Bibliography

[1]   D. K. Schroder and J. A. Babcock, “Negative bias temperature instability: Road to cross in deep submicron silicon semiconductor manufacturing,” J.Appl.Phys., vol. 94, no. 1, pp. 1–18, 2003.

[2]   D. K. Schroder, “Negative bias temperature instability: What do we understand?,” Microelectronics Reliability, vol. 47, pp. 841–852, 2007.

[3]   A. Goetzberger and H. Nigh, “Surface charge after annealing of Al-SiO2-Si structures under bias,” Proc.IEEE, vol. 54, no. 10, pp. 1454–1454, 1966.

[4]   Y. Miura and Y. Matukura, “Investigation of silicon-silicon dioxide interface using MOS structure,” Jap.J.Appl.Phys., vol. 5, p. 180, 1966.

[5]   G. Groeseneken, R. Degraeve, B. Kaczer, and K. Martens, “Trends and perspectives for electrical characterization and reliability assessment in advanced CMOS technologies,” in Proc. ESSDERC, pp. 64–72, 2010.

[6]   A. Kerber and W. McMahon, “Front end of line (FEOL) reliability in CMOS technologies,” in IEEE Int. Reliab. Phys. Symp. Tutorial Notes, 2012.

[7]   K. Jeppson and C. Svensson, “Negative bias stress of MOS devices at high electric fields and degradation of MNOS devices,” J.Appl.Phys., vol. 48, no. 5, pp. 2004–2014, 1977.

[8]   H. Kufluoglu and M. Alam, “Theory of interface-trap-induced NBTI degradation for reduced cross section MOSFETs,” IEEE Trans.Electron Devices, vol. 53, pp. 1120 – 1130, May 2006.

[9]   T. Grasser, W. Goes, and B. Kaczer, “Dispersive transport and negative bias temperature instability: Boundary conditions, initial conditions, and transport models,” IEEE Trans.Device and Materials Reliability, vol. 8, pp. 79 –97, March 2008.

[10]   S. Ogawa and N. Shiono, “Generalized diffusion-reaction model for the low-field charge build up instability at the Si/SiO2 interface,” Physical Review B, vol. 51, no. 7, pp. 4218–4230, 1995.

[11]   B. Kaczer, V. Arkhipov, R. Degraeve, N. Collaert, G. Groeseneken, and M. Goodwin, “Disorder-controlled-kinetics model for negative bias temperature instability and its experimental verification,” in Proc. Intl.Rel.Phys.Symp., pp. 381–387, 2005.

[12]   H. Reisinger, O. Blank, W. Heinrigs, A. Mühlhoff, W. Gustin, and C. Schlünder, “Analysis of NBTI degradation- and recovery-behavior based on ultra fast V th-measurements,” in Proc. Intl.Rel.Phys.Symp., pp. 448–453, 2006.

[13]   T. Grasser, W. Goes, V. Sverdlov, and B. Kaczer, “The universality of NBTI relaxation and its implications for modeling and characterization,” in Proc. Intl.Rel.Phys.Symp., pp. 268 –280, April 2007.

[14]   T. Grasser, B. Kaczer, W. Gös, H. Reisinger, T. Aichinger, P. Hehenberger, P.-J. Wagner, F. Schanovsky, J. Franco, P. J. Roussel, and M. Nelhiebel, “Recent advances in understanding the bias temperature instability,” in Proc. Intl.Electron Devices Meeting, pp. 82 – 85, 2010.

[15]   S. Mahapatra, V. D. Maheta, A. E. Islam, and M. A. Alam, “Isolation of NBTI stress generated interface trap and hole-trapping components in PNO p-MOSFETs,” IEEE Trans.Electron Devices, vol. 56, pp. 236–242, Feb. 2009.

[16]   S. Mahapatra, A. Islam, S. Deora, V. Maheta, K. Joshi, A. Jain, and M. Alam, “A critical re-evaluation of the usefulness of R-D framework in predicting NBTI stress and recovery,” in Proc. Intl.Rel.Phys.Symp., pp. 6A.3.1 –6A.3.10, April 2011.

[17]   S. Mahapatra, A. Islam, S. Deora, V. Maheta, K. Joshi, and M. Alam, “Characterization and modeling of NBTI stress, recovery, material dependence and AC degradation using R-D framework,” in Proc. Intl.Symp. on Physical and Failure Analysis of Integrated Circuits, pp. 1–7, July 2011.

[18]   K. Joshi, S. Mukhopadhyay, N. Goel, and S. Mahapatra, “A consistent physical framework for N and P BTI in HKMG MOSFETs,” in Proc. Intl.Rel.Phys.Symp., pp. 5A.3.1–10, 2012.

[19]   A. Islam, H. Kufluoglu, D. Varghese, S. Mahapatra, and M. Alam, “Recent issues in negative-bias temperature instability: Initial degradation, field dependence of interface trap generation, hole trapping effects, and relaxation,” IEEE Trans.Electron Devices, vol. 54, pp. 2143 –2154, Sept. 2007.

[20]   A. E. Islam, H. Kufluoglu, D. Varghese, and M. A. Alam, “Critical analysis of short-term negative bias temperature instability measurements: Explaining the effect of time-zero delay for on-the-fly measurements,” Appl.Phys.Lett., vol. 90, no. 8, p. 083505, 2007.

[21]   H. Kufluoglu and M. Alam, “A generalized reaction-diffusion model with explicit H-H2 dynamics for negative-bias temperature-instability (NBTI) degradation,” IEEE Trans.Electron Devices, vol. 54, pp. 1101 – 1107, May 2007.

[22]   A. Islam, H. Kufluoglu, D. Varghese, and M. Alam, “Temperature dependence of the negative bias temperature instability in the framework of dispersive transport,” Appl.Phys.Lett., vol. 90, no. 1, pp. 083505–1–083505–3, 2007.

