1 / 24

Phonon thermal transport in N ano-transistors

Phonon thermal transport in N ano-transistors. Anes BOUCHENAK-KHELLADI Advisors : - Jér ô me Saint-Martin - Philippe DOLLFUS Institut d’Electronique Fondamentale. Contents. A - General Introduction (page 3 to 8) B - Simulation Results (page 10 to 23) 1. Fourier equation

ronat
Download Presentation

Phonon thermal transport in N ano-transistors

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. Phonon thermal transport in Nano-transistors Anes BOUCHENAK-KHELLADI Advisors : - Jérôme Saint-Martin - Philippe DOLLFUS Institutd’ElectroniqueFondamentale

  2. Contents • A - General Introduction (page 3 to 8) • B - Simulation Results(page 10 to 23) • 1. Fourier equation • 2. Boltzmann Transport equation PHONON THERMAL TRANSPORT

  3. A. General introduction What’s a phonon ? Thermal agitation In a uniform solid material and vibrate Atoms in a regular lattice : Wave propagating inside the crystal Phonon A quantum of energy of this vibration is a PHONON THERMAL TRANSPORT

  4. A. General introduction But Why are we interested in “ Phonons ” ? PHONON THERMAL TRANSPORT

  5. A. General introduction Mr. electron In metals heat But !!! In Semiconductors and insulators Lattice vibration “Mr. Phonon” PHONON THERMAL TRANSPORT

  6. A. General introduction • Some phonon characteristics : - Behave as particles (quasi-particles) and as waves. - Described by a periodic dispersion : Pulsation Energy - Particles described by a wave-packet - The group velocity of wave-packet is determined by : - Obey to Bose-Einstein statics just like photons : PHONON THERMAL TRANSPORT

  7. A. General introduction Electrons Phonons Fermi-Dirac statics Bose-Einstein statics Why not ! Would you like to come with me ? I will vibrate ! Each energy state can be occupied by any number of phonons PHONON THERMAL TRANSPORT

  8. A. General introduction • The dispersion approximation: • We have then : • 1 LA • 2 TA • 1 LO • 2 TO The slope ? ! Why this order ? ! PHONON THERMAL TRANSPORT

  9. Contents • A - General Introduction • B - Simulation Results • 1. Fourier equation • 2. Boltzmann Transport equation PHONON THERMAL TRANSPORT

  10. B. Simulation Results But what’s the “ Purpose ” ? PHONON THERMAL TRANSPORT

  11. B. Simulation Results our device : Y Thermal reservoirs at equilibrium Channel characterized by a dispersion Assumed to be ideal contacts T1 T2 Propagation axes X PHONON THERMAL TRANSPORT

  12. B. Simulation Results The goal is to get the temperature profile inside our device ! So, just solve the Heat diffusion equation (Fourier equation) ! Euhhh … ! Not exactly … ! … ? PHONON THERMAL TRANSPORT

  13. Contents • A - General Introduction • B - Simulation Results • 1. Fourier equation • 2. Boltzmann Transport equation PHONON THERMAL TRANSPORT

  14. B. Simulation results 1. Fourier equation • In a medium : - Isotropic • with constant thermo-physical parameters The heat diffusion equation is : The Fourier law : Then, at equilibrium => So, the variable is T ! but how could we resolve this equation ? PHONON THERMAL TRANSPORT

  15. B. Simulation results1. Fourier equation First step: Discretization (mesh of our silicon nano-wire) PHONON THERMAL TRANSPORT

  16. B. Simulation results1. Fourier equation Then: Simply resolve the linear system: Second step: Write the right program in MATLAB After : Check the results !! PHONON THERMAL TRANSPORT

  17. B. Simulation results1. Fourier equation Third step: Admire the results Ti = 9 nm = 150 nm TGrilles = 300 K Tsource = Tdrain = 300 K PHONON THERMAL TRANSPORT

  18. Contents • A - General Introduction • B - Simulation Results • 1. Fourier equation • 2. Boltzmann Transport equation PHONON THERMAL TRANSPORT

  19. B. Simulation results 2. Boltzmann Transport equation The general form is : What we need to resolve is this: The RTA say : Then => So, the variable is Ns ! but how could we resolve this equation ? PHONON THERMAL TRANSPORT

  20. B. Simulation results2. Boltzmann Transport equation As we work in 2D, the above equation become : First step: Discretization (mesh of our silicon nano-wire both along x and y and in the reciprocal space (the Brillouin zone)) fBrown III, Thomas W., et Edward Hensel. « Statistical phonon transport model for multiscale simulation of thermal transport in silicon: Part I – Presentation of the model ». International Journal of Heat and Mass Transfer 55, no 25‑26 (décembre 2012): 7444‑7452. PHONON THERMAL TRANSPORT

  21. B. Simulation results2. Boltzmann Transport Equation (BTE) Then: Simply resolve the linear system: with Second step: Write the right program in MATLAB After : Check the results !! Third step: Admire the results ! Euhh … ! Not yet ! • We have to find a way to compute the TemperatureusingNs (or more exactlyEs = h’.w.Ns) PHONON THERMAL TRANSPORT

  22. B. Simulation results2. Boltzmann Transport Equation (BTE) So, we compute the equilibrium local phonon energy After, we draw the E(T) graph … ! Euhh ! In fact, we drawT(E) Then, we make a polynomial fit to get T(E) PHONON THERMAL TRANSPORT

  23. B. Simulation results2. Boltzmann Transport Equation (BTE) And : The temperature profile … PHONON THERMAL TRANSPORT

  24. B. Simulation results2. Boltzmann Transport Equation (BTE) Pending Work … ! But almost done ! PHONON THERMAL TRANSPORT

More Related