1. INTRODUCTION  Time and Length Scales  Energy Transport in Microelectronics  Ultra Short Pulse Laser Processing  Transport Laws and Thermal Transport Modeling

2. 0 Length, m 10 -18 10 -15 10 -12 10 -9 10 -6 10 -3 10 -10 Typical atom, One Angstrom 10 -4 Electron radius Animal cell mean diameter, Fine dust Length Scales Human hair 10 -5 micronanopico Diameter of AIDS virus femtoattomilli DNA < 3 nm Protein 2~5 nm 10 -7 2.8179 × 10 -15 Mean-free path of phonon in Si at T = 300 K 100 nm

3. 0 Time, s 10 -18 10 -15 10 -6 10 -3 10 -13 Time Scales micronanopicofemtoattomilli X-Rays ignition time in nuclear fusion reactor Phonon intercollision period in Si at T = 300 K Oscillation period of lattice vibration (acoustic phonons) of aluminum oxide Light travels one micrometer 3.3 × 10 -15 10 -12 Thermal diffusion 10 -11 10 -9

4. 10 1 십 ( 十 ) 10 20 해 ( 垓 ) 10 2 백 ( 百 ) 10 24 시 ( 枾 ) 10 3 천 ( 千 )10 28 양 ( 穰 ) 10 4 만 ( 萬 ) 10 32 구 ( 溝 ) 10 8 억 ( 億 ) 10 36 간 ( 澗 ) 10 12 조 ( 兆 ) 10 40 정 ( 正 ) 10 16 경 ( 京 ) 10 44 재 ( 載 ) 10 24 Yotta 10 27 Taxo Numbering Systems (1)

5. 10 -6 微 미 Micro 10 -7 纖 섬 10 -8 沙 사 10 -9 塵 진 Nano 10 -10 埃 애 10 -11 渺 묘 10 -12 漠 막 Pico 10 -13 模湖 모호 10 -14 逡巡 준순 10 -15 須臾 수유 Femto 10 -16 瞬息 순식 10 -17 彈指 탄지 10 -18 刹那 찰나 Atto 10 -19 六德 육덕 10 -20 虛空 허공 10 -21 淸淨 청정 Zepto Numbering Systems (2)

6. Significance of Length Scales (1) Pond skater Water stride

7. Significance of Length Scales (2)

8. Molecule-Based Gear Significance of Length Scales (3)

9. Body force to Surface tension Ratio Scaling law: Reynolds number Significance of Length Scales (4)

10. SOI Transistor Channel length current: 65 nm phonon mean free path in Si at 300 K: O(100 nm)

11. d phonon  Phonon-Boundary Scattering  Si@300K = 300 nm

12. Thermal Conductivity of Silicon

13. 4.2 J/cm 2 @ 3.3 ns Steel foil 100  m in thickness Nanosecond Machining Process surface debris recast layer ejected molten drops long pulse laser beam damage to adjacent structure

14. 0.5 J/cm 2 @ 200 fs no surface debris no recast layer ultrafast laser pulses no damage to adjacent structures plasma plume no melt zone no microcracks no shock wave hot, dense ion /electron soup no heat transfer to surrounding material Femtosecond Machining Process

15. Non-equilibrium Phenomenon Carriers (Electron-Hole Pairs) Silicon Lattice (Phonons) Laser Irradiation  Electron relaxation time ~ 100 fs  Within this time period, electrons do not lose energy to phonons.  t C-L ~ 0.5 ps

16. 1) t c : collision time or duration of collision smallest time scale on the order of the wavelength of the carrier divided by the propagation speed for phonons 100 fs (Si at 300 K) Time Scales (1) 2) t : average time between collisions or mean free time For time scales t < t, carriers travel ballistically and the evolution of the system depends strongly on the details of the initial state. not relaxation time since it takes several collisions to reach equilibrium generally t >> t c