[23]   A. Islam and M. Alam, “Analyzing the distribution of threshold voltage degradation in nanoscale transistors by using reaction-diffusion and percolation theory,” J.Comp.Elect., pp. 1–11, 2011. 10.1007/s10825-011-0369-4.

[24]   F. Schanovsky and T. Grasser, “On the microscopic limit of the reaction-diffusion model for negative bias temperature instability,” in Proc. Intl.Integrated Reliability Workshop, pp. 17–21, 2011.

[25]   F. Schanovsky and T. Grasser, “On the microscopic limit of the modified reaction-diffusion model for negative bias temperature instability,” in Proc. Intl.Rel.Phys.Symp., pp. XT.10.1–6, 2012.

[26]    T. Grasser, B. Kaczer, W. Goes, T. Aichinger, P. Hehenberger, and M. Nelhiebel, “A two-stage model for negative bias temperature instability,” in Proc. Intl.Rel.Phys.Symp., pp. 33–44, 2009.

[27]   T. Grasser, B. Kaczer, and W. Gös, “An energy-level perspective of bias temperature instability,” in Proc. Intl.Rel.Phys.Symp., pp. 28–38, 2008.

[28]   T. Grasser, W. Gös, and B. Kaczer, “Modeling bias temperature instability during stress and recovery,” in Proc. Simu.Semicond.Proc.Dev., pp. 65–68, 2008.

[29]   T. Grasser, B. Kaczer, T. Aichinger, W. Gös, and M. Nelhiebel, “Defect creation stimulated by thermally activated hole trapping as the driving force behind negative bias temperature instability in SiO2, SiON and high-k gate stacks,” in Proc. Intl.Integrated Reliability Workshop, pp. 91–95, 2008.

[30]   A. Lelis and T. Oldham, “Time dependence of switching oxide traps,” IEEE Trans.Nucl.Science, vol. 41, pp. 1835 –1843, dec. 1994.

[31]   T. Grasser, H. Reisinger, P. Wagner, and B. Kaczer, “Time-dependent defect spectroscopy for characterization of border traps in metal-oxide-semiconductor transistors,” Physical Review B, vol. 82, pp. 245318–1, 2010.

[32]   T. Grasser, H. Reisinger, P.-J. Wagner, and B. Kaczer, “The time dependent defect spectroscopy (TDDS) for the characterization of the bias temperature instability,” in Proc. Intl.Rel.Phys.Symp., pp. 16–25, 2010.

[33]   M. Toledano-Luque, B. Kaczer, P. J. Roussel, M. Cho, T. Grasser, and G. Groeseneken, “Temperature dependence of the emission and capture times of SiON individual traps after positive bias temperature stress,” J.Vac.Sci.Technol.B, vol. 29, pp. 01AA04–1 – 01AA04–5, 2011.

[34]   M. Kirton and M. Uren, “Capture and emission kinetics of individual Si:SiO2 interface states,” Appl.Phys.Lett., vol. 48, pp. 1270–1272, 1986.

[35]   D. Fleetwood, H. Xiong, Z.-Y. Lu, C. Nicklaw, J. Felix, R. Schrimpf, and S. Pantelides, “Unified model of hole trapping, 1/f noise, and thermally stimulated current in mos devices,” IEEE Trans.Nucl.Sci., vol. 49, no. 6, pp. 2674–2683, 2002.

[36]   P. Wagner, T. Aichinger, T. Grasser, M. Nelhiebel, and L. Vandamme, “Possible correlation between flicker noise and bias temperature stress,” in Proc. Int. Conf. on Noise and Fluctuations, pp. 621 – 624, 2009.

[37]   T. Grasser, “Stochastic charge trapping in oxides: From random telegraph noise to bias temperature instabilities,” Microelectronics Reliability, vol. 52, no. 1, pp. 39 – 70, 2012.

[38]   P. M. Lenahan and J. J. F. Conley, “What can electron paramagnetic resonance tell us about the Si/SiO2 system?,” J.Vac.Sci.Technol.B, vol. 16, no. 4, pp. 2134–2153, 1998.

[39]   C. R. Helms and E. H. Poindexter, “The silicon-silicon dioxide system: Its microstructure and imperfections,” Rep.Prog.Phys., vol. 57, no. 8, p. 791, 1994.

[40]   S. P. Karna, H. A. Kurtz, A. C. Pineda, W. M. Shedd, and R. D. Pugh, Point Defects in Si-SiO2 systems: Current Understanding, pp. 699–615. Kluwer Academic Publishers, 2000.

[41]   P. M. Lenahan, Defects in Microelectronic Materials and Devices, ch. Dominating Defects in the MOS System Pb and ECenters, pp. 163–214. CRC Press, 2009.

[42]   J. Ryan, P. Lenahan, T. Grasser, and H. Enichlmair, “Recovery-free electron spin resonance observations of NBTI degradation,” in Proc. Intl.Rel.Phys.Symp., pp. 43–49, 2010.

[43]   P. M. Lenahan and P. V. Dressendorfer, “An electron spin resonance study of radiation-induced electrically active paramagnetic centers at the Si/SiO2 interface,” J.Appl.Phys., vol. 54, no. 3, pp. 1457–1460, 1983.

[44]   E. H. Poindexter, G. J. Gerardi, M.-E. Rueckel, P. J. Caplan, N. M. Johnson, and D. K. Biegelsen, “Electronic traps and Pb centers at the Si/SiO2 interface: Band-gap energy distribution,” Journal of Applied Physics, vol. 56, no. 10, pp. 2844–2849, 1984.

[45]   A. Stesmans, B. Nouwen, and V. V. Afanas’ev, “Pb1 interface defect in thermal (100)SiSiO2 : 29Si hyperfine interaction,” Phys. Rev. B, vol. 58, pp. 15801–15809, Dec 1998.

