. Nat. Nanotechnol. 6 (5), 287290.Google Scholar
Grotjohn, T. A., Tran, D. T., Yaran, M. K., Demlow, S. N. & Schuelke, T. 2014 Heavy phosphorus doping by epitaxial growth on the (111) diamond surface. Diamond Relat. Mater. 44, 129133.Google Scholar
Hall, P. M. 1968 Resistance calculations for thin film patterns. Thin Solid Films 1 (4), 277295.Google Scholar
Han, J. W. & Meyyappan, M. 2014 Introducing the Vacuum Transistor: A Device Made of Nothing, 23 June, 2014; http://spectrum.ieee.org/semiconductors/devices/introducing-the-vacuum-transistor-a-device-made-of-nothing.Google Scholar
Han, J.-W., Oh, J. S. & Meyyappan, M. 2012 Vacuum nanoelectronics: back to the future? – Gate insulated nanoscale vacuum channel transistor. Appl. Phys. Lett. 100 (21), 213505.Google Scholar
Harris, J. R., Jensen, K. L., Shiffler, D. A. & Petillo, J. J. 2015 Shielding in ungated field emitter arrays. Appl. Phys. Lett. 106 (20), 201603.Google Scholar
Holm, R. 1967 Electric Contacts: Theory and Application, 4th edn. Springer.Google Scholar
Hommelhoff, P., Kealhofer, C. & Kasevich, M. A. 2006 Ultrafast electron pulses from a Tungsten tip triggered by low-power femtosecond laser pulses. Phys. Rev. Lett. 97 (24), 247402.Google Scholar
Hommelhoff, P. & Kling, M.(Eds) 2014 Attosecond Nanophysics: From Basic Science to Applications, 1 edn. Wiley-VCH.Google Scholar
Ilkov, M., Torfason, K., Manolescu, A. & Valfells, Á. 2015 Terahertz pulsed photogenerated current in microdiodes at room temperature. Appl. Phys. Lett. 107 (20), 203508.Google Scholar
Jensen, K. L. 2010 Space charge effects in field emission: three dimensional theory. J. Appl. Phys. 107 (1), 14905.Google Scholar
Jensen, K. L., Lau, Y. Y., Feldman, D. W. & O’Shea, P. G. 2008 Electron emission contributions to dark current and its relation to microscopic field enhancement and heating in accelerator structures. Phys. Rev. Special Top. Accel. Beams 11 (8), 81001.Google Scholar
Jensen, K. L., Shiffler, D. A., Rittersdorf, I. M., Lebowitz, J. L., Harris, J. R., Lau, Y. Y., Petillo, J. J., Tang, W. & Luginsland, J. W. 2015 Discrete space charge affected field emission: flat and hemisphere emitters. J. Appl. Phys. 117 (19), 194902.Google Scholar
Kao, K. C. 2004 Dielectric Phenomena in Solids, 1 edn. Academic.Google Scholar
Koh, W. S. & Ang, L. K. 2008 Quantum model of space–charge-limited field emission in a nanogap. Nanotechnology 19 (23), 235402.Google Scholar
Landauer, R. 1996 Spatial variation of currents and fields due to localized scatterers in metallic conduction (and comment). J. Math. Phys. 37 (10), 52595268.Google Scholar
Langmuir, I. 1913 The effect of space charge and residual gases on thermionic currents in high vacuum. Phys. Rev. 2 (6), 450486.Google Scholar
Latham, R. V. 1995 High Voltage Vacuum Insulation: Basic Concepts and Technological Practice, 1 edn. Academic.Google Scholar
Lau, Y. Y. 2001 Simple theory for the two-dimensional Child–Langmuir law. Phys. Rev. Lett. 87 (27), 278301.Google Scholar
Lau, Y. Y., Chernin, D., Colombant, D. G. & Ho, P.-T. 1991 Quantum extension of Child–Langmuir law. Phys. Rev. Lett. 66 (11), 14461449.Google Scholar
Lau, Y. Y. & Tang, W. 2009 A higher dimensional theory of electrical contact resistance. J. Appl. Phys. 105 (12), 124902.CrossRefGoogle Scholar
Li, C., Thostenson, E. T. & Chou, T.-W. 2007 Dominant role of tunneling resistance in the electrical conductivity of carbon nanotube–based composites. Appl. Phys. Lett. 91 (22), 223114.Google Scholar
Liu, Y. L., Zhang, P., Chen, S. H. & Ang, L. K. 2015a Maximal charge injection of consecutive electron pulses with uniform temporal pulse separation. Phys. Plasmas 22 (8), 84504.Google Scholar
