Tunneling through ultrathin SiO2 gate oxides from microscopic models

We investigate theoretically coherent electron tunneling through three-dimensional microscopic Si[100]/SiO2/Si[100] model junctions with oxide thicknesses between 0.4 and 4.6 nm. The transmission probabilities of these structures were calculated using a semiempirical tight-binding scattering method. Our calculations provide a basis for the microscopic understanding of the observed independence of tunneling transmission on the orientation of the bulk silicon and on the nature of inelastic defect-assisted tunneling. We document significant differences between transmission coefficients obtained with the present scheme and with the popular effective-mass-based approaches. The energy dependence of the effective tunneling mass in bulk silicon dioxide is predicted.

[1]  Structure and energetics of the Si- SiO2 interface , 1999, Physical review letters.

[2]  García,et al.  Self-consistent image potential in a metal surface. , 1986, Physical review. B, Condensed matter.

[3]  D. Vanderbilt,et al.  Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. , 1990, Physical review. B, Condensed matter.

[4]  R. L. Meirhaeghe,et al.  Tunnel oxides grown by rapid thermal oxidation , 1993 .

[5]  W. Mizubayashi,et al.  Analysis of Tunnel Current through Ultrathin Gate Oxides , 1998 .

[6]  Yu,et al.  Multiband treatment of quantum transport in interband tunnel devices. , 1992, Physical review. B, Condensed matter.

[7]  Andreas Schenk,et al.  Modeling and simulation of tunneling through ultra-thin gate dielectrics , 1997 .

[8]  Kevin J. Yang,et al.  Analytic model for direct tunneling current in polycrystalline silicon-gate metal–oxide–semiconductor devices , 1999 .

[9]  M. Nakayama,et al.  Effective-mass approximation in the presence of an interface , 1979 .

[10]  G. Klimeck,et al.  Physical oxide thickness extraction and verification using quantum mechanical simulation , 1997, International Electron Devices Meeting. IEDM Technical Digest.

[11]  H. Iwai,et al.  1.5 nm direct-tunneling gate oxide Si MOSFET's , 1996 .

[12]  Alexander A. Demkov,et al.  Growth Study and Theoretical Investigation of the Ultrathin Oxide SiO 2 − Si Heterojunction , 1999 .

[13]  S. Tiwari,et al.  Self‐consistent modeling of accumulation layers and tunneling currents through very thin oxides , 1996 .

[14]  P. Dollfus,et al.  STUDY OF DIRECT TUNNELING THROUGH ULTRATHIN GATE OXIDE OF FIELD EFFECT TRANSISTORS USING MONTE CARLO SIMULATION , 1999 .

[15]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[16]  Elyse Rosenbaum,et al.  Mechanism of stress-induced leakage current in MOS capacitors , 1997 .

[17]  Ih-Chin Chen,et al.  Electrical breakdown in thin gate and tunneling oxides , 1985 .

[18]  Yuji Ando,et al.  Calculation of transmission tunneling current across arbitrary potential barriers , 1987 .

[19]  M. Schlüter,et al.  Electron states in α-quartz: A self-consistent pseudopotential calculation , 1977 .

[20]  Miyamoto,et al.  Atomic and electronic structures of an interface between silicon and beta -cristobalite. , 1990, Physical review. B, Condensed matter.

[21]  Pantelides,et al.  Bonding arrangements at the Si-SiO2 and SiC-SiO2 interfaces and a possible origin of their contrasting properties , 2000, Physical review letters.

[22]  Boykin.  Tunneling calculations for systems with singular coupling matrices: Results for a simple model. , 1996, Physical review. B, Condensed matter.

[23]  A. Hartstein,et al.  Effect of silicon orientation and hydrogen anneal on tunneling from Si into SiO2 , 1983 .

[24]  S. Laux,et al.  Understanding hot‐electron transport in silicon devices: Is there a shortcut? , 1995 .

[25]  Carlo Jacoboni,et al.  Quantum Transport in Semiconductors , 1992 .

[26]  B. Brar,et al.  Direct extraction of the electron tunneling effective mass in ultrathin SiO2 , 1996 .

[27]  Andreas Schenk,et al.  Field and high‐temperature dependence of the long term charge loss in erasable programmable read only memories: Measurements and modeling , 1995 .

[28]  J. Lambe,et al.  Tunneling in Solids , 1973 .

[29]  Akira Toriumi,et al.  Stress‐induced leakage current in ultrathin SiO2 films , 1994 .

[30]  Gianfranco Pacchioni,et al.  On the origin of the 5.0 and 7.6 eV absorption bands in oxygen deficient α-quartz and amorphous silica. A first principles quantum-chemical study , 1997 .

[31]  M. Lenzlinger,et al.  Fowler‐Nordheim Tunneling into Thermally Grown SiO2 , 1969 .

[32]  G. E. Pikus,et al.  Superlattices and Other Heterostructures , 1995 .

[33]  Shinichi Takagi,et al.  Experimental evidence of inelastic tunneling in stress-induced leakage current , 1999 .

[34]  Eugene A. Irene,et al.  Thickness and effective electron mass measurements for thin silicon dioxide films using tunneling current oscillations , 1995 .

[35]  Marvin L. Cohen,et al.  Electronic structure of solids , 1984 .

[36]  G. Kresse,et al.  Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .

[37]  D. Ting,et al.  An embedded quantum wire model of dielectric breakdown , 1999 .