[46]   P. Lenahan and J. Conley, J.R., “A comprehensive physically based predictive model for radiation damage in MOS systems,” IEEE Trans.Nucl.Science, vol. 45, pp. 2413 –2423, December 1998.

[47]   P. M. Lenahan and P. V. Dressendorfer, “Hole traps and trivalent silicon centers in metal/oxide/silicon devices,” J.Appl.Phys., vol. 55, no. 10, pp. 3495–3499, 1984.

[48]   P. M. Lenahan, W. L. Warren, D. T. Krick, P. V. Dressendorfer, and B. B. Triplett, “Interaction of molecular hydrogen with trapped hole Ecenters in irradiated and high field stressed metal/oxide/silicon oxides,” J.Appl.Phys., vol. 67, no. 12, pp. 7612–7614, 1990.

[49]   V. V. Afanas’ev, J. M. M. de Nijs, P. Balk, and A. Stesmans, “Degradation of the thermal oxide of the Si/SiO2/Al system due to vacuum ultraviolet irradiation,” J.Appl.Phys., vol. 78, no. 11, pp. 6481–6490, 1995.

[50]   E. H. Pointdexter and W. L. Warren, “Paramagnetic point defects in amorphous thin films of SiO2 and Si3N4: Updates and additions,” J.Electrochem.Soc., vol. 142, pp. 2508–2516, 1995.

[51]   P. E. Bunson, M. D. Ventra, S. T. Pantelides, D. M. Fleetwood, and R. D. Schrimpf, “Hydrogen-related defects in irradiated SiO2,” IEEE Trans.Nucl.Sci., vol. 47, pp. 2289–2296, 2000.

[52]   V. Afanas’ev and A. Stesmans, “Leakage currents induced in ultrathin oxides on (100)Si by deep-UV photons,” Mat.Sci.Eng.B, vol. 71, no. 1-3, pp. 56 – 61, 2000.

[53]   V. V. Afanas’ev and A. Stesmans, “Proton nature of radiation-induced positive charge in SiO2 layers on Si,” Eur.Phys.Lett., vol. 53, no. 2, p. 233, 2001.

[54]   K. L. Yip and W. B. Fowler, “Electronic structure of E’1 centers in SiO2,” Physical Review B, vol. 11, pp. 2327–2338, 1975.

[55]   E. P. O’Reilly and J. Robertson, “Theory of defects in vitreous silicon dioxide,” Physical Review B, vol. 27, pp. 3780–3795, Mar 1983.

[56]   J. K. Rudra, W. B. Fowler, and F. J. Feigl, “Model for the E’2 center in alpha quartz,” Physical Review Letters, vol. 55, pp. 2614–2617, 1985.

[57]   J. K. Rudra and W. B. Fowler, “Oxygen vacancy and the E1center in crystalline SiO2,” Physical Review B, vol. 35, no. 15, pp. 8223–8230, 1987.

[58]   M. Boero, A. Pasquarello, J. Sarnthein, and R. Car, “Structure and hyperfine parameters of E1 centers in α-quartz and in vitreous SiO2,” Physical Review Letters, vol. 78, pp. 887–890, Feb 1997.

[59]   P. E. Blöchl, “First-principles calculations of defects in oxygen-deficient silica exposed to hydrogen,” Physical Review B, vol. 62, pp. 6158–6178, September 2000.

[60]   T. Uchino, M. Takahashi, and T. Yoko, “E’ centers in amorphous SiO2 revisited: A new look at an old problem,” Physical Review Letters, vol. 86, pp. 5522–5525, 2001.

[61]   A. Stirling and A. Pasquarello, “First-principles modeling of paramagnetic Si dangling-bond defects in amorphous SiO2,” Physical Review B, vol. 66, p. 245201, Dec 2002.

[62]   D. J. Chadi, “Negative-U property of the oxygen vacancy defect in SiO2 and its implication for the E1 center in alpha-quartz,” Appl.Phys.Lett., vol. 83, no. 3, pp. 437–439, 2003.

[63]   M. Busso, S. Casassa, C. Pisani, and V. B. Sulimov, “Ab initio simulation of the oxygen vacancy bistability in pure and Ge-doped α-quartz,” Modelling and Simulation in Materials Science and Engineering, vol. 10, no. 1, p. 21, 2002.

[64]   Z.-Y. Lu, C. J. Nicklaw, D. M. Fleetwood, R. D. Schrimpf, and S. T. Pantelides, “Structure, properties, and dynamics of oxygen vacancies in amorphous SiO2,” Physical Review Letters, vol. 89, p. 285505, Dec 2002.

[65]   C. J. Nicklaw, Z.-Y. Lu, D. Fleetwood, R. Schrimpf, and S. Pantelides, “The structure, properties, and dynamics of oxygen vacancies in amorphous SiO2,” IEEE Trans.Nucl.Sci., vol. 49, pp. 2667–2673, 2002.

[66]   V. B. Sulimov, P. V. Sushko, A. H. Edwards, A. L. Shluger, and A. M. Stoneham, “Asymmetry and long-range character of lattice deformation by neutral oxygen vacancy in α-quartz,” Physical Review B, vol. 66, p. 024108, Jul 2002.

[67]   L. Martin-Samos, Y. Limoge, N. Richard, J. P. Crocombette, G. Roma, E. Anglada, and E. Artacho, “Oxygen neutral defects in silica: Origin of the dirstribution of the formation energies,” Eur.Phys.Lett., vol. 66, pp. 680–686, 2004.

[68]   S. Mukhopadhyay, P. V. Sushko, A. M. Stoneham, and A. L. Shluger, “Modeling of the structure and properties of oxygen vacancies in amorphous silica,” Physical Review B, vol. 70, p. 195203, Nov 2004.

[69]   S. Mukhopadhyay, P. V. Sushko, A. M. Stoneham, and A. L. Shluger, “Correlation between the atomic structure, formation energies, and optical absorption of neutral oxygen vacancies in amorphous silica,” Physical Review B, vol. 71, p. 235204, Jun 2005.

