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Modeling Transport Across Thin Dielectric Barriers

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Advanced Physical Models for Silicon Device Simulation

Part of the book series: Computational Microelectronics ((COMPUTATIONAL))

Abstract

In modern microelectronics the transport of carriers across thin and ultra-thin dielectric barriers is of considerable interest. Well-known problems are the highenergy injection of carriers into gate oxides of MOSFETs [5.13, 5.43] leading to a long-term shift of their threshold voltage (so-called degradation), the strong tunnel currents during the erase mode of electrically erasable programmable read only memories (EPROMs) [5.68], the current-voltage characteristics of metal-insulator-semiconductor (MIS) solar cells [5.15, 5.25, 5.69, 5.78], or the tunneling leakage occurring in memory cells [5.5, 5.33]. Apart from a realistic distribution function, the simulation of the current requires a good knowledge of the quantum-mechanical transmission probability.

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References

  1. J. L. Alay, M. Fukuda, K. Nakagawa, S. Yokoyama, and M. Hirose. The Valence Band Alignment at Ultra-Thin SiO2/Si(100) Interfaces Determined by High-Resolution X-Ray Photoelectron Spectroscopy. In Proc. Int. Conf. Sol. State Devices and Materials (Japan), 1995.

    Google Scholar 

  2. R. M. Alexander. Accelerated Testing in FAMOS Devices-8K EPROM. Int. Reliability Physics Symposium, pp. 229–232, 1978.

    Google Scholar 

  3. Y. Ando and T. Itoh. Calculation of Transmission Tunneling Current Across Arbitrary Potential Barriers. J. Appl. Phys., 61(4): 1497–1502, 1987.

    Article  Google Scholar 

  4. M. Av-Ron, M. Shatzkes, T. H. DiStefano, and R. A. Gdula. Electron Tunneling at Al-SiO2 Interfaces. J. Appl. Phys., 52(4):2897–908, 1981.

    Article  Google Scholar 

  5. S. K. Banerjee, D. J. Coleman, W. Richardson, and A. Shah. Leakage Mechanism in the Trench Transistor DRAM Cell. IEEE Trans. Electron Devices, ED-35(1):108–115, 1988.

    Article  Google Scholar 

  6. J. Bardeen. Tunneling from a Many-Particle Point of View. Phys. Rev. Lett., 6(2):57–62, 1961.

    Article  Google Scholar 

  7. G. Binnig, N. Garcia, H. Rohrer, J. M. Soler, and F. Flores. Electron-Metal-Surface Interaction Potential with Vacuum Tunneling: Observation of the Image Force. Phys. Rev. B, 30(8):4816–18, 1984.

    Article  Google Scholar 

  8. J. R. Chelikowsky and M. Schlüter. Electron States in α-Quartz: A Selfconsistent Pseu-dopotential Calculation. Phys. Rev. B, 15(8):4020–29, 1977.

    Article  Google Scholar 

  9. F. I. Dalidchik. Mnogofononije Tunnelnije Protzessi w Odnorodnom Elektritcheskom Polje. J. Eks. Theo. Fiz., 74:472–482, 1978.

    Google Scholar 

  10. F. I. Dalidchik. Resonance Tunneling for an Ordered Distribution of Scattering Centers. Soviet Physics Solid State, 25:1289–1291, 1983.

    Google Scholar 

  11. B. E. Deal, E. H. Snow, and C. A. Mead. Barrier Energies in Metal-Silicon Dioxide-Silicon Structures. J. Phys. Chem. Solids, 27:1873–79, 1966.

    Article  Google Scholar 

  12. M. Depas, B. Vermeire, P. W. Mertens, R. L. van Meirhaeghe, and M. M. Heyns. Determination of Tunneling Parameters in Ultra-Thin Oxide Layer Poly-Si/SiO2/Si Structures. Solid-State Electronics, 38(8): 1465–71, 1995.

    Article  Google Scholar 

  13. D. J. DiMaria and E. Cartier. Mechanism for Stress-Induced Leakage Currents in Thin Silicon Dioxide Films. J. Appl. Phys., 78(6):3883–94, 1995.

    Article  Google Scholar 

  14. D. J. DiMaria and D. R. Kerr. Interface Effects and High Conductivity in Oxides Grown from Polycrystalline Silicon. Appl. Phys. Lett., 27(9):505–07, 1975.

