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Physics on femtoscale L. Nánai Univ. of Szeged, TTIK, Dept. of Exp. Phys. H-6720 SZEGED DÓM t 9 Summer School on Optics June 7-10, 2015 Siófok (H) 1 Fundamentals of laser-matter interactions •Classical model •Optical characteristic of materials •Linear and nonlinear optics •Material processing (general) •Melting, damage, vaporization, surface, plasma formation •Heat treatment •Cleaing •Laser ablation •Laser induced surface patterning •Gas and liquid phase processes •Role of pulse duration (thermal vs photoinduced processes) 2 3 General tasks of laser-matter interaction • • • • • • • • • • • Surface modifications include oxidation/nitridation of metals, surface doping, etc. PLA: pulsed laser ablation PLD: pulsed laser deposition LA: laser annealing LC: laser cleaning LIS: laser-induced isotope separation/IRlaser photochemistry MPA (MPI): Multiphoton absorption (ionization) LSDW (LSCW): laser-supported detonation (combustion) LCVD (LCLD): laser-induced chemical vapour (liquid)-phase deposition LEC: laser-induced electrochemical plating/etching RED/OX: long pulse or cw CO2 laseinduced reduction/oxidation 4 Interaction processes depend on many parameters The most important ones are: Laser Wavelength Pulse length Fluence (energy density) Materials Optical properties Surface structure Thermal characteristics Generally, the most important effect is heating, which can lead to phase transformation. 5 Light absorption Absorption in a medium with refraction index n n1 + in2 is given by the Beer-Lambert law I(z) = I0 e- z where I0 is the light intensity at z = 0 and I(z) is the intensiy at depth z. The attenuation coefficient is = -(1/I)(dI/dz)=2n2/c=4 n2/ Penetration depth is given by -1 For UV radiation: dielectrics For metals and semiconductors 1 cm-1 = (2-3)x106 cm-1 6 Light absorption THE PARTITION OF THE ABSORBED ENERGY IS NOT THERMAL AT FIRST LASER LIGHT PRODUCES: • PARTICLE EXCESS ENERGY • EXCITATION ENERGY OF BOUND ELECTRONS • KINETIC ENERGY OF FREE ELECTRONS • EXCESS PHONONS 7 Heat propagation Heath conduction equation I a ( x, y, t )V z T 2 k T e t cp Where k=KV/cp heat diffusivity K: thermal conductivity Ia=(1-R)Io: unreflected part of the incident irradiance 8 Free carriers FREE-CARRIER GENERATION IS THE MOST IMPORTANT SELF-INDUCED COUPLING EFFECT IN NON-METALS. THE EFFECTS OF FREE CARRIERS IS TO REDUCE THE REAL PART AND TO INCREASE THE IMAGINARY PART OF n. THIS INCREASES THE ABSORPTION COEFFICIENT = 4 n2/ 9 Free carriers IN SEMICONDUCTORS HOLES AND ELECTRONS ARE IN EQUAL NUMBERS. IT IS CONVENIENT TO TREAT THEM TOGETHER AND TO WRITE =0+Neheh WHERE 0 is the lattice absorption coefficient Neh = Ne = Nh eh = absorpt. cross section of a carrier pair eh scales with , making the free-carrier absorption mainly 2 relevant for infrared beams. 10 Evaporation and plasma formation EVAPORATION USUALLY OCCURS FROM A LIQUID. PHASE EQUILIBRIUM BETWEEN A MELT AND ITS VAPOR REQUIRES EQUALITIES OF THE FREE ENERGIES. SINCE VAPORS ARE COMPRESSIBLE, THE EQUILIBRIUM CONDITIONS DEPEND ON p TOO. THE CHANGE OF FREE ENERGY WITH T CAN BE WRITTEN AS dG G G dp dp S V dT T p dT dT IT MUST HOLD FOR EACH PHASE INDIVIDUALLY. AT EQUILIBRIUM THE PRESSURE INSIDE THE LIQUID AND THE VAPOR MUST BE THE SAME 11 Interaction of ultrashort laser pulses with solids • Optical parameters n and k • Role in excitation of electronic subsystem • linear and nonlinear response of target • Energy transfer – electromagnetic field e-e „thermalization” transfer to ionic subsystem • role of „time scale” 12 Solids in Very Intense Laser Field Linear optics: validity of the superposition theory P E Nonlinear optics: at high enough intensities Pi (1) Ei ( 2) Ei Ek (3) Ei Ek E j Limit (classical): m 2e5 9 Eat 4 5 . 