[70]   P. Sushko, S. Mukhopadhyay, A. Stoneham, and A. Shluger, “Oxygen vacancies in amorphous silica: structure and distribution of properties,” Microelectronic Engineering, vol. 80, no. 0, pp. 292 – 295, 2005.

[71]   P. V. Sushko, S. Mukhopadhyay, A. S. Mysovsky, V. B. Sulimov, A. Taga, and A. L. Shluger, “Structure and properties of defects in amorphous silica: new insights from embedded cluster calculations,” J.Phys.:Condensed Matter, vol. 17, no. 21, p. S2115, 2005.

[72]   A. Kimmel, P. Sushko, A. Shluger, and G. Bersuker, “Positive and negative oxygen vacancies in amorphous silica,” ECS Trans., vol. 19, pp. 3–17, 2009.

[73]   D. M. Fleetwood and J. H. Scofield, “Evidence that similar point defects cause 1/ f noise and radiation-induced-hole trapping in metal-oxide-semiconductor transistors,” Physical Review Letters, vol. 64, pp. 579–582, Jan 1990.

[74]   D. Fleetwood, “Fast and slow border traps in mos devices,” IEEE Trans.Nucl.Science, vol. 43, pp. 779 –786, jun 1996.

[75]   A. Yokozawa, A. Oshiyama, Y. Miyamoto, and S. Kumashiro, “Oxygen vacancy with large lattice distortion as an origin of leakage currents in SiO2,” in Proc. Intl.Electron Devices Meeting, pp. 703 –706, December 1997.

[76]   J. W. McPherson and H. C. Mogul, “Underlying physics of the thermochemical E model in describing low-field time-dependent dielectric breakdown in SiO2 thin films,” J.Appl.Phys., vol. 84, no. 3, pp. 1513–1523, 1998.

[77]   A. Edwards, P. Sushko, A. Shluger, and V. Sulimov, “Embedding techniques for irradiation-induced defects in crystalline SiO2,” in Radiation and Its Effects on Components and Systems, 2001. 6th European Conference on, pp. 98 – 104, sept. 2001.

[78]   S. Mukhopadhyay, P. V. Sushko, A. H. Edwards, and A. L. Shluger, “Calculation of relative concentrations of Ecentres in amorphous silica,” Journal of Non-Crystalline Solids, vol. 345-346, no. 0, pp. 703 – 709, 2004.

[79]   R. A. Weeks and M. Abraham, “Electron spin resonance of irradiated quartz: Atomic hydrogen,” J.Chem.Phys., vol. 42, no. 1, pp. 68–71, 1965.

[80]   E. H. Poindexter, “Chemical reactions of hydrogenous species in the SiSiO2 system,” Journal of Non-Crystalline Solids, vol. 187, no. 0, pp. 257 – 263, 1995.

[81]   E. Cartier and J. Stathis, “Atomic hydrogen-induced degradation of the SiSiO2 structure,” Microelectronic Engineering, vol. 28, no. 1-4, pp. 3 – 10, 1995.

[82]   M. Nelhiebel, J. Wissenwasser, T. Detzel, A. Timmerer, and E. Bertagnolli, “Hydrogen-related influence of the metallization stack on characteristics and reliability of a trench gate oxide,” Microelectronics Reliability, vol. 45, no. 9-11, pp. 1355 – 1359, 2005.

[83]   V. V. Afanas’ev and A. Stesmans, “H-complexed oxygen vacancy in SiO2: Energy level of a negatively charged state,” Appl.Phys.Lett., vol. 71, no. 26, pp. 3844–3846, 1997.

[84]   P. E. Blöchl and J. H. Stathis, “Hydrogen electrochemistry and stress-induced leakage current in silica,” Physical Review Letters, vol. 83, pp. 372–375, July 1999.

[85]   F. Schanovsky, W. Goes, and T. Grasser, “Multi-phonon hole-trapping from first principles,” J.Vac.Sci.Technol.B, vol. 29, pp. 01A201–1, 2011.

[86]   F. Schanovsky, W. Goes, and T. Grasser, “An advanced description of oxide traps in MOS transistors and its relation to DFT,” J.Comp.Elect., vol. 9, pp. 135–140, 2010.

[87]   B. Kaczer, T. Grasser, J. Martin-Martinez, E. Simoen, M. Aoulaiche, P. Roussel, and G. Groeseneken, “NBTI from the perspective of defect states with widely distributed time scales,” in Proc. Intl.Rel.Phys.Symp., pp. 55–60, 2009.

[88]   M. Born and R. Oppenheimer, “Zur quantentheorie der molekeln,” Ann.Phys., vol. 84, pp. 457–484, 1927.

[89]   J. J. Markham, “Electron-nuclear wave functions in multiphonon processes,” Physical Review, vol. 103, no. 3, pp. 588–597, 1956.

[90]   M. Born and K. Huang, Dynamical Theory of Crystal Lattices. Oxford University Press, 1954.

[91]   A. M. Stoneham, Theory of Defects in Solids. Oxford University Press, 1975.

[92]   M. Born, “Kopplung der Elektronen- und Kernbewegung in Molekeln und Kristallen,” Gött. Nachr. math. phys., 1951.

[93]   D. R. Hartree, “The wave mechanics of an atom with a non-coulomb central field. part I. theory and methods,” Proc. Cambridge Philosoph. Society, vol. 24, pp. 89–110, 1928.

[94]   D. R. Hartree, “The wave mechanics of an atom with a non-coulomb central field. part II. some results and discussion,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 24, pp. 111–132, 0 1928.

[95]   D. R. Hartree, “The wave mechanics of an atom with a non-coulomb central field. part III. term values and intensities in series in optical spectra,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 24, pp. 426–437, 6 1928.

[96]   R. M. Martin, Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press, 2004.

[97]   I. N. Levine, Quantum Chemistry. Person Prentice Hall, 2009.

