1 / 33

Multisubband Monte Carlo simulations for p- MOSFETs

Multisubband Monte Carlo simulations for p- MOSFETs. David Esseni DIEGM, University of Udine (Italy) Many thanks to: M.De Michielis, P.Palestri, L.Lucci, L.Selmi. Acknowledg : NoE. SINANO (EU), PullNano (EU).

berne
Télécharger la présentation

Multisubband Monte Carlo simulations for p- MOSFETs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multisubband Monte Carlo simulations for p-MOSFETs David Esseni DIEGM, University of Udine (Italy) Many thanks to: M.De Michielis, P.Palestri, L.Lucci, L.Selmi Acknowledg: NoE.SINANO (EU), PullNano (EU)

  2. Support of the physically based transport modelling to the generalized scaling scenario • Band-structure calculation and optimization: • Carrier velocity and maximum attainablecurrent IBL • Scattering rates, hence realcurrent ION and BR=(ION/IBL) • Link the properties and advantages of: Mobility in Long MOSFETs (Uniform transport) ION in nano-MOSFETs (far from equilibr. transport) • Provide sound interpretation to characterization D.Esseni, University of Udine

  3. y x z Multisubband Monte Carlo (MSMC) approach for MOS transistors VG2 • Solve 1D Schrödinger equation in the Z direction ei(x) along the channel VS VD VG1 • Driving Force in each subband: z D.Esseni, University of Udine

  4. Multisubband Monte Carlo (MSMC) for n-MOS transistors(electron inversion layers) D.Esseni, University of Udine

  5. y x X z MSMC for n-MOS transistors (1) (Effective Mass Approximation) VG2 Subband “j” VD Subband “i” VG1 • SchrÖdinger-like equation: • Energy dispersion versus k: • mx, my, mz expressed in terms of mt and mlof the bulk crystal D.Esseni, University of Udine

  6. y x z MSMC for n-MOS transistors (2) (Effective Mass Approximation) VG2 VD VG1 Energy dispersion: Driving force: Velocity: D.Esseni, University of Udine

  7. Transport in the MSMC approach(2D carrier gas) Force: Band structure Kinematics: Rates of scattering D.Esseni, University of Udine

  8. Bandstructure for a hole inversion layer: • Single-band effective mass approx. is not viable: • Three almost degenerate bands at the Gpoint • Spin-orbit interaction k·pmethod for hole inversion layers D.Esseni, University of Udine

  9. y x z k·pmethod for inverted layers: VG2 Differently from EMA: one eigenvalue problem for each in-plane (kx,ky) VS VD • Finite differencesmethod: • √ section and√in-planek: • eigenvalue problem 6Nzx6Nz VG1 • Entirely numerical description of the energy dispersion Computationally very heavy for simulations of pMOSFETs Simplified models for energy dispersion of 2D holes D.Esseni, University of Udine

  10. MSMC for pMOSFETs • Semi-analytical model for 2D holes • Basic idea and full development of the model • Implementation in a Monte Carlo tool • Simulation results D.Esseni, University of Udine

  11. Semi-analytical model for 2D holes Three groups of subbands: • Calculation of the eigenvalues ev,i • New analytical expression for in-plane energy Ep(k) k·presults D.Esseni, University of Udine

  12. Semi-analytical model for 2D holes 1) Bottom of the 2D subbands (the relatively easy part) D.Esseni, University of Udine

  13. Semi-analytical model for 2D holes(bottom of the 2D subbands) Schrödinger equation as in EMA (mz): Good agreement also in square well mn,z fitted using triangular wells D.Esseni, University of Udine

  14. 2) Energy dependence on k (the by no means easy part) Semi-analytical model for 2D holes D.Esseni, University of Udine

  15. Semi-analytical model for 2D holes(energy dispersion is anisotropic) k·presults Si(100) • Strongly anisotropic • Periodic of p/2 D.Esseni, University of Udine

  16. k·presults Semi-analytical model for 2D holes(energy dispersion is non-parabolic) Analytical dispersion in the symmetry directions: D.Esseni, University of Udine

  17. Semi-analytical model for 2D holes(angular dependence) Fourier series expansion: A, B, C calculated with no additional fitting parameters: D.Esseni, University of Udine

  18. Bottom of the 2D subbands • Energy dependence on k Semi-analytical model for 2D holes D.Esseni, University of Udine

  19. MSMC for pMOSFETs • Semi-analytical model for 2D holes • Calibration and validation • Implementation in a Monte Carlo tool • p-MOSFETs: Simulation results D.Esseni, University of Udine

  20. Calibration of the semi-analytical model(bottom of the 2D subbands) Schrödinger equation in the EMA (mz): Good agreement also in square well mn,z fitted using triangular wells D.Esseni, University of Udine

  21. Calibration of the semi-analytical model(non parabolicity along symmetry directions) Si(100), Fc=0.3MV/cm • Good results with the proposed non parabolic expression: D.Esseni, University of Udine

  22. Validation of the semi-analytical model(overall energy dependence on k) Si(001) • Calculation conditions: • Triangular well: FC=0.3 MV/cm • E-e0=75 meV • The model seems to grasp fairly well the complex, anisotropic energy dispersion D.Esseni, University of Udine

  23. Si(001) Validation of the semi-analytical model(2D Density Of States - DOS) Acoustic Phonon scattering: D.Esseni, University of Udine

  24. Validation of the semi-analytical model(average hole velocity: vx, vy) • Analytical Model:  Analytical expression for: Pinv=5.6x1012[cm-2] Average: [0,p/4] • k·presults(numerical • determination): D.Esseni, University of Udine

  25. MSMC for pMOSFETs • Semi-analytical model for 2D holes • Implementation in a Monte Carlo tool • Integration of the motion equation • p-MOSFETs: Simulation results D.Esseni, University of Udine

  26. Fx1 Fx2 MSMC Implementation (integration of motion during free flights) (1) Constant electric field Fx in each section: No simple expressions for:  No analytical integration of the motion !!! D.Esseni, University of Udine

  27. Fx1 Fx2 MSMC Implementation (integration of motion during free flights) (2) No analytical integration of: Constant electric field Fx in each section: D.Esseni, University of Udine

  28. MSMC Implementation (integration of motion: validation) • Trajectories in the phase space validate the approach to the motion equation 2) 1) D.Esseni, University of Udine

  29. MSMC for pMOSFETs • Semi-analytical model for 2D holes • Implementation in a Monte Carlo tool • p-MOSFETs: Simulation results D.Esseni, University of Udine

  30. p-MOSFETs: MSMC Simulation results (Mobility calibration and validation) • Phonon and roughness parameters calibrated at 300k good agreement at different temperatures D.Esseni, University of Udine

  31. p-MOSFETs: MSMC Simulation results (IDS-VGS and ballisticity ratio) • Ballisticity ratios comparable to n-MOSFETs D.Esseni, University of Udine

  32. Conclusions: • 2D hole bandstructure is main the issue in the development of a MSMC for p-MOSFETs • New semi-analytical, non-parabolic, anisotropic bandstructure model and implementation in a self-consistent MSMC for p-MOSFETs • Results for mobility, on-currents, ballisticity ratios Future work: • Extension of the approach to different crystal orientations and strain D.Esseni, University of Udine

  33. MSMC for n-MOS transistors (3) (Effective Mass Approximation) • Development of a complete • MSMS simulator for n-MOSFETs • (L.Lucci et al., IEDM 2005, TED’07) Ball S VirtualSource D Scatt D.Esseni, University of Udine

More Related