14 10 _ V / cm 3 (40 ) I at 0 cEat 2 2 (for H) 3.5 1016 _ W / cm 2 13 Optical properties and () n() () () (): electric dipole approximation p p ( ) 1 xcv i ( cv ) i ( cv ) cv vc cv while , _ H (t ) (e) xE(t ), _ xcv c x v 2 e2 0h In solids: b ,k ub ,k ( x)ei k x _ Bloch 1 x 2 1 p 2 im12 3 2 d k p e ( ) 1 m 2 2 3 pcv (k ) i ( Ecv (k ) ) 0 8 vc Ecv (k ) 2 For semiconductors: im ( ) 12 J ( ) 14 Metals • Linear optics if I< 1015 W/cm2 • Free carrier absorption (through inverse Bremsstrahlung) =(5-10)*10-5 cm-1 up to -1=10-20 nm - role of ballistic transport (vb~ 106 m/s for 100 fs ~ 100-200 nm) - role of density of states (DOS) at Fermi level • ballistic transport of non-thermalized electrons and diffusive transport of thermalized electrons Heat transport from electronic subsystem to initially cold lattice 15 Two temperature models (TTM) Te e t z Tl l t z C C k g (T T ) S ( z, t ) k g (T T ) Te e z Tl l z e e l l S ( z, t ) I (t ) A exp( z ) Where Ce, ke and Cl, kl are the lattice and electron capacity and thermal conductivity, S(z,t) is the laser heating source term. Nolte model: t Te ( z, t ) exp ( z ) L ( z ) a exp( z ) b exp( z ) Tl Te Tp- excitation radius Tl- relaxation radius 16 t Te ( z, t ) Teq T exp e l eq t e Tl ( z , t ) Teq T exp e l eq L eq Fa l 2 2 1 1 Teq Te ( z,0) exp( z ) exp( z ) 2 2 l eff Cl e l l T Te ( z ,0) Tl ( z,0) eq e l e l e=Ce/g and l=Cl/g are the electron cooling and lattice heating times eq Caracteristic timescale of the thermal equilibration Teq final equilibration temperature 17 Temporal distribution of electron Te and lattice Tl surface temperature for a copper target irradiated by a 120 fs, 800 nm pulse at a laser intensity I0=5x1012 W/cm2 Comparison between nickel and gold surface temperatures dynamics, in the same conditions as previous fig. 18 Semiconductors • One-photon excitation yielding electron-hole pairs (interband transition) if hn< Eg multiphoton abs. ~ IN • Free carrier absorption • Impact ionization Relaxation by several channels: - radiative - nonradiative 19 TTM for semiconductors: U e (keTe ) g eo (Te To ) (1 R)( n) I ( z, t ) (1 R) 2 2 I 2 ( z, t ) t U o g eo (Te To ) g ol (To Ta ) t U a (k a Ta ) g oa (To Ta ) t Uo=CoTo and Ua=CaTa are the optical and acoustic phonon energy g is the coupling coefficient is the free carrier absorption coefficient 20 Dielectrics • multiphoton transition • avalanche ionization Two photon absorption 21 Temperature evolution The temperature, T, at a depth, x, below the surface of a material hit by an ultrashort laser pulse is governed by the Quantum Heat Transport equation: 1 2T m T 2T 2 2 2 v t t x v: thermal pulse propagation speed m: heat carrier mass Two-part solution: x p: laser pulse duration t x x v e v H t : mv2/2ħ Ballistic: TB ( x, t ) Sech 2 p v H: Heaviside’s step function 2 2 x I1 y x t Diffusive: v x 2 t y y TD ( x, t ) Sech e dy H t 2 v vx v p y2 x v 22 Evolution of Carrier Densities The densities of the electrons and holes created when an ultrashort laser pulse hits a semiconductor were calculated using the following equation: 4 ln 2 x nc t 2 D 2 I 0e t x 2 p2 (1 R)e x l I0: peak laser intensity (adjusted to get max carrier density of 1018 1/cm3) c: speed of light n: index of refraction p: FWHM pulse duration (Gaussian pulse) : absorption constant R: reflectivity (0.286) l: electron-hole pair lifetime D: diffusivity 23 Dember Electric Field The diffusivity of the electrons is about 20 times larger