[98]   C. Cohen-Tannoudji, B. Diu, and F. L. V. . 2, Quantenmechanik. deGruyter, 2009.

[99]   J. B. Foresman and A. Frisch, Exploring Chemistry with Electronic Structure Methods. Gaussian, Inc., 1996.

[100]   R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules. Oxford University Press, 1989.

[101]   J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, pp. 3865–3868, 1996.

[102]   R. M. Nieminen, Theory of Defects in Semiconductors, ch. Supercell Methods for Defect Calculations, pp. 29–67. Springer, 2010.

[103]   P. Deák, L. C. Snyder, R. K. Singh, and J. W. Corbett, “Evaluation of semiempirical quantum-chemical methods in solid-state applications. I. molecular-cluster calculations of defects in silicon,” Physical Review B, vol. 36, pp. 9612–9618, Dec 1987.

[104]   P. Deák and L. C. Snyder, “Evaluation of semiempirical quantum-chemical methods in solid-state applications. II. cyclic-cluster calculations of silicon,” Physical Review B, vol. 36, pp. 9619–9627, Dec 1987.

[105]   K. C. Snyder and W. B. Fowler, “Oxygen vacancy in α-quartz: A possible bi- and metastable defect,” Phys. Rev. B, vol. 48, pp. 13238–13243, Nov 1993.

[106]   D. E. Boucher and G. G. DeLeo, “Tight-binding quantum molecular-dynamics simulations of hydrogen in silicon,” Physical Review B, vol. 50, pp. 5247–5254, August 1994.

[107]   M. Tang, L. Colombo, J. Zhu, and T. Diaz de la Rubia, “Intrinsic point defects in crystalline silicon: Tight-binding molecular dynamics studiesof self-diffusion, interstitial-vacancy recombination, and formation volumes,” Physical Review B, vol. 55, pp. 14279–14289, Jun 1997.

[108]   R. Biswas, L. Qiming, B. C. Pan, and Y. Yoon, “Mechanism for hydrogen diffusion in amorphous silicon,” Physical Review B, vol. 57, pp. 2253–2256, January 1998.

[109]   M. Schaible, “Empirical molecular dynamics modeling of silicon and silicon dioxide: A review,” Crit. Rev. Solid State Mat. Sci., vol. 24, pp. 265–323, 1999.

[110]   K. Vollmayr, W. Kob, and K. Binder, “Cooling-rate effects in amorphous silica: A computer-simulation study,” Physical Review B, vol. 54, pp. 15808–15826, 1996.

[111]   R. M. van Ginhoven, H. Jonsson, and L. R. Corrales, “Silica glass structure generation for ab initio calculations using small samples of amorphous silica,” Physical Review B, vol. 71, pp. 024208–1, 2005.

[112]   M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press, 2010.

[113]   R. Biswas, Y.-P. Li, and B. Pan, “Isotopic effect between hydrogen and deuterium emission in silicon,” Journal of Non-Crystalline Solids, vol. 266-269, pp. 176–179, 2000.

[114]   D. Gillespie, “A general method for numerically simulating the stochastic time evolution of coupled chemical reactions,” J.Comp.Phys., vol. 22, pp. 403–434, 1976.

[115]   D. T. Gillespie, “Simulation methods in systems biology,” in Proc. Int. Conf. Form. Meth. Sys. Bio., SFM’08, (Berlin, Heidelberg), pp. 125–167, Springer-Verlag, 2008.

[116]   H. Sumi, “Phonon-kick mechanism for defect reactions enhanced by electronic excitation,” J.Phys.:Condensed Matter, vol. 17, no. 34, p. 6071, 1984.

[117]   C. H. Henry and D. V. Lang, “Nonradiative capture and recombination by multiphono emission in gaas and gap,” Physical Review B, vol. 15, pp. 989–1016, January 1977.

[118]   T. Grasser, T. Aichinger, G. Pobegen, H. Reisinger, P. Wagner, J. Franco, M. Nelhiebel, and B. Kaczer, “The ‘permanent’ component of NBTI: Composition and annealing,” in Proc. Intl.Rel.Phys.Symp., pp. 6A.2.1 –6A.2.9, April 2011.

[119]   J. M. Haile, Molecular Dynamics Simulation. Wiley, 1997.

[120]   D. Frenkel and B. Smit, Understanding Molecular Simulation. Academic Press, 2002.

[121]   A. F. Voter, F. Montalenti, and T. C. Germann, “Extending the time scale in atomistic simulation of materials,” Ann.Rev.Mater.Res., vol. 32, pp. 321–346, 2002.

[122]   K. Mikkelsen and M. Ratner, “Electron tunneling in solid-state electron-transfer reactions,” chemrev, vol. 87, pp. 113–153, 1987.

[123]   V. Abakumov, V. Perel, and I. Yassievich, Nonradiative recombination in semiconductors. North-Holland, 1991.

[124]   M. D. Newton, “Quantum chemical probes of electron-transfer kinetics: the nature of donor-acceptor interactions,” Chem.Rev., vol. 91, pp. 767–792, 1991.

[125]   D. M. Adams, L. Brus, C. E. D. Chidsey, S. Creager, C. Creutz, C. R. Kagan, P. V. Kamat, M. Lieberman, S. Lindsay, R. A. Marcus, R. M. Metzger, M. E. Michel-Beyerle, J. R. Miller, M. D. Newton, D. R. Rolison, O. Sankey, K. S. Schanze, J. Yardley, and X. Zhu, “Charge transfer on the nanoscale: Current status,” J.Phys.Chem.B, vol. 107, no. 28, pp. 6668–6697, 2003.

[126]   P. E. S. Wormer and A. van der Avoird, Theory and Applications of Computational Chemistry: The First Forty Years, ch. Forty Years of Ab Initio Calculations on Intermolecular Forces, pp. 1047–1091. Elsevier, 2005.

