The impact of an keV atomic particle onto a solid surface initiates a complex sequence of collisions among target atoms in a near-surface region. The temporal and spatial evolution of this atomic collision cascade leads to the emission of particles from the surface - a process usually called sputtering. In modern surface analysis the so called SIMS technology uses the flux of sputtered particles as a source of information on the microscopical stoichiometric structure in the proximity of the bombarded surface spots. By laterally varying the bombarding spot on the surface, the entire target can be scanned and chemically analyzed. However, the particle detection, which bases upon deflection in electric fields, is limited to those species that leave the surface in an \textit{ionized} state. Due to the fact that the ionized fraction of the total flux of sputtered atoms often only amounts to a few percent or even less, the detection is often hampered by rather low signals. Moreover, it is well known, that the ionization probability of emitted particles does not only depend on the elementary species, but also on the local environment from which a particle leaves the surface. Therefore, the measured signals for different sputtered species do not necessarily represent the stoichiometric composition of the sample. In the literature, this phenomenon is known as the Matrix Effect in SIMS. In order to circumvent this principal shortcoming of SIMS, the present thesis develops an alternative computer simulation concept, which treats the electronic energy losses of all moving atoms as excitation sources feeding energy into the electronic sub-system of the solid. The particle kinetics determining the excitation sources are delivered by classical molecular dynamics. The excitation energy calculations are combined with a diffusive transport model to describe the spread of excitation energy from the initial point of generation. Calculation results yield a space- and time-resolved excitation energy density profile E(r,t) within the volume affected by the atomic collision cascade.The distribution E(r,t) is then converted into an electron temperature, which in a further step can be utilized to calculate the ionization probabilities of sputtered atoms using published theory.