than for the holes. The electrons diffuse faster into the material than the holes causing the net charge density to be positive near the surface and negative deeper into the material. This produces a strong „Dember” electric field that can be calculated as follows: E ( x) e r 0 x ( x' ) ( x' )dx' h e 0 e: elementary charge 0: permittivity of free space r: dielectric constant h: density of holes e: density of electrons 24 Solutions to the QHT equation for a 50 attosecond laser pulse 25 Solutions to the QHT equation for a 20 femtosecond laser pulse 26 Calculated density of holes (a) and electrons (b) created by a 50 as laser pulse 27 Density of holes (dark line) and electrons (light line) at the surface (up) and a depth of 500 nm below the surface (right) for a 20 fs laser pulse 28 Density of holes (dark line) and electrons (light line) at the surface (up) and a depth of 250 nm below the surface (right) for a 50 as laser pulse 29 Dember electric field versus depth in material for 50 as laser pulses Dember electric field versus depth in material for 20 fs laser pulses 30 Summary of temperature Evolution For a 50-as pulse: - Ballistic solution dominates - A short thermal pulse propagates into the medium For a 20-fs pulse: - Diffusive solution dominates - Temperature at the surface is high for a period of time approximately equal to the laser pulse duration 31 Structural Changes - Thermal model: rapid Equilibration of hot el-ns with lattice heating up to melting temperature (ns, ps) - Plasma model: destabilization of the covalent bonds due to electronic exitation (slow rate of phonon emission) (fs) 32 Pump and Probe measurements Ti:sapphire laser Output power: 400 mW Rep.rate: 90 MHz Energy/pulse: 4.4 nJ Central wavelength: 820 nm (FWHM: 43 nm) AOM freq.: 25 kHz Pump power: 25 mW Probe power: 2.5 mW 33 Reflectivity at different sample orienteation normalized 34 Fourier transformations of the scans FFT 4pstoto10ps FFT 5ps FFT 0.5ps to 8ps 4ps Amplitude (a.u.) Amplitude (a.u.) Amplitude (a.u.) 1,8E-02 1,8E-02 8,E-02 1,6E-02 1,6E-02 7,E-02 1,4E-02 1,4E-02 6,E-02 1,2E-02 1,2E-02 5,E-02 1,0E-02 1,0E-02 4,E-02 8,0E-03 8,0E-03 6,0E-03 3,E-02 6,0E-03 90deg 90deg 90deg 75deg 75deg 75deg 60deg 60deg 45deg 60deg 45deg 30deg 45deg 5x 5x 30deg 30deg 5x 5x 4,0E-03 2,E-02 4,0E-03 2,0E-03 5x 1,E-02 2,0E-03 5x 0,0E+00 0,0E+00 0,E+00 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Wavenumber(1/cm) Wavenumber(1/cm) Wavenumber(1/cm) 600 600 600 700 700 700 35 75deg FFT 90deg FFT 0.5ps to 4ps 4ps to 8ps 0.5ps to 4ps 5ps to 10ps 4ps to 8ps 5ps to 10ps 2,0E-03 1,4E-02 1,8E-03 5x 1,2E-02 Amplitude (a.u.) Amplitude (a.u.) 1,6E-03 1,0E-02 8,0E-03 5x 6,0E-03 4,0E-03 1,4E-03 1,2E-03 1,0E-03 8,0E-04 6,0E-04 4,0E-04 2,0E-03 2,0E-04 0,0E+00 0,0E+00 0 100 200 300 400 500 600 700 0 100 200 300 Wavenumber (1/cm) 4ps to 8ps 5ps to 10ps 10X Amplitude (a.u.) 1,5E-02 10X 1,0E-02 0,0E+00 400 Wavenumber (1/cm) 500 600 700 10X 10X 4,0E-02 0,0E+00 300 700 5ps to 10ps 6,0E-02 2,0E-02 200 4ps to 8ps 8,0E-02 5,0E-03 100 600 1,0E-01 2,0E-02 Amplitude (a.u.) 0.5ps to 4 ps 1,2E-01 2,5E-02 0 500 45deg FFT 60deg FFT 0.5ps to 4ps 400 Wavenumber (1/cm) 0 100 200 300 400 Wavenumber (1/cm) 500 600 700 36 37 Reflectivity at different TeO2 sample orienteation -12 Amplitude X3 90 deg 5 to 60 8 ps deg -12 2x10 2,0x10 Amplitude -4(a.u.) 45 deg 2 to 5 ps -12 1x10 30 deg Amplitude X3 0 deg 0,0 Reflectivity (a.u.) 4,0x10 -4 3x10 deg FFTvs. of time TeOdelay Dynamic45 reflectivity 2 0,1 to 3,5 ps 0 50 2000 100 4000 150 200 6000 250 8000 -1 Wavenumber (cm ) Time delay (fs) 38 Thank You For Your Attention ! 40