Liu, Y. L., Zhang, P., Chen, S. H. & Ang, L. K. 2015b Maximal charge injection of a uniform separated electron pulse train in a drift space. Phys. Rev. Special Top. Accel. Beams 18 (12), 123402.Google Scholar
Luginsland, J. W., Lau, Y. Y. & Gilgenbach, R. M. 1996 Two-dimensional Child–Langmuir law. Phys. Rev. Lett. 77, 4668.Google Scholar
Luginsland, J. W., Lau, Y. Y., Umstattd, R. J. & Watrous, J. J. 2002 Beyond the Child–Langmuir law: a review of recent results on multidimensional space-charge-limited flow. Phys. Plasmas 9 (5), 23712376.Google Scholar
Maksymovych, P. 2013 Distance dependence of tunneling thermovoltage on metal surfaces. J. Vacuum Sci. Technol. B 31 (3), 31804.Google Scholar
Miller, R., Lau, Y. Y. & Booske, J. H. 2007 Electric field distribution on knife-edge field emitters. Appl. Phys. Lett. 91 (7), 74105.Google Scholar
Mortensen, N. A., Johnsen, K., Jauho, A.-P. & Flensberg, K. 1999 Contact resistance of quantum tubes. Superlatt. Microstruct. 26 (6), 351361.Google Scholar
Myöhänen, P., Tuovinen, R., Korhonen, T., Stefanucci, G. & van Leeuwen, R. 2012 Image charge dynamics in time-dependent quantum transport. Phys. Rev. B 85 (7), 75105.Google Scholar
Newns, D. M. 1969 Fermi–Thomas response of a metal surface to an external point charge. J. Chem. Phys. 50 (10), 45724575.Google Scholar
Nouchi, R. & Tanigaki, K. 2014 Path of the current flow at the metal contacts of graphene field-effect transistors with distorted transfer characteristics. Appl. Phys. Lett. 105 (3), 33112.Google Scholar
Pant, M. & Ang, L. K. 2013 Time-dependent quantum tunneling and nonequilibrium heating model for the generalized Einstein photoelectric effect. Phys. Rev. B 88 (19), 195434.Google Scholar
Park, M., Cola, B. A., Siegmund, T., Xu, J., Maschmann, M. R., Fisher, T. S. & Kim, H. 2006 Effects of a carbon nanotube layer on electrical contact resistance between copper substrates. Nanotechnology 17 (9), 2294.Google Scholar
Pedersen, A., Manolescu, A. & Valfells, Á. 2010 Space-charge modulation in vacuum microdiodes at THz frequencies. Phys. Rev. Lett. 104 (17), 175002.Google Scholar
Peralta, E. A., Soong, K., England, R. J., Colby, E. R., Wu, Z., Montazeri, B., McGuinness, C., McNeur, J., Leedle, K. J., Walz, D. et al. 2013 Demonstration of electron acceleration in a laser-driven dielectric microstructure. Nature 503 (7474), 9194.Google Scholar
Portman, J., Zhang, H., Tao, Z., Makino, K., Berz, M., Duxbury, P. M. & Ruan, C.-Y. 2013 Computational and experimental characterization of high-brightness beams for femtosecond electron imaging and spectroscopy. Appl. Phys. Lett. 103 (25), 253115.Google Scholar
Rokhlenko, A. 2015 Child–Langmuir flow with periodically varying anode voltage. Phys. Plasmas 22 (2), 22126.Google Scholar
Rokhlenko, A. & Lebowitz, J. L. 2003 Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field. Phys. Rev. Lett. 91 (8), 85002.Google Scholar
Ropers, C., Solli, D. R., Schulz, C. P., Lienau, C. & Elsaesser, T. 2007 Localized multiphoton emission of femtosecond electron pulses from metal nanotips. Phys. Rev. Lett. 98 (4), 43907.Google Scholar
Rose, A. 1955 Space-charge-limited currents in solids. Phys. Rev. 97 (6), 15381544.Google Scholar
Rundquist, A., Durfee, C. G., Chang, Z., Herne, C., Backus, S., Murnane, M. M. & Kapteyn, H. C. 1998 Phase-matched generation of coherent soft x-rays. Science 280 (5368), 14121415.Google Scholar
Savage, K. J., Hawkeye, M. M., Esteban, R., Borisov, A. G., Aizpurua, J. & Baumberg, J. J. 2012 Revealing the quantum regime in tunnelling plasmonics. Nature 491 (7425), 574577.Google Scholar