17. 3) t r : relaxation time (collision induced equilibrium) associated with local thermodynamic equilibrium equilibrium achieved in 5 to 20 collisions, t r > t 4) t d : diffusion time on the order of t d ~ L 2 / a, where L is the size of the object and a is the thermal diffusivity, a ~  2 t, where  is particle speed t d ~ where t b is the time it takes for the particle to ballistically travel the distance L at speed  For ballistic transport over a distance L, t ~ t d Time Scales (2)

18. Length Scales 2) L : mean free path associated mean free time between collision, L =  t 3) l r : associated with relaxation time the characteristic size of a volume over which local thermodynamic equilibrium can be defined typically l < L < l r 1) l : wavelength of the energy carrier associated with the collision process shortest length scale

19. 1) When L ~ l Wave phenomena such as diffraction, tunneling, and interference are important. Photon : wave optics based on Maxewll’s equation Electrons and phonons: quantum transport laws Transport Laws (1) 2) When L ~ L, l r and t >> t, t r Transport is ballistic in nature and local thermodynamic equilibrium cannot be defined. This transport is nonlocal in space. One has to resort to time-averaged statistical particle transport equations. Eq. Phonon Radiative Transfer

20. 3) When L >> L, l r and t ~ t, t r Time-dependent terms cannot be averaged. Approximation of local thermodynamic equilibrium can be assumed over space. The nonlocality is in time but not in space. 4) When both L ~ L, l r and t ~ t, t r Statistical transport equations in full form should be used. No spatial or temporal averages can be made. Transport Laws (2) Hyperbolic Heat Eq. BTE Based Eq.

21. 5) When both L >> L, l r and t >> t, t r Local thermodynamic equilibrium can be applied over space and time, leading to macroscopic transport laws such as the Fourier law. Transport Laws (3)

22. Thermal Transport Modeling rr Eq. Phonon Radiative Transfer Fourier’s Law Hyperbolic Heat Eq. Boltzmann Transport Eq. Molecular Dynamics  lrlr L  l r Length Scale t  r  cc Time Scale

23. fsps ss 1 nm 10 nm 100 nm 1  m 10  m Classical MD QMD continuum ns MD simulation records Limitation of MD

24. Boltzmann Transport Equation (BTE) Drift termScattering term Acceleration term (~ 0 for phonons) BTE applies to all ensembles of particles : electrons, ions, phonons, photons, gas molecules

25. Equilibrium distribution Relaxation-time approximation Relaxation Time Approximation f 0 : equilibrium distribution : relaxation time as a function of position and momentum  Maxwell-Boltzmann for gas molecules  Fermi-Dirac for electrons  Bose-Einstein for photons or phonons

26. Title Ultrashort Pulse Laser Processing Carriers (Electron-Hole Pairs) Silicon Lattice (Phonons) Laser Irradiation

27. Carrier Number Density Carrier Temperature Lattice Temperature where, Auger recombination Carrier/lattice energy transport Thermal diffusion Laser absorption Two-Temperature Equation

28. Auger Recombination ECEC EvEv 12 3  1 st carrier and 2 nd carrier of same type collide instantly annihilating the electron-hole pair (1 st and 3 rd carriers)  The energy lost in the annihilation process is given to the 2 nd carrier  2 nd carrier gives off a series of phonons until it’s energy returns to equilibrium energy ( E = E C ) Very important at high carrier concentration Non-radiative, thermal process Related to the two-peak structure of carrier temperature

29. Maximum values of carrier and lattice temperatures, and carrier number density for different laser pulses when = 790 nm and J = 3.82 mJ/cm 2 for case 1 Maximum Temperatures Non-equilibrium Equilibrium

30. Transient behaviors of the carrier and lattice temperatures, and the carrier number density for different laser pulses when = 530 nm and J = 50.0 mJ/cm 2 for case 2 Two peaks One peak Auger recombination Laser Pulse Effect

31. Small is more powerful !!!

32. Paradigm Shift