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N ational Technical University of Ukraine “Kyiv Polytechnic Institute”

NTUU "KPI" 1898. Department of physical and biomedical electronics. N ational Technical University of Ukraine “Kyiv Polytechnic Institute”. Q uantum transport simulation tool, supplied with GUI. Authors: Fedyay Artem, Volodymyr Moskaliuk, Olga Yaroshenko. Presented by: Fedyay Artem.

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N ational Technical University of Ukraine “Kyiv Polytechnic Institute”

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  1. NTUU "KPI" 1898 Department of physical and biomedical electronics National Technical University of Ukraine“Kyiv Polytechnic Institute” Quantum transport simulation tool, supplied with GUI Authors: Fedyay Artem, Volodymyr Moskaliuk, Olga Yaroshenko Presented by:Fedyay Artem ElNano XXXI 13, April 2011 Kyiv, Ukraine

  2. Overview • Objects of simulation • Physical model • Computational methods • Simulation tool • Examples of simulation fedyay@phbme.ntu-kpi.kiev.ua

  3. Objects to be simulated Layered structures with transverse electron transport: • resonant-tunneling diodes (RTD) with 1, 2, 3, … barriers; • Supperlattices Reference topology (example): fedyay@phbme.ntu-kpi.kiev.ua

  4. Physical model. Intro ENVELOPE FUNCTION (EFFECTIVE MASS) METHOD • Envelope of what? of the electron wave function: in case of homogeneous s/c and flat bands (Bloch waves) • What if not flat-band? fedyay@phbme.ntu-kpi.kiev.ua

  5. Physical model. Type ENVELOPE FUNCTION (EFFECTIVE MASS) METHOD fedyay@phbme.ntu-kpi.kiev.ua

  6. Model’s restrictionh/s withband wraps of type I (II) TYPE III InAs-GaSb Band structures sketches TYPE I GaAs – AlGaAs GaSb – AlSb GaAs – GaP InGaAs – InAlAsInGaAs – InP TYPEII InP-Al0.48In0.52As InP-InSb BeTe–ZnSe GaInP-GaAsP Si-SiGe fedyay@phbme.ntu-kpi.kiev.ua

  7. Physical model.Type  What do we combine? Sometimes referred to as“COMBINED” we combine semiclassical and “quantum-mechanical” approaches for different regions (*) homogeneous , (**) almost equilibrium high-doped (*) nanoscaled heterolayers , (**) non-equilibrium intrinsic fedyay@phbme.ntu-kpi.kiev.ua

  8. Physical model.Electron gas fedyay@phbme.ntu-kpi.kiev.ua

  9. Physical model.Master equations.(1 band) fedyay@phbme.ntu-kpi.kiev.ua

  10. Physical model.Electrical current.Coherent component Coherent component of current flow is well described by Tsu-Esaki formulation: fedyay@phbme.ntu-kpi.kiev.ua

  11. Physical model.Electrical current.(!)Coherent component fedyay@phbme.ntu-kpi.kiev.ua

  12. Physical model. Y? We need |YL|2 and |YR |2 for calculation of CURRENT and CONCENTRAION  Which equation YL and YR are eigenfunction of? fedyay@phbme.ntu-kpi.kiev.ua

  13. 2-band model. What for? fedyay@phbme.ntu-kpi.kiev.ua

  14. 2-band model. What for? ! [100] • Current re-distribution between valleys changing of a total current • Electrons re-distribution  changing potential fedyay@phbme.ntu-kpi.kiev.ua

  15. Physical model. YГ,YX? It was derived from k.p-method that instead of eff.m.Schr.eq. it must be a following system: which “turns on” Г-X mixing at heterointerfaces (points zi) by means of a. It of course reduces to 2 independent eff.m.Shcr.eqs. for X and Г-valley fedyay@phbme.ntu-kpi.kiev.ua

  16. Physical model.Boundary conditions for Schr. eq. We have to formulate boundary conditions for Schrödinger equation. They are quite natural (QuantumTransmissionBoundaryMethod). Wave functions in the reservoirs are plane waves. Transmission coefficient needs to be found for current calculation fedyay@phbme.ntu-kpi.kiev.ua