Schroder, D. K. 1998 Semiconductor Material and Device Characterization, 2nd edn. Wiley-Blackwell.Google Scholar
Sharvin, Y. V. 1965 A possible method for studying Fermi surfaces. Sov. Phys.-JETP 21, 655.Google Scholar
Shiffler, D., Statum, T. K., Hussey, T. W., Zhou, O. & Mardahl, P. 2005 High-power microwave sources. In Modern Microwave and Millimeter Wave Power Electronics, p. 691. IEEE.Google Scholar
Simmons, J. G. 1963a Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film. J. Appl. Phys. 34 (6), 17931803.Google Scholar
Simmons, J. G. 1963b Electric tunnel effect between dissimilar electrodes separated by a thin insulating film. J. Appl. Phys. 34 (9), 25812590.Google Scholar
Solomon, P. M. 2011 Contact resistance to a one-dimensional quasi-ballistic nanotube/wire. IEEE Electron Device Lett. 32 (3), 246248.Google Scholar
Sotthewes, K., Hellenthal, C., Kumar, A. & Zandvliet, H. J. W. 2014 Transition voltage spectroscopy of scanning tunneling microscopy vacuum junctions. RSC Advances 4 (61), 3243832442.Google Scholar
Spindt, C. A. 1968 A thin-film field-emission cathode. J. Appl. Phys. 39 (7), 35043505.Google Scholar
Spindt, C. A., Brodie, I., Humphrey, L. & Westerberg, E. R. 1976 Physical properties of thin-film field emission cathodes with molybdenum cones. J. Appl. Phys. 47 (12), 52485263.Google Scholar
Srisonphan, S., Jung, Y. S. & Kim, H. K. 2012 Metal-oxide-semiconductor field-effect transistor with a vacuum channel. Nat. Nanotechnol. 7 (8), 504508.Google Scholar
Stoner, B. R. & Glass, J. T. 2012 Nanoelectronics: nothing is like a vacuum. Nat. Nanotechnol. 7 (8), 485487.Google Scholar
Tan, S. F., Wu, L., Yang, J. K. W., Bai, P., Bosman, M. & Nijhuis, C. A. 2014 Quantum plasmon resonances controlled by molecular tunnel junctions. Science 343 (6178), 14961499.Google Scholar
Tang, W., Shiffler, D. & Cartwright, K. L. 2011 Analysis of electric field screening by the proximity of two knife-edge field emitters. J. Appl. Phys. 110 (3), 34905.Google Scholar
Tang, W., Shiffler, D., Golby, K., LaCour, M. & Knowles, T. 2012 Experimental study of electric field screening by the proximity of two carbon fiber cathodes. J. Vacuum Sci. Technol. B 30 (6), 61803.Google Scholar
Tao, Z., Chen, C., Szilvási, T., Keller, M., Mavrikakis, M., Kapteyn, H. & Murnane, M. 2016 Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids. Science 353 (6294), 6267.Google Scholar
Tao, Z., Zhang, H., Duxbury, P. M., Berz, M. & Ruan, C.-Y. 2012 Space charge effects in ultrafast electron diffraction and imaging. J. Appl. Phys. 111 (4), 44316.Google Scholar
Teague, E. C. 1986 Room temperature gold-vacuum-gold tunneling experiments. J. Res. Natl Bur. Stand. 91 (4), 171233.Google Scholar
Timsit, R. S. 1999 Electrical contact resistance: properties of stationary interfaces. IEEE Trans. Compon. Packag. Technol. 22 (1), 8598.Google Scholar
Trouwborst, M. L., Martin, C. A., Smit, R. H. M., Guédon, C. M., Baart, T. A., van der Molen, S. J. & van Ruitenbeek, J. M. 2011 Transition voltage spectroscopy and the nature of vacuum tunneling. Nano Lett. 11 (2), 614617.Google Scholar
Valfells, Á., Feldman, D. W., Virgo, M., O’Shea, P. G. & Lau, Y. Y. 2002 Effects of pulse-length and emitter area on virtual cathode formation in electron guns. Phys. Plasmas 9 (5), 23772382.Google Scholar
Vlahos, V., Booske, J. H. & Morgan, D. 2007 Ab initio study of the effects of thin CsI coatings on the work function of graphite cathodes. Appl. Phys. Lett. 91 (14), 144102.Google Scholar
Wu, G., Wei, X., Gao, S., Chen, Q. & Peng, L. 2016 Tunable graphene micro-emitters with fast temporal response and controllable electron emission. Nat. Commun. 7, 11513.Google Scholar
