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Treatment of Point Defects in Nanowire MOSFETs using Nonequilibrium Green’s Function Formalism

Explore the treatment of point defects in nanowire MOSFETs through the Nonequilibrium Green's Function formalism. Discuss the influence of impurity location and type on energy subbands, transverse modes, and current characteristics. Learn about the impact of Coulombic potential and on-site potentials on device performance.

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Treatment of Point Defects in Nanowire MOSFETs using Nonequilibrium Green’s Function Formalism

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  1. International Workshop of Computational Electronics Purdue University, 26th of October 2004 Treatment of Point Defects in Nanowire MOSFETs Using the Nonequilibrium Green’s Function Formalism M. Bescond, J.L. Autran*, N. Cavassilas, D. Munteanu, and M. Lannoo Laboratoire Matériauxet Microélectroniquede Provence UMR CNRS 6137 - Marseille/Toulon (France) - www.l2mp.fr * Also Institut Universitaire de France (IUF)

  2. Outline • Introduction • MOSFETs downscaling: statistical fluctuations of doping impurity positions • 3D Quantum simulation of point defects in nanowire transistors • Nonequilibrium Green Function formalism: Mode-Space approach • Treatment of point defects • Results: influence of the impurity location and type • Energy subbands • Transverse modes • Current characteristics • Conclusions and perspectives

  3. Dimensions of nanowire MOSFETs • p-type channel region: Volume = LWSiTSi=1053=150 nm3 If doping concentration=1019 cm-3 1.5 impurity on average. • Source and drain region: continuous doping of 1020 cm-3. • Dimensions: L=8 nm, WSi=3 nm, and TSi=3 nm, TOX=1 nm. • Channel region: discrete doping of 1019 cm-3, with 1 impurity on average.  Discrete distribution and statistical location.  Effect of the impurity type and location.

  4. Nonequilibrium Green’s function formalism • Point Defect Treatment

  5. ith eigenstate of the nth atomic plan The 3D Mode Space Approach* 1D (transport)  The 3D Schrödinger = 2D (confinement) + 1D ( transport) 2D (confinement) • Hypothesis: n,i is constant along the transport axis. * J. Wang et al. J. Appl. Phys. 96, 2192 (2004).

  6. The 3D Mode Space Approach  Electron distribution along subbands (valley (010)):  For each subband i: i=3 : Transverse eigenstate i=2 : Transverse eigenvalue : 1D Green function i=1 • Simplified tight-binding approach: cubic lattice with ax, ay, az. • - 1 orbital/atom: : position z=laz, y=may, x=nax. • - Interactions between first neighbors.

  7. Energy Impurity • Point Defect = On-site Potential + Coulomb Tail Point defect description Treated as a macroscopic variation  Included in the self-consistent mode-space approach without coupling the electron subbands Treated as a localized variation = Chemical structure • Included in the real space approach based on the Dyson equation. [G=(I-G0V)-1G0]

  8. Treatment of on-site potential • After achieving self-consistence including the Coulomb Tail, the device is subdivided at the point defect location: • Calculation of the Green’s functions of the surfaces S1 and S2:

  9. Treatment of on-site potential • Ud is then included using the Dyson equation: Intra-atomic potential matrix • Retarded Green function of the uncoupled system: • Calculation of the current*: * M. Bescond et al., Solid-State Electron. 48, 567 (2004).

  10. Results • Influence of point defect

  11. Simulation results • Electronic subbands: Effect of the Coulombic potential (valley (010)) • Subband profile is affected by the impurity. • Subbands are still independant: justification of the mode-space approach. • Acceptor impurity increases the channel barrier.

  12. Defect free Centered defect Defect in the corner z Simulation results • Evolution the 1st confinement eigenstate (valley (010)): • Highest variations of the eigenstate with centered impurity. • Scalar product : weak variations.

  13. Simulation results • First subband profile and current characteristics: VG=0 V VDS=0.4 V Ud=2 eV • Defect in the corner: weak influence on the subband profile. • Defect free: highest current. • Centered defect: lowest current. • Defect in the corner: intermediate behavior: current decrease of 50%. • Variation of the subthreshold slope.

  14. Simulation results • Influence of Coulomb potential: VDS=0.4 V • On-site potential defect does not affect the total current. • Coulombic potential has the most significant impact. • Electrons can be transmitted through the unperturbated neighboring atoms.

  15. Conclusion  Modeling of electron-ion interaction based on the NEGF formalism. • Study of the effect the acceptor impurity in terms of physical properties. • Centered impurity involves a significant degradation of the current. • Not only a shift of the current but rather a subthreshold slope variation. • The Coulomb potential has a prevalent rule compared to the on-site potential of the impurity. • Treatment of donor impurities in source and drain.

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