    Article  Google Scholar 

  15. M. Y. Doghish and F. D. Ho. A Comprehensive Analytical Model for Metal-Insulator-Semiconductor (MIS) Devices. IEEE Trans. Electron Devices, ED-39(12):2771–80, 1992.

    Article  Google Scholar 

  16. G. Dorda and M. Pulver. Tunnel Mechanism in MNOS Structures. phys. stat sol. (a), 1:71–79, 1970.

    Article  Google Scholar 

  17. P. V. Dressendorfer and R. C. Barker. Photoemission Measurements of Interface Barrier Energies for Tunnel Oxides on Silicon. Appl. Phys. Lett., 36(11):933–35, 1980.

    Article  Google Scholar 

  18. C. B. Duke and M. E. Alferieff. Field Emission Through Atoms Adsorbed on a Metal Surface. J. Chem. Phys., 46(3):923–943, 1967.

    Article  Google Scholar 

  19. M. V. Fischietti, S. E. Laux, and E. Crabbé. Understanding Hot-Electron Transport in Silicon Devices: Is There a Shortcut? J. Appl. Phys., 78(2): 1058–87, 1995.

    Article  Google Scholar 

  20. S. Fleischer, P. T. Lai, and Y. C. Cheng. Simplified Closed-Form Trap-Assisted Tunneling Model Applied to Nitrided Oxide Dielectric Capacitors. J. Appl. Phys., 72:5711–5715, 1992.

    Article  Google Scholar 

  21. R. H. Fowler and L. W. Nordheim. Electron Emission in Intense Electric Fields. Proc. Roy. Soc., A 119:173–81, 1928.

    Article  MATH  Google Scholar 

  22. W. Franz. Handbuch der Physik, Vol. 17 of Handbook on Semiconductors, ed. S. Flügge, p. 155. Springer, Berlin, 1956.

    Google Scholar 

  23. Y. Fu and M. Willander. Evanescent Channels in Calculation of Phonon-Assisted Tunneling Spectrum of a Semiconductor Tunneling Structure. J. Appl. Phys., 73(4): 1848–1852, 1993.

    Article  Google Scholar 

  24. J. W. Gadzuk. Resonance Tunneling Through Impurity States in Metal-Insulator-Metal Junctions. J. Appl. Phys., 41(1):286–291, 1970.

    Article  Google Scholar 

  25. M. A. Green, F. D. King, and J. Shewchun. Minority Carrier MIS Tunnel Diodes and their Application to Electron-and Photo-Voltaic Energy Conservation-I. Theory. Solid-State Electronics, 17:551–61, 1974.

    Article  Google Scholar 

  26. B. Gu, M. Mangiantini, and C. Coluzza. Analysis of Mechanism for Resonant Tunneling via Localized States in Thin SiO2-Films. J. Appl. Phys., 64(12):6867–70, 1988.

    Article  Google Scholar 

  27. K. H. Gundlach. Zur Berechnung des Tunnelstroms durch eine trapezförmige Potentialstufe. Solid-State Electronics, 9:949–57, 1966.

    Article  Google Scholar 

  28. W. A. Harrison. Tunneling from an Independent-Particle Point of View. Phys. Rev., 123(1):85–89, 1961.

    Article  Google Scholar 

  29. A. Hartstein and Z. A. Weinberg. On the Nature of the Image Force in Quantum Mechanics with Application to Photon Assisted Tunneling and Photoemission. J. Phys. C., 11:L469–73, 1978.

    Article  Google Scholar 

  30. A. Hartstein and Z. A. Weinberg. Unified Theory of Internal Photoemission and Photon-Assisted Tunneling. Phys. Rev. B, 20(4): 1335–38, 1979.

    Article  Google Scholar 

  31. A. Hartstein, Z. A. Weinberg, and D. J. DiMaria. Experimental Test of the Quantum-Mechanical Image-Force Theory. Phys. Rev. B, 25(12):7174–82, 1982.

    Article  Google Scholar 

  32. S. Heike, Y. Wada, S. Kondo, and M. Lutwyche. Evaluation of Thin SiO2 Layers by Beam Assisted Scanning Tunneling Microscope. In Proc. Int. Conf. Sol. State Devices and Materials (Japan), 1994.