[127]   K. Huang and A. Rhys, “Theory of light absorption and non-radiative transitions in f-centers,” Proc. Roy. Soc. A, vol. 204, pp. 406–423, 1950.

[128]   R. Kubo, “Thermal ionization of trapped electrons,” Physical Review, vol. 86, pp. 929–937, 1952.

[129]   T. H. Keil, “Shapes of impurity absorption bands in solids,” Physical Review, vol. 140, pp. A601–A617, 1965.

[130]   B. K. Ridley, “Multiphonon, non-radiative transition rate for electrons in semiconductors and insulators,” J.Phys.:Condensed Matter, vol. 11, pp. 2323–2341, 1978.

[131]   A. M. Stoneham, “Non-radiative transitions in semiconductors,” Rep.Prog.Phys., vol. 44, pp. 1251–1295, 1981.

[132]   K. Huang, “Adiabatic approximation theory and static coupling theory of nonradiative transition,” Scientia Sinica, vol. 24, pp. 27–34, 1981.

[133]   K. Peuker and A. Schenk, “Grundlagen der Theorie der strahlungslosen Multi-Phonon-Rekombination,” Wiss. Z. d. Humboldt-Univ. Berlin, vol. 31, pp. 267–270, 1982.

[134]   G. Helmis, “Zur Theorie der Störstellenelektronen. I Optische Übergänge,” Ann.Phys., vol. 452, no. 6-8, pp. 356–370, 1956.

[135]   G. Helmis, “Zur Theorie der Störstellenelektronen. II Strahlungslose Übergänge,” Ann.Phys., vol. 454, no. 1-2, pp. 41–54, 1956.

[136]   E. Gutsche, “Non-condon approximations and the static approach in the theory of non-radiative multiphonon transitions,” Phys.stat.sol.(b), vol. 109, no. 2, pp. 583–597, 1982.

[137]   M. G. Burt, “On the relation between static and adiabatic coupling schemes for calculating non-radiative multiphonon transition rates,” J.Phys.C:Solid State Phys., vol. 15, pp. L381–L384, 1982.

[138]   M. G. Burt, “The relation between various coupling schemes for calculating non-radiative multiphonon transition rates,” J.Phys.C:Solid State Phys., vol. 16, pp. 4137–4149, 1983.

[139]   A. F. J. Levi, Applied Quantum Mechanics Second Edition. Cambridge, 2006.

[140]   F. Schanovsky, O. Baumgartner, V. Sverdlov, and T. Grasser, “A multi scale modeling approach to non-radiative multi phonon transitions at oxide defects in MOS structures,” J.Comp.Elect., vol. 11, pp. 218–224, 2012.

[141]   M. Lax, “The franck-condon principle and its application to crystals,” J.Chem.Phys., vol. 20, pp. 1752–1760, 1952.

[142]   A. Schenk, K. Irmscher, D. Suisky, R. Enderlein, F. Bechstedt, and H. Klose, “(Mo-P-10) field dependence of the emission rate at deep centers in Si and GaAs,” Act.Phys.Polon., vol. A67, pp. 73–76, 1985.

[143]   S. Makram-Ebeid and M. Lannoo, “Electric-field-induced phonon-assisted tunnel ionization from deep levels in semiconductors,” Physical Review Letters, vol. 48, pp. 1281–1284, May 1982.

[144]   S. Makram-Ebeid and M. Lannoo, “Quantum model for phonon-assisted tunnel ionization of deep levels in a semiconductor,” Physical Review B, vol. 25, pp. 6406–6424, May 1982.

[145]   D. A. McQuarrie, “Stochastic approach to chemical kinetics,” J.Appl.Prob., vol. 4, no. 3, pp. 413–478, 1967.

[146]   P. Hänggi, P. Talkner, and M. Borkovec, “Reaction-rate theory: fifty years after Kramers,” Rev.Mod.Phys, vol. 62, no. 2, pp. 251–342, 1990.

[147]   S. Torquato and C. L. Y. Yeong, “Universal scaling for diffusion-controlled reactions among traps,” J.Chem.Phys., vol. 106, pp. 8814–8820, 1997.

[148]   S. S. Andrews and D. Bray, “Stochastic simulation of chemical reactions with spatial resolution and single molecule detail,” Phys.Biol., vol. 1, pp. 137–151, 2004.

[149]   R. Erban and S. J. Chapman, “Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions,” Phys.Biol., vol. 6, p. 046001, 2009.

[150]   S. A. Isaacson and D. Isaacson, “Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials,” Physical Review E, vol. 80, p. 066106, 2009.

[151]   D. Fange, O. G. Berg, P. Sjöberg, and J. Elf, “Stochastic reaction-diffusion kinetics in the microscopic limit,” Proc.Nat.Acad.Sci., vol. 107, no. 46, pp. 19820–19825, 2010.

[152]   G. Malavasi, M. C. Menziani, A. Pedone, and U. Segre, “Void size distribution in MD-modelled silica glass structures,” Journal of Non-Crystalline Solids, vol. 352, no. 3, pp. 285 – 296, 2006.

[153]   A. Bongiorno, L. Colombo, and F. Cargnoni, “Hydrogen diffusion in crystalline SiO2,” Chem.Phys.Lett., vol. 264, pp. 435–440, 1997.

[154]   V. Huard, M. Denais, and C. Parthasarathy, “NBTI degradation: From physical mechanisms to modelling,” Microelectronics Reliability, vol. 46, no. 1, pp. 1–23, 2006.

[155]   B. Tuttle, “Energetics and diffusion of hydrogen in SiO2,” Physical Review B, vol. 61, pp. 4417–4420, February 2000.

[156]   S. T. Pantelides, L. Tsetseris, S. Rashkeev, X. Zhou, D. Fleetwood, and R. Schrimpf, “Hydrogen in MOSFETs - a primary agent of reliability issues,” Microelectronics Reliability, vol. 47, no. 6, pp. 903 – 911, 2007.