[38]  R. M. Swanson,et al.  Electron tunneling in Si‐SiO2‐Al structures: A comparison between 〈100〉 oriented and 〈111〉 oriented Si , 1981 .

[39]  D. Newns,et al.  Image force effects and the dielectric response of SiO2 in electron transport across metal–oxide–semiconductor structures , 1997 .

[40]  Georg Kresse,et al.  Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements , 1994 .

[41]  E. Cartier,et al.  MECHANISM FOR STRESS-INDUCED LEAKAGE CURRENTS IN THIN SILICON DIOXIDE FILMS , 1995 .

[42]  M. Scheffler,et al.  Proceedings of the 23rd International Conference on THE PHYSICS OF SEMICONDUCTORS , 1996 .

[43]  Tierney,et al.  Ballistic electron transport in thin silicon dioxide films. , 1987, Physical review. B, Condensed matter.

[44]  Ziqin,et al.  Random successive growth model for pattern formation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[45]  Yia-Chung Chang,et al.  Complex band structures of crystalline solids: An eigenvalue method , 1982 .

[46]  John B. Pendry,et al.  Quasi-extended electron states in strongly disordered systems , 1987 .

[47]  Y. Taur,et al.  Quantum-mechanical modeling of electron tunneling current from the inversion layer of ultra-thin-oxide nMOSFET's , 1997, IEEE Electron Device Letters.

[48]  J. Maserjian,et al.  Observation of positively charged state generation near the Si/SiO2 interface during Fowler–Nordheim tunneling , 1982 .

[49]  Z. Weinberg,et al.  Tunneling of electrons from Si into thermally grown SiO2 , 1977 .

[50]  Alfredo Pasquarello,et al.  Structurally relaxed models of the Si(001)-SiO2 interface , 1996 .

[51]  Theoretical insights into CoSi2/CaF2 tunneling diodes , 1999 .

[52]  V. Ryzhii,et al.  Semiclassical interband tunnelling probability in semiconductor heterostructures , 1994 .

[53]  Robert M. Wallace,et al.  Evaluating the minimum thickness of gate oxide on silicon using first-principles method , 1998 .

[54]  Alfredo Pasquarello,et al.  Interface structure between silicon and its oxide by first-principles molecular dynamics , 1998, Nature.

[55]  Tadahiro Ohmi,et al.  Conduction mechanism and origin of stress‐induced leakage current in thin silicon dioxide films , 1996 .

[56]  S. Zafar,et al.  Study of tunneling current oscillation dependence on SiO2 thickness and Si roughness at the Si/SiO2 interface , 1995 .

[57]  S. Kumashiro,et al.  Oxygen vacancy with large lattice distortion as an origin of leakage currents in SiO/sub 2/ , 1997, International Electron Devices Meeting. IEDM Technical Digest.

[58]  Seiichi Miyazaki,et al.  Quantitative Analysis of Tunneling Current through Ultrathin Gate Oxides , 1995 .

[59]  T. M. Kalotas,et al.  A new approach to one‐dimensional scattering , 1991 .

[60]  H. Juretschke,et al.  Introduction to Solid-State Theory , 1978 .

[61]  J. C. Slater,et al.  Simplified LCAO Method for the Periodic Potential Problem , 1954 .

[62]  M. De.  Handbuch der Physik , 1957 .

[63]  Z. Weinberg,et al.  On tunneling in metal‐oxide‐silicon structures , 1982 .

[64]  L. Register,et al.  Tight-binding investigation of electron tunneling through ultrathin SiO2gate oxides , 2000 .

[65]  T. Morimoto,et al.  Study of the manufacturing feasibility of 1.5-nm direct-tunneling gate oxide MOSFETs: uniformity, reliability, and dopant penetration of the gate oxide , 1998 .

[66]  Peter J. Price,et al.  Anisotropic Conduction in Solids Near Surfaces , 1960, IBM J. Res. Dev..

[67]  D. Muller,et al.  The electronic structure at the atomic scale of ultrathin gate oxides , 1999, Nature.

[68]  Hafner,et al.  Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium. , 1994, Physical review. B, Condensed matter.

[69]  J. Stathis,et al.  HYDROGEN ELECTROCHEMISTRY AND STRESS-INDUCED LEAKAGE CURRENT IN SILICA , 1999 .

[70]  E. Cartier,et al.  Determination of the energy-dependent conduction band mass in SiO2 , 1999 .

[71]  T. H. DiStefano,et al.  Electron tunneling at Al‐SiO2 interfaces , 1981 .

[72]  D. Eastman,et al.  The band edge of amorphous SiO2 by photoinjection and photoconductivity measurements , 1971 .

[73]  H. Kroemer,et al.  Interface connection rules for effective-mass wave functions at an abrupt heterojunction between two different semiconductors , 1983 .

[74]  R. Dreizler,et al.  Density-Functional Theory , 1990 .

[75]  J. Maserjian,et al.  Oscillations in MOS tunneling , 1975 .

[76]  U. Kunze,et al.  Tunnel spectroscopy of subband structure in n-inversion layers on (111) and (100) Si surfaces , 1982 .

[77]  C. Hu,et al.  Stress-induced current in thin silicon dioxide films , 1992, 1992 International Technical Digest on Electron Devices Meeting.

[78]  Jacek A. Majewski,et al.  Exact exchange Kohn-Sham formalism applied to semiconductors , 1999 .