    Google Scholar 

  33. M. Herrmann and A. Schenk. Field and High-Temperature Dependence of the Long Term Charge Loss in Electrically Programable Read Only Memories — Measurements and Modeling. J. Appl. Phys., 77(9):4522–40, 1995.

    Article  Google Scholar 

  34. P. Hesto. The Nature of Electronic Conduction in Thin Insulating Layers. In G. Barbottin and A. Vapaille (eds.), Instabilities in Silicon Devices, Chapt. 5, pp. 265–314. Elsevier Science, North-Holland, Amsterdam, 1986.

    Google Scholar 

  35. M. Hiroshima, T. Yasaka, S. Miyazaki, and M. Hirose. Electron Tunneling through Ultra-Thin Gate Oxides Formed on Hydrogen-Terminated Si(100) Surfaces. In Proc. Int. Conf. Sol. State Devices and Materials, Makuhari, (Japan), 1993.

    Google Scholar 

  36. D. Hsu, M. Dsu, C. Tan, and Y. Y. Wang. Calculations of Resonant Tunneling Levels Across Arbitrary Potential Barriers. J. Appl. Phys., 72(10):4972–74, 1992.

    Article  Google Scholar 

  37. N. Hwang, Burnette S. S. Or, and L. Forbes. Tunneling and Thermal Emission of Electrons from a Distribution of Dep Traps in SiO2. IEEE Trans. Electron Devices, ED-40(6):1100–03, 1993.

    Article  Google Scholar 

  38. ISE Integrated Systems Engineering AG, Zurich, Switzerland. DESSIS 3.0: Manual, 1996.

    Google Scholar 

  39. G. Jin, R. W. Dutton, Y.-J. Park, and H.-S. Min. An Isotropic Two Band Model for the Hot Electron Transport in Silicon: Including Electron Emission Probability into SiO2. J. Appl. Phys., 78(5):3174–84, 1995.

    Article  Google Scholar 

  40. M. Jonson. Tunneling times in quantum mechanical tunneling. In D. K. Ferry and C. Jacoboni (eds.), Quantum Transport in Semiconductors, pp. 193–239. Plenum Press, New York, 1992.

    Google Scholar 

  41. L. V. Keldysh. Behavior of Non-metallic Crystals in Strong Electric Fields. Soviet Physics JETP, 6(4):763–770, 1958.

    Google Scholar 

  42. L. V. Keldysh. Influence of the Lattice Vibrations of a Crystal on the Production of Electron-Hole Pairs in a Strong Electric Field. Soviet Physics JETP, 7(4):665–669, 1958.

    Google Scholar 

  43. Q. D. M. Khosru, N. Yasuda, K. Taniguchi, and C. Hamaguchi. Generation and Relaxation Phenomena of Positive Charge and Interface Trap in a Metal-Oxide-Semiconductor Structure. J. Appl. Phys., 77(9):4494–4503, 1995.

    Article  Google Scholar 

  44. M. Kleefstra and G. C. Herman. Influence of the Image Force on the Band Gap in Semiconductors and Insulators. J. Appl. Phys., 51(9):4923–26, 1980.

    Article  Google Scholar 

  45. K. Kobayashi, A. Teramoto, M. Hirayama, and Y. Fujita. Model for the Substrate Hole Current Based on Thermionic Hole Emission from the Anode During Fowler-Nordheim Electron Tunneling in n-Channel Metal-Oxide-Semiconductor Field-Effect Transistors. J. Appl. Phys., 77(7):3277–82, 1995.

    Article  Google Scholar 

  46. G. Krieger and R. M. Swanson. Fowler-Nordheim Electron Tunneling in Thin Si-SiO2-Al Structures. J. Appl. Phys., 52(9):5710–17, 1981.

    Article  Google Scholar 

  47. A. Kriveris, S. Kudzmauskas, and P. Pipinys. Release of Electrons from Traps by an Electric Field with Phonon Participation. phys. stat. sol. (a), 37:321–327, 1976.

