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List of Symbols

$ {A}$ area
$ {A}_{\text{ref}}$ reference area
$ {\vec{b}}_{\text{max}}$ maximum index vector of a rectangular axis aligned box
$ {\vec{b}}_{\text{min}}$ minimum index vector of a rectangular axis aligned box
$ {\mathcal{B}}$ rectangular axis aligned box
$ {C_\text{CFL}}$ CFL number
$ {d}$ diameter
$ {D}$ number of dimensions
$ {D}^{-}_i$ backward difference operator
$ {D}^0_i$ central difference operator
$ {D}^{+}_i$ forward difference operator
$ {\mathcal{D}}$ tangential disk
$ {e}$ elementary charge $ =\SI{1.602e-19}{\coulomb}$
$ {\vec{e}}_i$ unit vector in $ {x}_i$ -direction
$ {E}$ energy
$ {F}$ flux on surface $ {\mathcal {S}}$
$ {F}^{\text{src}}$ flux on source plane $ {\mathcal {P}}$
$ {F}^{\text{tot}}$ total flux through source plane $ {\mathcal {P}}$
$ {\vec{g}}^{\text{max}}$ maximum index vector of grid
$ {\vec{g}}^{\text{min}}$ minimum index vector of grid
$ {G}$ reemission probability function
$ {\mathcal{G}}$ set of all grid point index vectors, $ {\mathcal{G}}\subseteq\mathbb{Z}^{D}$
$ {H}$ Hamiltonian
$ {\hat{H}}$ numerical approximation to the Hamiltonian
$ {I}$ electric current
$ {k_B}$ Boltzmann constant $ =\SI{1.381e-23}{\joule\per\kelvin}$
$ {\mathcal{L}}$ layer of grid points, $ {\mathcal{L}}\subseteq{\mathcal{G}}$
$ {m}$ mass
$ {M}$ number of different material regions
$ {\mathcal{M}}$ material region
$ {\vec{n}}$ normal unit vector on $ {\mathcal {S}}$ , $ {\vec{n}}=\left({n}_1,\ldots,{n}_{D}\right)$
$ {\vec{n}}_{\mathcal{P}}$ normal unit vector on $ {\mathcal {P}}$ pointing towards $ {\mathcal {S}}$
$ {{N}_{\text{B}}}$ number of boxes of the spatial subdivision
$ {{N}_\text{CPU}}$ number of CPUs
$ {{N}_\text{D}}$ number of defined grid points
$ {{N}_\text{E}}$ number of edges in a graph
$ {{N}_\text{R}}$ number of surface rates
$ {{N}_\text{P}}$ number of simulated particles
$ {{N}_\text{V}}$ number of vertices in a graph
$ {\mathcal{O}}$ big O notation
$ {\vec{p}}$ grid point indices, $ {\vec{p}}=\left({p}_1,\ldots,{p}_{D}\right)\in\mathbb{Z}^{D}$
$ {P}$ pressure
$ {\mathcal {P}}$ source plane
$ {q}$ particle species
$ {Q}$ number of process relevant particle species
$ {r}$ radius
$ {R}$ surface rate
$ {s}$ sticking probability
$ {\mathcal {S}}$ surface
$ {t}$ time
$ {T}$ temperature
$ {\bar{{v}}}$ mean particle velocity
$ {V}$ surface velocity (field)
$ {w}$ particle weight factor
$ {\vec{x}}$ point in space, $ {\vec{x}}=\left({x}_1,\ldots,{x}_{D}\right)\in\mathbb{R}^{D}$
$ {\vec{x}}_{\text{cp}}$ closest point on surface
$ {Y}$ yield function
$ {Y}^{\text{tot}}$ total sputter rate
$ {\Gamma}$ arrival flux distribution on surface $ {\mathcal {S}}$
$ {\Gamma}_{\text{re}}$ reemitted flux distribution on surface $ {\mathcal {S}}$
$ {\Gamma}_{\text{src}}$ arrival flux distribution on source plane $ {\mathcal {P}}$
$ \delta$ Dirac/Kronecker delta function
$ \Delta{t}$ time increment
$ {\Delta x}$ grid spacing
$ {\eta }$ surface reaction order
$ {\theta}$ polar angle
$ {\Theta}$ surface coverage
$ {\kappa}$ mean curvature
$ {\bar{\lambda}}$ mean free path
$ {\nu}$ exponent in power cosine distribution
$ {\rho}$ bulk density
$ {\sigma}$ standard deviation
$ {\phi}$ azimuthal angle
$ {\chi}$ weight factor for SAH
$ {\vec{\omega}}$ direction unit vector
$ {\Omega}$ solid angle

next up previous contents
Next: 1. Introduction Up: Dissertation Otmar Ertl Previous: List of Abbreviations
Otmar Ertl: Numerical Methods for Topography Simulation