[157]   G. Panagopoulos and K. Roy, “A physics-based three-dimensional analytical model for RDF-induced threshold voltage variations,” IEEE Trans.Electron Devices, vol. 58, pp. 392 –403, Feb. 2011.

[158]   S. Choi, Y. Park, C.-K. Baek, and S. Park, “An improved 3D Monte Carlo simulation of reaction diffusion model for accurate prediction on the NBTI stress/relaxation,” in Proc. Simu.Semicond.Proc.Dev., pp. 185–188, 2012.

[159]   G. Pacchioni and G. Ieranò, “Ab initio formation energies of point defects in pure and Ge-doped SiO2,” Physical Review B, vol. 56, pp. 7304–7312, Sep 1997.

[160]   N. Lopez, F. Illas, and G. Pacchioni, “Mechanisms of proton formation from interaction of H2 with Eand oxygen vacancy centers in SiO2: Cluster model calculations,” J.Phys.Chem.B, vol. 104, no. 23, pp. 5471–5477, 2000.

[161]   M. Vitiello, N. Lopez, F. Illas, and G. Pacchioni, “H2 cracking at SiO2 defect centers,” J.Phys.Chem.A, vol. 104, no. 20, pp. 4674–4684, 2000.

[162]   A. H. Edwards, W. Shedd, and R. Pugh, “Theory of H in SiO2,” Journal of Non-Crystalline Solids, vol. 289, no. 13, pp. 42 – 52, 2001.

[163]   A. S. Mysovsky, P. V. Sushko, S. Mukhopadhyay, A. H. Edwards, and A. L. Shluger, “Calibration of embedded-cluster method for defect studies in amorphous silica,” Physical Review B, vol. 69, no. 8, p. 085202, 2004.

[164]   S. Mukhopadhyay, P. V. Sushko, V. A. Mashkov, and A. L. Shluger, “Spectroscopic features of dimer and dangling bond Ecentres in amorphous silica,” J.Phys.:Condensed Matter, vol. 17, no. 8, p. 1311, 2005.

[165]   A. Alkauskas and A. Pasquarello, “Effect of improved band-gap description in density functional theory on defect energy levels in α-quartz,” Physica B, vol. 401402, no. 0, pp. 670 – 673, 2007.

[166]   J. Sarnthein, A. Pasquarello, and R. Car, “Structural and electronic properties of liquid and amorphous SiO2: An Ab Initio molecular dynamics study,” Physical Review Letters, vol. 74, pp. 4682–4685, Jun 1995.

[167]   J. Sarnthein, A. Pasquarello, and R. Car, “Model of vitreous SiO2 generated by an ab initio molecular-dynamics quench from the melt,” Physical Review B, vol. 52, pp. 12690–12695, Nov 1995.

[168]   E. Calabrese and W. Fowler, “Electronic energy-band structure of α quartz,” Physical Review B, vol. 18, no. 6, pp. 2888–2896, 1978.

[169]   G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Physical Review B, vol. 54, no. 11, pp. 11169–11186, 1996.

[170]   G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmented-wave method,” Physical Review B, vol. 59, p. 1758, 1999.

[171]   G. Kresse, M. Marsman, and J. Furthmüller, VASP Manual. Universität Wien, Sensengasse 8, A-1130 Wien, Austria, 2009.

[172]   G. Henkelman, B. P. Uberuaga, and H. Jónsson, “A climbing image nudged elastic band method for finding saddle points and minimum energy paths,” J.Chem.Phys., vol. 113, no. 22, pp. 9901–9904, 2000.

[173]   E. H. Nicollian and J. R. Brews, MOS (Metal Oxide Semiconductor) Physics and Technology. Wiley, 1982.

[174]   R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem. McGraw-Hill, 1992.

[175]   K. M. Kramer and W. N. G. Hitchon, Semiconductor Devices: A Simulation Approach. Prentice Hall, 1997.

[176]   M. Anantram, M. Lundstrom, and D. Nikonov, “Modeling of nanoscale devices,” Proc.IEEE, vol. 96, pp. 1511 –1550, sept. 2008.

[177]   A. Schenk, Advanced Physical Models for Silicon Device Simulation. Springer, 1998.

[178]   T. Ayalew, T. Binder, J. Cervenka, K. Dragosits, R. Entner, A. Gehring, T. Grasser, M. Gritsch, R. Klima, M. Knaipp, H. Kosina, R. Mlekus, V. Palankovski, R. Rodriguez-Torres, M. Rottinger, G. Schrom, S. Selberherr, M. Stockinger, and S. Wagner, Minimos-NT device and circuit simulator Release 2.0. Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, P.O. Box U1987, Perth 6845, Western Australia, 2004.

[179]   M. Karner, A. Gehring, S. Holzer, M. Pourfath, M. Wagner, W. Goes, M. Vasicek, O. Baumgartner, C. Kernstock, K. Schnass, G. Zeiler, T. Grasser, H. Kosina, and S. Selberherr, “A multi-purpose schrödinger-poisson solver for tcad applications,” J.Comp.Elect., vol. 6, pp. 179–182, 2007.

[180]   A. Palma, A. Godoy, J. A. Jemènez-Tejada, J. E. Carceller, and J. A. Lòpez-Villanueva, “Quantum two-dimensional calculation of time constants of random telegraph signals in metal-oxide-semiconductor structures,” Physical Review B, vol. 56, pp. 9565–9574, October 1997.

[181]   D. Garetto, Y. M. Randiamihaja, D. Rideau, E. Dornel, W. F. Clark, A. Schmid, V. Huard, H. Jaouen, and Y. Leblebic, “Small signal analysis of electrically-stressed oxides with poisson-schroedinger based multiphonon capture model,” in Proc. Intl.Worksh.Comput.Electron., pp. 327–330, 2010.