    Article  Google Scholar 

  48. M. Lenzlinger and E. H. Snow. Fowler-Nordheim Tunneling into Thermally Grown SiO2. J. Appl. Phys., 40:278–283, 1969.

    Article  Google Scholar 

  49. W. W. Lui and M. Fukuma. Exact Solution of the Schrödinger Equation Across an Arbitrary One-dimensional Piecewise-linear Potential Barrier. J. Appl. Phys., 60(5): 1555–1559, 1986.

    Article  Google Scholar 

  50. B. Majkusiak and A. Strojwas. Influence of Oxide Thickness Nonuniformities on the Tunnel Current-Voltage and Capacitance-Voltage Characteristics of the Metal-Oxide-Semiconductor System. J. Appl. Phys., 74(9):5638–47, 1993.

    Article  Google Scholar 

  51. J. Maserjian. Tunneling in Thin MOS Structures. J. Vac. Sci. Techn., 11(6):996–1003, 1974.

    Google Scholar 

  52. M. Matsuda, K. Watanabe, M. Yasutake, and T. Hattori. Electron Tunneling through Chemical Oxide of Silicon. In Proc. Int. Conf. Sol. State Devices and Materials (Japan), 1995.

    Google Scholar 

  53. H. S. Momose, M. Ono, T. Yoshitomi, T. Ohguro, S. Nakamura, M. Saito, and H. Iwai. 1.5 nm Direct-Tunneling Gate Oxide Si MOSFET’s. IEEE Trans. Electron Devices, 43(8): 1233–41, 1996.

    Article  Google Scholar 

  54. S. Nagano, M. Tsukiji, K. Ando, E. Hasegawa, and A. Ishitani. Mechanism of Leakage Current through the Nano Scale SiO2 Layer. J. Appl. Phys., 75(7):3530–3535, 1994.

    Article  Google Scholar 

  55. T. H. Ning. Hot-Electron Emission from Silicon into Silicon Dioxide. Solid-State Electronics, 21:273–82, 1978.

    Article  Google Scholar 

  56. L. W. Nordheim. The Effect of the Image Force on the Emission and Reflexion of Electrons by Metals. Proc. Roy. Soc., A 121:626–39, 1928.

    Article  MATH  Google Scholar 

  57. H. Nozawa and S. Kohoyama. Thermionic Electron Emission Model for Charge Retention in SAMOS Structures. Jap. J. Appl. Phys., 21:111–112, 1982.

    Article  Google Scholar 

  58. C. S. Pan, K. Wu, D. Chin, G. Sery, and J. Kiely. High-Temperature Charge Loss Mechanism in a Floating-Gate EPROM with an Oxide-Nitride-Oxide (ONO) Interpoly Stacked Dielectric. IEEE Electron Device Letters, 12(9):506–509, 1991.

    Article  Google Scholar 

  59. C. S. Pan, K. Wu, and G. Sery. Physical Origin of Long-Term Charge Loss Mechanism in a Floating-Gate EPROM with an Oxide-Nitride-Oxide Interpoly Stacked Dielectric. IEEE Electron Device Letters, 12(2):51–53, 1991.

    Article  Google Scholar 

  60. G. H. Parker and C. A. Mead. The Effect of Trapping States on Tunneling in Metal-Semiconductor Junctions. Appl. Phys. Lett., 14(1):21–23, 1969.

    Article  Google Scholar 

  61. J. C. Penley. Tunneling through Thin Films with Traps. Phys. Rev., 128(2):596–602, 1962.

    Article  MATH  Google Scholar 

  62. W. Pötz. Self-consistent Model of Transport in Quantum Well Tunneling Structures. J. Appl. Phys., 66(6):2458–66, 1989.

    Article  Google Scholar 

  63. P. J. Price and J. M. Radcliffe. Esaki Tunneling. IBM Journal, Oct.:364–371, 1959.

    Google Scholar 

  64. A. Puri and W. L. Schaich. Comparison of Image-Potential Theories. Phys. Rev B, 28(4): 1781–84, 1983.

    Article  Google Scholar 

  65. B. Ricco, M. Ya. Azbel, and M. H. Brodsky. Novel Mechanism for Tunneling and Breakdown of Thin SiO2 Films. Phys. Rev. Lett., 51(19): 1795–98, 1983.

