List of Symbols

List of Symbols a au A A2 A3 An An-1 Apipe b bmax B Bo c c [Cu] [Cu2*] d ds dso D e e E f F h Specific evaporation rate Born radius (0.529 Å) An individual atom Two atom cluster Three body cluster Cluster containing n atoms Cluster containing n-1 atoms Area of the inlet flow tube Impact parameter Maximum range of interaction of atoms involved in a collision event Beam energy Initial beam energy Speed Average speed Concentration of metal monomer Concentration of unstable dimers Diameter Local film thickness on a flat substrate Maximum film thickness Distance Binary collision encounters Charge on an electron Kinetic energy Velocity distribution function External force Thickness vi List of Symbols vii hv H ∆H [He] I I Io k Kn l L n n n N m mc mv M M M* no NA Nav P Pc Pcollision Pd Po Source to substrate separation distance Total Enthalpy Enthalpy Concentration of background gas Intensity Beam current Initial intensity Boltzmann’s constant (1.381x10-23 J/K) Knudsen number Atomic jump distance on crystal surface Characteristic dimension of a modeled volume Exponent in vapor density distribution function Gas atom number density Number of jumps Number of molecules in an ensemble Mass Carrier gas atom mass Vapor atom mass Three-body collision partner Mach number Energized third member of cluster collision event Direction unit vector Avogadro’s number (6.0221x1023 atoms/mol) Average size of clusters Pressure Carrier gas pressure Probability of a collision Downstream pressure at a nozzle or inside a processing chamber Upstream pressure before a nozzle List of Symbols viii Ps q q r rmin re rs R Re Rs s t T Tc Td To Tv u u ui U Ull U⊥ Uc Uccm Uv Uvcm Upipe · U pipe Saturated vapor pressure Direction vector Heat flux Distance between atoms Distance of closest interatomic approach Evaporation rate Distance from midpoint of substrate Universal gas constant (8.314 J/(mol K)) Electron range Specific gas constant Direction vector Time Absolute temperature Carrier gas temperature Downstream temperature Upstream temperature Absolute temperature of an evaporant Speed in first coordinate direction Average speed in first coordinate direction Velocity Speed of carrier gas stream Carrier gas velocity parallel to primary flow Carrier gas velocity perpendicular to primary flow Velocity of carrier gas stream Velocity of carrier gas atom in center-of-mass system prior to collision Velocity of vapor atom Velocity of vapor atom in center-of-mass system prior to collision Speed of carrier gas through inlet flow tube Pumping capacity List of Symbols ix · U pump v v V V V(r) w w W W x x xm z ZA ZB ZCu2-He χ χcutoff ε γ λ λe θ φ ρ ρo σji σ(χ) Pumping capacity Speed in second coordinate direction Average speed in second coordinate direction Volume Molar density of material Interatomic potential Speed in third coordinate direction Average speed in third coordinate direction Molecular weight of an evaporant Power Collision Position Mach disk distance from nozzle exit Third coordinate axis Atomic number of carrier gas Atomic number of vapor atom Volume collision frequency Center of mass scattering angle Minimum angle used during scattering calculations Efficiency of energy utilization Ratio of specific heats (cp/cv) Mean free path Effective mean free path Angle Magnitude of normal distribution for specific value of Uc Density Settling chamber gas density Viscous stress tensor Angular differential cross-section List of Symbols x σaCu σaCu2 σd σrCu σrCu τ µ µ/ρ ξ Activity radius of a copper atom Activity radius of an unstable dimer Directed momentum transfer cross-section Hard sphere radius of a copper atom Hard sphere radius of a helium atom Time of flight Reduced mass of a collision event Mass absorption coefficient Standard deviation