[182]   P. Hehenberger, W. Gös, O. Baumgartner, J. Franco, B. Kaczer, and T. Grasser, “Quantum-mechanical modeling of NBTI in high-k SiGe MOSFETs,” in Proc. Simu.Semicond.Proc.Dev., pp. 11 – 14, 2011.

[183]   G. D. Mahan, Many-Particle Physics. Plenum Press, 1990.

[184]   A. Schenk, K. Irmscher, D. Suisky, R. Enderlein, F. Bechstedt, and H. Klose, “Electric field effect on multiphonon transitions at deep centers,” in Proc. Intl. Conf. Phys. Semi., 1985.

[185]   W. B. Fowler, J. K. Rudra, M. E. Zvanut, and F. J. Feigl, “Hysteresis and franck-condon relaxation in insulator-semiconductor tunneling,” Physical Review B, vol. 41, no. 12, pp. 8313–8317, 1990.

[186]   F. Schanovsky, “Ab-initio calculation of the vibrational influence on hole-trapping,” in Proc. Intl.Worksh.Comput.Electron., pp. 163 – 166, 2010.

[187]   O. Engstrom and H. G. Grimmeiss, “Vibronic states of silicon-silicon dioxide interface traps,” Semicond.Sci.Technol., vol. 4, no. 12, p. 1106, 1989.

[188]   O. Engström, “Influence of entropy properties on measured trap energy distributions at insulator-semiconductor interfaces,” Appl.Phys.Lett., vol. 55, no. 1, pp. 47–49, 1989.

[189]   C. G. Van de Walle and J. Neugebauer, “First-principles calculations for defects and impurities: Applications to III-nitrides,” J.Appl.Phys., vol. 95, no. 8, pp. 3851–3879, 2004.

[190]   W. Gös and T. Grasser, “First-principles investigation on oxide trapping,” in Simulation of Semiconductor Processes and Devices 2007 (T. Grasser and S. Selberherr, eds.), pp. 157–160, Springer Vienna, 2007.

[191]   W. Goes, M. Karner, V. Sverdlov, and T. Grasser, “A rigorous model for trapping and detrapping in thin gate dielectrics,” in Proc. Intl.Symp. on Physical and Failure Analysis of Integrated Circuits, pp. 1 –6, july 2008.

[192]   A. Alkauskas, P. Broqvist, and A. Pasquarello, “Defect energy levels in density functional calculations: Alignment and band gap problem,” Physical Review Letters, vol. 101, p. 046405, Jul 2008.

[193]   W. Goes, M. Karner, V. Sverdlov, and T. Grasser, “Charging and discharging of oxide defects in reliability issues,” Device and Materials Reliability, IEEE Transactions on, vol. 8, pp. 491 –500, sept. 2008.

[194]   A. Alkauskas, J. L. Lyons, D. Steiauf, and C. G. Van de Walle, “First-principles calculations of luminescence spectrum line shapes for defects in semiconductors: The example of gan and zno,” Physical Review Letters, vol. 109, p. 267401, Dec 2012.

[195]   A. Schenk, “(Mo-P-22) field-dependent emission rate at deep centers in GaAs by using a two-phonon mode model,” Act.Phys.Polon., vol. A69, no. 5, pp. 813–815, 1986.

[196]   A. Schenk, “A model for the field and temperature dependence of Shockley-Read-Hall lifetimes in silicon,” Solid-State Electron., vol. 35, pp. 1585–1596, 1992.

[197]   F. Ansbacher, “A note on the overlap integral of two harmonic oscillator wave functions,” Z.Naturforschg, vol. 14a, pp. 889–892, 1959.

[198]   B. Zapol, “New expressions for the overlap integral of two linear harmonic oscillator wavefunctions,” Chem.Phys.Lett., vol. 93, no. 6, pp. 549–552, 1982.

[199]   F. Iachello and M. Ibrahim, “Analytic and algebraic evaluation of Franck-Condon overlap integrals,” J.Phys.Chem.A, vol. 102, pp. 9427–9432, 1998.

[200]   P. P. Schmidt, “Computationally efficient recurrence relations for one-dimensional franck-condon overlap integrals,” Molecular Physics, vol. 108, pp. 1513–1529, 2010.

[201]   M. Wastl, “Berechnung eindimensionaler Überlappintegrale des harmonischen Oszillators,” bakkalaureatsarbeit, TU Wien, 2011.

[202]   J. H. Zheng, H. S. Tan, and S. C. Ng, “Theory of non-radiative capture of carriers by multiphonon processes for deep centers in semiconductors,” J.Phys.:Condensed Matter, vol. 6, pp. 1695–1706, 1994.

[203]   J. D. Gale, General Utility Lattice Program. Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, P.O. Box U1987, Perth 6845, Western Australia, 2003.

[204]   A. Alkauskas and A. Pasquarello, “Alignment of hydrogen-related defect levels at the interface,” Physica B, vol. 401-402, no. 0, pp. 546 – 549, 2007.

[205]   B. R. Tuttle, “Theoretical investigation of the valence-band offset between si(001) and SiO2,” Physical Review B, vol. 70, p. 125322, Sep 2004.

[206]   T. Grasser, H. Reisinger, K. Rott, M. Toledano-Luque, and B. Kaczer, “On the microscopic origin of the frequency dependence of hole trapping in pMOSFETs,” in Proc. Intl.Electron Devices Meeting, 2012.

[207]   O. Baumgartner, M. Karner, and H. Kosina, “Modeling of high-k-metal-gate-stacks using the non-equilibrium Green’s function formalism,” in Proc. Simu.Semicond.Proc.Dev., pp. 353–356, 2008.

[208]   S. Datta, Electronic Transport in Mesoscopic Systems. Cambridge, 1995.

[209]   W. Shockley and W. T. Read, “Statistics of the recombinations of holes and electrons,” Physical Review, vol. 87, pp. 835–842, 1952.