    Article  Google Scholar 

  66. A. Schenk. A Model for the Field and Temperature Dependence of Shockley-Read-Hall Lifetimes in Silicon. Solid-State Electronics, 35(11): 1585–96, 1992.

    Article  Google Scholar 

  67. P. A. Serena, J. M. Soler, and N. Garcia. Self-Consistent Image Potential in a Metal Surface. Phys. Rev., B 34(10):6767–69, 1986.

    Google Scholar 

  68. R. B. Sethi, U. S. Kim, I. Johnson, P. Cacharelis, and M. Manley. Electron Barrier Height Change and its Influence on EEPROM Cells. IEEE Electron Device Letters, 13(5):244–46, 1992.

    Article  Google Scholar 

  69. J. Shewchun, R. Singh, and M. A. Green. Theory of Metal-Insulator-Semiconductor Solar Cells. J. Appl. Phys., 48(2):765–70, 1977.

    Article  Google Scholar 

  70. R. E. Shiner, J. M. Caywood, and B. L. Euzent. Data Retention in EPROMs. Int. Reliability Physics Symposium, pp. 238–243, 1980.

    Google Scholar 

  71. J. G. Simmons. Richardson-Schottky Effect in Solids. Phys. Rev. Lett., 15:967–968,1965.

    Article  Google Scholar 

  72. A. Spitzer and R. Baunach. The Physics of ONO Layer Dielectrics. In Applied Surface Science, Vol. 39, pp. 192–199. Elsevier Science, North-Holland, Amsterdam, 1989.

    Google Scholar 

  73. F. Stern. Image Potential near a Gradual Interface between two Dielectrics. Phys. Rev. B, 17(12):5009–15, 1978.

    Article  Google Scholar 

  74. R. Stratton. Volt-Current Characteristics for Tunneling through Insulating Films. J. Phys. Chem. Solids, 23:1177–1190, 1962.

    Article  Google Scholar 

  75. E. Suzuki, D. K. Schroder, and Y. Hayashi. Carrier Conduction in Ultrathin Nitrided Oxide Films. J. Appl. Phys., 60(10):3616–3621, 1986.

    Article  Google Scholar 

  76. C. M. Svensson and I. K. Lundström. Trap-Assisted Charge Injection in MNOS Structures. J. Appl. Phys., 44:4657–4663, 1973.

    Article  Google Scholar 

  77. S. M. Sze. Physics of Semiconductor Devices, 2nd ed. John Wiley and Sons, New York, 1981.

    Google Scholar 

  78. V. A. K. Temple, M. A. Green, and J. Shewchun. Equilibrium-to-Nonequilibrium Transition in MOS (Surface Oxide) Tunnel Diode. J. Appl. Phys., 45(11):4934–43, 1974.

    Article  Google Scholar 

  79. Z. A. Weinberg. Tunneling of Electrons from Si into Thermally Grown SiO2. Solid-State Electronics, 22:11–18, 1977.

    Article  Google Scholar 

  80. Z. A. Weinberg. On Tunneling in Metal-Oxide Silicon Structures. J. Appl. Phys., 53(7):5052–56, 1982.

    Article  Google Scholar 

  81. Z. A. Weinberg and A. Hartstein. Photon Assisted Tunneling from Aluminium into Silicon Dioxide. Solid State Comm., 20:179–82, 1976.

    Article  Google Scholar 

  82. Z. A. Weinberg and A. Hartstein. Effect of Silicon Orientation and Hydrogen Anneal on Tunneling from Si to SiO2. J. Appl. Phys., 54(5):2517–21, 1983.

    Article  Google Scholar 

  83. N. Yasuda, N. Patel, and A. Toriumi. A Two-Step Tunneling Model for the Stress Induced Leakage Current in Thin Silicon Dioxide Films. In Ext. Abstracts Solid State Devices and Materials SSDM, pp. 847–849, Chiba, Japan, 1993.

    Google Scholar 

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  1. Institut für Integrierte Systeme, ETH Zürich, Schweiz

    Priv.-Doz. Dr. rer. nat. Andreas Schenk

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Schenk, A. (1998). Modeling Transport Across Thin Dielectric Barriers. In: Advanced Physical Models for Silicon Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6494-5_5

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  • DOI: https://doi.org/10.1007/978-3-7091-6494-5_5

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