Appendix a Definitions and Symbols
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Appendix A Definitions and Symbols A.1 Symbols and Conversion Factors A absorptivity a distance aperture b net increase in number of molecules per formula unit; b = μ − 1 C constant C Euler’s constant; C = 0.577 Cp heat capacity c speed of light; c = 2.998 ×1010 cm/s cp specific heat at constant pressure [J/gK, J/molK] cv specific heat at constant volume [J/gK, J/molK] D heat diffusivity [cm2/s] transmittivity 2 Di molecular diffusion coefficient of species i [cm /s] d lateral width of laser-processed features [μm, cm] diameter E electric field [V/cm] energy [J] −2 kBT (T = 273.15 K) = 2.354 ×10 eV 1 kcal/mol =# 0.043 eV =# 5.035 ×102 K 1eV=# 1.1604 ×104 K =# 1.602 ×10−19 J 1 kcal =# 4.187 ×103 J 1cm−1 =# 1.24 ×10−4 eV =# 1.439 K 1J=# 2.39 ×10−4 kcal EF Fermi energy E activation temperature [K]; E = E/kB E ∗ normalized activation temperature; E ∗ = E /T (∞) E activation energy [eV; kcal/mol] Em activation energy for melting Ev activation energy for vaporization at Tb D. Bäuerle, Laser Processing and Chemistry, 4th ed., 739 DOI 10.1007/978-3-642-17613-5, C Springer-Verlag Berlin Heidelberg 2011 740 Appendix A Eg bandgap energy = energy distance between (lowest) conduction and (highest) valence bands E laser-pulse energy [J] e elementary charge; e = 1.602 ×10−19 C ee≈ 2.718 eV electron Volt 1eV/particle = 23.04 kcal/mol F area Faraday constant; F = 96485 C/mol f focal length [cm] Gr Grashof number G Gibbs free energy g acceleration due to gravity gT temperature discontinuity coefficient H total enthalpy [J/cm3,J/g, J/mol] reaction enthalpy H a [J/atom]= H [J/cm3]·M/ρL = H [J/g]·M/L = H [J/mol]/L Hv heat of vaporization at Tb Hm heat of melting Ht total latent heat Ht = Hm + Hv h Planck’s constant; h = 6.626 ×10−34 Js ◦ height, thickness or depth of laser-processed patterns [A, μm] h1 thickness of single evaporated or sputtered layer on a substrate hi thickness of layer i on a substrate hl thickness of a liquid layer, or an adsorbate hs thickness of slab or substrate h change in layer thickness ◦ ablated layer thickness per pulse [A/pulse] hν photon energy hν[eV]≈1240/λ[nm] I intensity [W/cm2] Ia absorbed laser-light intensity Ith threshold intensity Iv evaporation intensity J flux 2 Ji flux of species i [species/cm s] j current density K force k kinetic (rate) constant k0 pre-exponential factor −23 kB Boltzmann constant; kB = 1.381 ×10 Ws/K rec ki recombination constant for species i k wavevector of laser radiation kT thermal diffusion ratio Appendix A 741 L Avogadro number (Loschmidt number); L = 6.022 ×1023 /mol L Langmuir [1 L = 10−6 Torr s] l characteristic length, depth [μm] lT heat-diffusion length [μm] − lα optical penetration depth [μm]; lα = α 1 M molar mass [g/mol] m mass exponent, e.g., in κ(T ) N total number of species (atoms, molecules, electrons, holes, etc.) per volume [cm−3] or per area [cm−2] −3 Ni number of species i per volume [cm ] or per area [cm−2] N number of laser pulses n refractive index (real part) exponent, e.g., in Di (T ) n normal vector nˆ unit vector √ n˜ complex refractive index; n˜ = ε = n + iκa ≡ n(1 + iκ0) P laser power [W] Pa absorbed laser power [W] p total gas pressure [mbar] 1 mbar =# 102 N/m2 =# 102 Pa ≈ 0.750 Torr =# 1.02 ×10−3 at[kp/cm2] =# 9.87 ×10−4 atm 1atm=# 2.688 ×1019[species/cm3] pi partial pressure of species i [mbar] Q source term q exponent, e.g., in equation of state q wavevector R optical (power) reflectivity electrical resistance ["] R sheet resistance ["/] RD optical reflection coefficient of deposited material RG gas constant; RG = 8.314 J/Kmol =# 1.987 cal/Kmol Ra Rayleigh number r radial distance rD radius of deposit S stress oversaturation S Poynting vector energy flux [J/cm2s] s sticking coefficient T temperature [K] Tb boiling temperature Tc center temperature 742 Appendix A Tg gas-phase temperature Tl temperature within liquid TM temperature within medium Tm melting temperature Ts substrate temperature surface temperature Tst stationary temperature Tth threshold temperature Tv temperature of vapor T (∞) temperature far away from irradiated zone T temperature rise T ∗ normalized temperature, e.g., T/T (∞) t time tv time to reach Tst (Fig. 11.2.2) t time interval tm time of existence of melt on surface V volume [cm3] Vn volume per molecule/atom v velocity [cm/s] mass average velocity vls velocity of liquid–solid interface vvl velocity of vapor–liquid interface v0 sound velocity vs scanning velocity of laser beam or substrate [μm/s] v thermal velocity of gas molecules W reaction rate heterogeneous reactions [number of species/scm2] homogeneous reactions [number of species/scm3] ◦ WA ablation rate [μm/s; A/pulse] ◦ WD deposition rate [μm/s; A/pulse] ◦ WE etch rate [μm/s; A/pulse] Wex excitation rate w radius of laser focus