  17. Physical model. Features • Combined quazi-1D. • Self-consistent (Hartee approach). • Feasibility of 1 or 2-valley approach. • Scattering due to POP and Г-X mixing is taking into acount. fedyay@phbme.ntu-kpi.kiev.ua

  18. Scientific content circumstantialevidence:direct use of works on modeling of nanostructures 1971-2010 fedyay@phbme.ntu-kpi.kiev.ua

  19. Computational methods Numerical problems and solutions: • Computation of concentrationn(z) needs integration of stiff function  using adaptive Simpson algorithm; • Schrodinger equation have to be represented as finite-difference scheme, assuring conservation, and needs prompt solution  using of conservative FD schemes and integro- interpolating Tikhonov-Samarskiy method; • Algorithm of self-consistence with good convergence should be used to find VH  using linearizing Gummel’s method ? Efficient method for FD scheme with 5-diagonal matrix solution (appeared in 2-band model, corresponding to Schrödinger equation) direct methods, using sparse matrix concept in Matlab (allowing significant memory economy) fedyay@phbme.ntu-kpi.kiev.ua

  20. Let’s try to simulate Al0.33Ga0.64As/GaAs RTD fedyay@phbme.ntu-kpi.kiev.ua

  21. Application with GUI fedyay@phbme.ntu-kpi.kiev.ua

  22. Emitter fedyay@phbme.ntu-kpi.kiev.ua

  23. Quantum region fedyay@phbme.ntu-kpi.kiev.ua

  24. Base fedyay@phbme.ntu-kpi.kiev.ua

  25. Materials data-base(1-valley case) (!) Each layer supplied with the following parameters: mГ(x), x – molar rate in AlxGa1-xAs mГ(x)=m00+km*x, DEc(x) – band off-set DEc(x)=U00*x e(x) is dielectric permittivity e(x)= e00+ke*x fedyay@phbme.ntu-kpi.kiev.ua

  26. Settings fedyay@phbme.ntu-kpi.kiev.ua

  27. Graphs fedyay@phbme.ntu-kpi.kiev.ua

  28. Calculation: in progress(few sec for nsc case) fedyay@phbme.ntu-kpi.kiev.ua

  29. Calculation complete fedyay@phbme.ntu-kpi.kiev.ua

  30. Concentration fedyay@phbme.ntu-kpi.kiev.ua

  31. Potential (self-consistent) fedyay@phbme.ntu-kpi.kiev.ua

  32. Concentration (self-consistent) fedyay@phbme.ntu-kpi.kiev.ua

  33. Transmissionprobability(self-consistent) fedyay@phbme.ntu-kpi.kiev.ua

  34. Local density of statesg (Ez,z)(self-consistent) fedyay@phbme.ntu-kpi.kiev.ua

  35. Local density of statesg (Ez,z) (in new window with legend) fedyay@phbme.ntu-kpi.kiev.ua

  36. Distribution functionN (Ez,z) (tone gradation) fedyay@phbme.ntu-kpi.kiev.ua

  37. I-V characteristic(non self-consistent case) fedyay@phbme.ntu-kpi.kiev.ua

  38. Resonant tunneling diode(2 valley approach) (!) Each layer supplied with additional parameters: mX DEХ-Г a CB in Г and X-points fedyay@phbme.ntu-kpi.kiev.ua

  39. LDOS in Г and X-valleys X-valley: barriers  wells Г-valley fedyay@phbme.ntu-kpi.kiev.ua

  40. Transmission coefficient2 valleys Г– valley only  (*) Fano resonances (**) additional channel of current both Гand Xvalleys fedyay@phbme.ntu-kpi.kiev.ua

  41. Another example:supperlattice AlAs/GaAs 100 layers CB profile LDOS  fedyay@phbme.ntu-kpi.kiev.ua

  42. Try it for educational purposes! Simulation tool corresponding to 1-band model w/o scattering will be available soon at: www.phbme.ntu-kpi.kiev.ua/~fedyay (!) Open source Matlab + theory + help Today you can order it by e-mail: fedyay@phbme.ntu-kpi.kiev.ua 2-band model contains unpublished results and will not be submitted heretofore THANK YOU FOR YOUR ATTENTION fedyay@phbme.ntu-kpi.kiev.ua

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