Xia, F., Perebeinos, V., Lin, Y., Wu, Y. & Avouris, P. 2011 The origins and limits of metal-graphene junction resistance. Nat. Nanotechnol. 6 (3), 179184.Google Scholar
Yaghoobi, P., Walus, K. & Nojeh, A. 2009 First-principles study of quantum tunneling from nanostructures: Current in a single-walled carbon nanotube electron source. Phys. Rev. B 80 (11), 115422.Google Scholar
Yalunin, S. V., Gulde, M. & Ropers, C. 2011 Strong-field photoemission from surfaces: theoretical approaches. Phys. Rev. B 84 (19), 195426.Google Scholar
Zhang, P.2012 Effects of surface roughness on electrical contact, RF heating and field enhancement. PhD thesis, The Unviersity of Michigan, Ann Arbor.Google Scholar
Zhang, P. 2015 Scaling for quantum tunneling current in nano- and subnano-scale plasmonic junctions. Scientific Rep. 5, 9826.Google Scholar
Zhang, P., Gu, Q., Lau, Y. Y. & Fainman, Y. 2016 Constriction resistance and current crowding in electrically pumped semiconductor nanolasers with the presence of undercut and sidewall tilt. IEEE J. Quantum Electron. 52 (3), 2000207.Google Scholar
Zhang, P. & Hung, D. M. H. 2014 An analytical model for ballistic diode based on asymmetric geometry. J. Appl. Phys. 115 (20), 204908.Google Scholar
Zhang, P., Hung, D. M. H. & Lau, Y. Y. 2013 Current flow in a 3-terminal thin film contact with dissimilar materials and general geometric aspect ratios. J. Phys. D: Appl. Phys. 46 (6), 65502.Google Scholar
Zhang, P. & Lau, Y. Y. 2010 Scaling laws for electrical contact resistance with dissimilar materials. J. Appl. Phys. 108 (4), 44914.Google Scholar
Zhang, P. & Lau, Y. Y. 2013 Constriction resistance and current crowding in vertical thin film contact. IEEE J. Electron Devices Soc. 1 (3), 8390.Google Scholar
Zhang, P. & Lau, Y. Y. 2014 An exact field solution of contact resistance and comparison with the transmission line model. Appl. Phys. Lett. 104 (20), 204102.Google Scholar
Zhang, P. & Lau, Y. Y. 2016 Ultrafast strong-field photoelectron emission from biased metal surfaces: exact solution to time-dependent Schrödinger equation. Scientific Rep. 6, 19894.Google Scholar
Zhang, P., Lau, Y. Y. & Gilgenbach, R. M. 2011 Thin film contact resistance with dissimilar materials. J. Appl. Phys. 109 (12), 124910.Google Scholar
Zhang, P., Lau, Y. Y. & Timsit, R. S. 2012 On the spreading resistance of thin-film contacts. IEEE Trans. Electron Devices 59 (7), 19361940.Google Scholar
Zhang, P., Lau, Y. Y. & Gilgenbach, R. M. 2015a Analysis of current crowding in thin film contacts from exact field solution. J. Phys. D: Appl. Phys. 48 (47), 475501.Google Scholar
Zhang, P., Luginsland, J. W., Lau, Y. Y., Booske, J. H., Gilgenbach, R. M., Jensen, K. L., Peckerar, M., Shiffler, D., Fairchild, S., Verboncoeur, J. P. et al. 2015b Ultrafast and nanoscale interfacial charge transport and its interaction with electromagnetic waves. In DoE Whitepaper on the Frontiers of Plasma Science. https://www.orau.gov/plasmawkshps2015/whitepapers.htm.Google Scholar
Zhang, X.-G., Lu, Z.-Y. & Pantelides, S. T. 2006 First-principles theory of tunneling currents in metal-oxide-semiconductor structures. Appl. Phys. Lett. 89 (3), 32112.Google Scholar
Ziegler, M., Harnack, O. & Kohlstedt, H. 2014 Resistive switching in lateral junctions with nanometer separated electrodes. Solid-State Electron. 92, 2427.Google Scholar
Zier, J., Gomez, M. R., French, D. M., Gilgenbach, R. M., Lau, Y. Y., Tang, W. W., Cuneo, M. E., Mehlhorn, T. A., Johnston, M. D. & Mazarakis, M. G. 2008 Wire-tension effects on plasma dynamics in a two-wire -pinch. IEEE Trans. Plasma Sci. 36 (4), 12841285.Google Scholar