with constant intensity distribution [μm] radius of laser focus at FWHM √ 2 we radius of laser focus (1/e intensity); we = 2w0 w0 radius of laser focus of Gaussian beam (1/e intensity) [μm] w probability width of reaction zone xi molar ratio of species i; xi = Ni /N x, xα set of space coordinates with α = 1, 2, 3, e.g., x, y, z Y Young’s modulus Z number of condensed atoms per molecule z charge of ions in units of e zR Rayleigh length of laser focus [μm] Appendix A 743 α optical absorption coefficient [cm−1] αT thermal diffusion constant β exchange coefficient exponent parameter symmetry factor factor βT coefficient of thermal expansion Γ increment parameter ratio aspect ratio [ratio of depth or height to width]; Γ = h/d γ exponent total reaction order adiabatic index; γ = cp/cv;1<γ ≤ 5/3 real part of increment γi reaction order with respect to species i difference δ delta function parameter ε dielectric constant permittivity spectral emissivity εa apparent emissivity −12 ε0 dielectric constant in vacuum; ε0 = 8.854 ×10 As/Vm εt total emissivity ζ parameter integer factor ζi stoichiometric coefficient of species i η dissociation yield dynamic viscosity [g/cm s]; η = ρνk reaction probability surface conductance [coefficient of surface heat transfer] [W/cm2K] % angle θ linearized temperature θ c center-temperature√ rise for Gaussian beam; θc = π Iaw0/2κ,see(7.1.4) %i coverage by species i ϑ angle κ thermal conductivity [W/cm K]; 1W/mK=# 2.39 ×10−3 cal/cmKs κa absorption index κa = nκ0 κD thermal conductivity of deposit κL, κ1 thermal conductivity of thin layer 744 Appendix A κM thermal conductivity of medium κs thermal conductivity of substrate κ0 attenuation index Λ parameter spacing function λ wavelength of electromagnetic radiation [nm, μm] λ[nm]≈1240/hν [eV] λm mean free path of molecules [cm] μ factor index integer chemical potential Poisson ratio μ = b + 1 2 μe, μh mobility of electrons and holes [cm /Vs] ν frequency [s−1] index 2 νk kinematic viscosity [cm /s] νr laser-pulse-repetition rate [Hz] ξ overpotential parameter product parameter π 3.14159 ρ electrical resistivity [" cm] 3 mass density [g/cm ] summation sign e.g., a ± b ∓ c ≡ (a + b − c) + (a − b + c) ± σ electrical conductivity [" cm]−1 surface tension [J/cm2] excitation cross section of species [cm2] −12 2 4 σr Stefan–Boltzmann constant; σr = 5.67 ×10 W/cm K τ relaxation time [s] τ laser-pulse duration [s] laser-beam dwell time [s]; τ = 2w/vs τm time for surface melting τT thermal relaxation time [s] Φ electrical potential φ laser fluence [J/cm2] angle φth threshold fluence ϕ angle Appendix A 745 χ magnetic susceptibility parameter Ψ function ψ wave function " total solid angle; " = 4π Ohm d" solid angle [sr] ω angular frequency [s−1]; ω = 2πν ⊥ normal (perpendicular) parallel ∇2 Laplace operator ∇ Nabla operator A.2 Abbreviations, Acronyms − acac [CH3COCHCOCH3] = acetylacetonate anion AdGC allyl-diglycol-carbonate AES Auger electron spectroscopy ALE atomic layer epitaxy AM1 sunlight illumination APD ablative photodecomposition BBS barium aluminum borosilicate BK7 boron crown glass CAD computer-aided design CAM computer-aided manufacturing CARS coherent anti-Stokes Raman scattering CBE chemical beam epitaxy CCD charge-coupled device CMR colossal magnetoresistance, same as GMR CPA chirped-pulse amplification CVD chemical vapor deposition DLC diamond-like carbon; dry laser cleaning EAL etching of atomic layers; excimer-laser ablation lithography EB electron beam EBCVD electron-beam-induced chemical vapor deposition EBE electron-beam evaporation EDX energy-dispersive X-ray analysis EELS electron-energy-loss spectroscopy EMF electromotive force ESCA electron spectroscopy for chemical analysis ESR electron spin resonance FEP tetrafluoroethylene-hexafluoropropylene FH fourth harmonic Foturan lithium aluminosilicate glass doped with (photoactive) Ce 746 Appendix A FWHM full width at half maximum GMR giant magnetoresistance HAZ heat-affected zone − hfacac [CF3COCHCOCF3] = hexafluoroacetylacetonate anion HPDS hexaphenyldisilane HTS high-temperature superconductors HV high vacuum (10−7 < p < 10−3 mbar) IBAD ion-beam assisted deposition IC integrated circuit IR infrared radiation ITO indium tin oxide Kapton polyimide (Du Pont) LA laser annealing LAL laser-ablation lithography LC laser cleaning; liquid crystal LCP laser-induced chemical processing LCVD laser-induced CVD LEC laser-enhanced electrochemistry LEE laser-enhanced electrochemical etching LEED low-energy electron diffraction LEP laser-enhanced electrochemical plating LI laser implantation LID laser-induced desorption LIF laser-induced fluorescence LIFT laser-induced forward transfer LIS laser isotope separation LMBE laser molecular beam epitaxy LPCVD laser-enhanced PCVD LPE laser-enhanced plasma etching LPPC laser-pulsed plasma chemistry LSA laser-surface